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PHYSICS
EDDY, CURRY and SHAW
With Applications in
AERONAUTICS, ENGINES, and GENERAL MECHANICS,
including Book 4 in the Elementary Technology Series:
Elements of RADIO and PHOTOGRAPHY
Published by
FLORIDA STATE DEPARTMENT OF EDUCATION
Colin English. Superintendent
A WARTIME COURSE IN
PHYSICS
BY
PAUL EDDY, Florida State Department of Education
MILTON T. CURRY, Carrabelle High School
PHILIP S. SHAW, Everglades High School
ASSISTED BY
O. J. DETRICK, G. E. MCKAY, P. H. MCALPINE, DAN P. FOLSOM, LAWTON W. BLANTON,
Science Instructors in Florida High Schools
ACKNOWLEDGMENT
THE MACMILLAN COMPANY for illustrations from the Florida State-adopted text, ELE-
MENTARY PRACTICAL PHYSICS, by Black and Davis, 1938. This text is both basic and sup-
plementary to A WARTIME COURSE IN PHYSICS. THE CIVIL AERONAUTICS ADMINISTRA-
TION for illustrations and text material from official C.A.A. bulletins. SARAH ETHEL
FERREL for art drawings, JAMES V. TODD for mechanical drawings, and E. ELIZABETH
LYNN, for assistance with radio manuscript.
BULLETIN NO. 41
COPYRIGHT, 1943
FLORIDA STATE DEPARTMENT OF EDUCATION
TALLAHASSEE
PRICE O0 CENTS, NET
Equipping Their Own
School Laboratory
This group is taking its
turn in cleaning up and
labeling all the parts of an
old Model A engine. These
parts will be used through-
out the course to demon-
strate simple applications
of important physical prin-
ciples.
How to Do It
1. Obtain a wornout en-
gine by telling a junk deal-
er about the purpose of the
course; or, have a civic
club sponsor the work and
obtain what is needed.
2. For cleaning up one
motor obtain about five
gallons of kerosene, two
pounds of rags, two scrub-
bing brushes, and a tub.
A foot tub is ideal.
3. Have the dealer of your
kind of motor give you an
old illustrated "parts" book
which gives the name of
each part in the engine.
4. Have a mechanic with
special tools join the class
and demonstrate how he
can "take it apart" in less
than one hour.
5. Clean up all parts and
label at least one of each
kind using tags and stick-
ers. Take them all to the
laboratory for display and
use.
MAKING MEN OF IRON
From deep within a pile o' junk
Across the railroad track
We found a veteran of days of old,
Quiet, forgotten, ugly, and cold.
His heart, his lungs, his arms, and legs
And all his cams and gears
Lay petrified so we could see
Just how it was he used to be.
Just how he ran so hard and fast
On a diet of oil and gas.
Just how his race of iron men
Can be bred up to run again
And faster, higher, skyward climb
To join with us and join in time
To win a fight for liberty!
-P. E.
Foreword
When bombs fell on Pearl Harbor physics became essential subject matter in general education in the
senior high schools of the nation.
This manual has been prepared by Florida teachers to meet wartime needs. It is based upon the present
state-adopted text Elementary Practical Physics by Black and Davis, Macmillan, 1938.
The course is designed primarily for an inexperienced physics teacher who has virtually none of. the
usual laboratory equipment at his disposal. The fact that less than one-fifth of the high schools had suit-
able physics equipment in 1941 is not a great handicap because the traditional apparatus was designed
largely to train future scientists rather than factory, airport, army and navy technicians and mechanics.
This manual attempts to simplify the teaching of essential physical principles. Lack of equipment in
the past may not be a disadvantage because equipment can now be obtained from an old automobile engine,
and such engines are available in every city and small town as junk. Junk dealers more than most other
persons know the value of this practical type of instruction, and they will gladly cooperate in loan-
ing an old motor or in selling it at junk prices with assurance that the money will be returned when
the motor parts are given back to them. Junk dealers are key persons in the nation's war effort and they
will be interested in knowing all about the school's plan for use of their materials.
This course fulfills the specifications for physics called for in A Wartime Program in Mathematics and
Physics proposed by the National Council of Chief State School Officers May 15, 1942, at their joint con-
ference with representatives of the War Department and the Navy Department. The official report of
this important conference, attended by specialists or state superintendents of education from 26 states, will
be mailed free to Florida teachers upon receipt of a personal request to the State Department of Educa-
tion. The price to others is 15 cents, postpaid.
SUPERINTENDENT
Contents
INTRODUCTION . . . .......
Chapter 1. WEIGHTS AND MEASURES .....
Concepts: 1A, Measurement; 1B, Speed; 1C, Density.
Chapter 2. SIMPLE MACHINES-LEVERS AND PULLEYS .....
Concepts: 2A, The Lever; 2B, Mechanical Advantage; 2C, Moments; 2D, Equilibrium;
2E, Center of Gravity; 2F, Crank and Axle; 2G, Block and Tackle.
Chapter 3. WORK, POWER, AND EFFICIENCY .......
Concepts: 3A, Work; 3B, Inclined Plane; 3C, The Wedge; 3D, The Screw; 3E, Power;
3F, Horsepower; 3G, Transmission of Power; 3H, Friction; 3J, Efficiency.
Chapter 4. MECHANICS OF LIQUIDS ..........
Concepts: 4A. Pressure and Shape of Vessel; 4B, Pressure and Direction; 4C, Speed
Reduces Pressure; 4D, Winglift; 4E, Pressure in Confined Liquid; 4F, Buoyancy; 4G.
Specific Gravity.
Chapter 5. MECHANICS OF GASES ...........
Concepts: 5A, Air Pressure; 5B, Barometer; 5C, Altimeter; 5D, Measurement of Pressure
on a Wing; 5E, Weather Prediction; 5F, Pumps; 5G, Buoyancy of Gas; 5H, Compression
in a Cylinder; Review of Winglift.
Chapter 6. PROPERTIES OF MATTER ........
Concepts: 6A, Stresses; 6B, Strain and Elasticity.
Chapter 7. FORCES ACTING AT A POINT ..........
Concepts: 7A, Composition of Forces; 7B. Resolution of Forces; TC, Forces on an
Airplane; 7D, Wind Drift.
Chapter 8. ACCELERATED MOTION ...........
Concepts: 8A, Velocity Units; SB, Acceleration; SC. Falling Motion: 8D, Projected
Bodies.
Chapter 9. THREE LAWS OF MOTION ..........
Concepts: 9A, Inertia : B, Acceleration and Momentum; 9C, Interaction.
Chapter 10.
Chapter 11.
Chapter 12.
Chapter 13.
Chapter 14.
POTENTIAL AND KINETIC ENERGY .......
Concepts: 10A, Energy of Position or Strain; 10B, Energy Due to Motion; 100,
Impulse, Momentum, and Conservation of Energy.
HEAT AND EXPANSION (Molecular Theory of Matter) .. . .....
Concepts: 11A. Heat is kinetic energy; 11B. Temperature; 11C, Contraction and Ex-
pansion; 11D, Absolute Zero; 11E. Constant Pressure: 11F, Constant Volume: 11](. (GIs
Equation; 11H, Diesel engines utilize heat of compression.
TRANSMISSION OF HEAT .. . . . . ..........
Concepts: 12A, Convection: 12B, (onduction by nmole(ular motion: 120. Radiation.
ICE, WATER, AND STEAM ........ .................
Concepts: 13A. Measuring Heat Energy: 13B, l'reezing water expands and exerts
pressure (heat of fusion) ; 13C, Increasing pressure upon a liquid raises boiling point:
decreasing pressure lowers it; 13D. Evaporation; 13E. Relative Humidity.
MECHANICAL EQUIVALENT OF HEAT: HEAT ENGINES .. . .....
Concepts: 14A. British thermal unit: 14B. Engines-internal combustion and external
combustion
SECOND SEMESTER
Chapter 15.
Chapter 16.
Chapter 17.
Chapter 18.
Chapter 19.
Chapter 20.
Chapter 21.
Chapter 22.
Chapter 23. LAMPS AND REFLECTORS . . ......
LENSES AND OPTICAL INSTRUMENTS . . . . . . .
Concepts: 24A, Bending of light rays: 24B, Lens; 24C, Optical Instruments. PHOTO-
GRAPIY: 24D. The Camera: 24E. Developing Negatives: 24F, Printing from Negatives.
Chapter 25. SPECTRA AND COLOR ... . . .
VACUUM TUBES AND RADIUM ... .
Concept : 26A. X-rays.
R ADIO . . .
Concepts: 27A, Batteries; 27B. Power Pack: (Transformers, Rectifiers, Filters, Trans-
mitter) ; 27C, Oscillator; 27D. Condenser; 27E, Chokes: 27F, Vacuum Tube; 27G, Grid:
27H, Microphone; 27J, Modulator; 27K, Antenna: 27L. "Phone" Transmitter: Main-
taining a True Wave Pattern, Radio Frequency. Action of Modulator on the Oscillator.
Coupling the Aerial with the Oscillator Circuit. Radio Receiver; 27M. Carrier Waves:
27N, Tuned Circuit; 27P, Vacuum tube "detects" or separates voice current from carrier
current; 27Q, Tickler Coil: 27R, The Receiver: 27S. Radio receiver can be used to
determine direction.
, 71
M AGNETISM . . .
Concepts: 15A, Like poles repel iand unlike poles attract; 1513, The field around a
magnet; 15C, The earth is a permanent natural magnet: The Magnetic Compass-
Swinging Ship. Finding Magnetic Course, Finding Compass Course, Finding Compass
Heading.
ELECTRICITY AT REST ..........
Concepts: 16A, Electrification produced by friction: (6B. Positive and Negative elec-
tricity; 16C, Positively or negatively charged bodies.
ELECTRIC CURRENTS AND CIRCUITS . . . . . . . .
Concepts: 17A. Potential Difference: 17B. Potential difference created by chemical
action; 17(, Electric and Electron Currents; 17D, Electric Circuit ("closed" circuit);
17E, Potential Difference and Resistance; 17F, The Ampere; 17G, The Ohm; 17H, The
Volt; 17J, Resistance of wire depends on material, length, cross-section and temperature;
17K, Connection in series, in parallel, and in combinations of the two; 17L, Connection
arrangements determined by voltage and amperage desired, and internal and external
resistances of circuit.
EFFECTS OF ELECTRIC CURRENT . . . . . . . . .
Concepts: 18A. Electric current causes magnetism 181, Electric current produces
chemical action: 18C. Electric current produces heat.
GENERATORS AND MOTORS . . . . . . . . .
Concepts: 19A,. ire cutting lines of magnetic force; 191. Magnetic field exerts force
on I conductor.
ALTERNATING CURRENTS . . . . . . .
Concepts: 20A, Principle of induced current: 201. Principle of induced current in a
coil; 20C, Induction Coil; 20D, Self-induction; 20E. Telephone Receiver; 20F. Telephone
Transmitter; 20(. The Transformer: 20H. Impedance: 20.1, The Condenser.
SOUND WAVES .. . . .
Concepts: 21A, Sound produced by a vibrating body; 21B. Sound Waves; 21C. Reflection
of Sound.
MUSICAL SOUNDS .... . . .
. 83
. 88
. 91
. 93
. 96
. 97
. 97
Chapter 24.
Chapter 26.
Chapter 27.
. 98
S. 107
S. 108
109
Introduction
All pupils should realize at the start that this course has special wartime significance; that it is assisting
them to prepare for service to their country. This is one reason why the first pupil activity may well be the
tearing down of a gas engine. Another reason is that the parts of this engine will quite thoroughly equip the
laboratory with the finest possible set of materials of instruction, materials that have application in almost
every chapter and section of the course. Then too, the course starts with real work experience, and with equip-
ment that is a challenge to almost every pupil.
These are some of the reasons why the success of this course requires the advance equipment of an old
gasoline engine of the type that is available in every junk yard in the country, and in many garages. Once
the engine is torn down, preferably with the assistance of a mechanic with special tools, it enters at once into
classroom service as a medium for actually making and using almost all the measurements called for in Chapter
1 of the text.
The committee which has prepared this manual recommends that the measurement of speed be included in
this chapter. If this is done additional problems and discussion should be devoted to understanding the con-
cept of time. Speed should be treated at once as a matter of relationship of distance traveled and time, just as
density is discussed in the text as the ratio of weight to volume.
Both of these ratios bring the simple algebraic equation into the course and show pupils the need for
remedial work in arithmetic and algebra. Here again the engine can motivate a very necessary activity which
is usually a disagreeable task-a brushup in mathematics. The dimensions used in engine problems in this
manual should be changed, wherever feasible, to apply to the dimensions of the motor which is observed and
measured firsthand by the members of the class.
This manual is prepared for use as a supplement to text books. Text assignments are basic and usually
should precede discussion or study of this material. Parallel assignments are shown throughout the manual
for the Florida state-adopted text, but this should no: handicap use of the material in conjunction with other
texts. Liberal space has been reserved in the left-hand column for teachers' notes, or for pupils' notes where
the manual is used as supplementary pupil material.
Chapter 1. WEIGHTS AND MEASURES
DEMONSTRATION MATERIALS: Outside caliper; inside caliper; gas engine parts.
S N I A
C CONCEPT_
S1A
The useful application of knowledge re-
quires the establishment of defined units
and the use of these units in measurement
of weight, distance, area, volume, and time.
TYPICAL GAS ENGINE MEASUREMENTS AND PROBLEMS
Study text pages 1 through
10.
Note: The pages listed in
this left-hand column are
recommended for study.
They are not listed on a
basis of daily assignments
but should be assigned as
pupil ability permits, and
p an n d in conjunction
with supplementary work
included in the manual. In
general, daily assignments
should be on an individual
ability basis with mastery
of the essential concepts as
a minimum. However, this
does not mean that each
concept discussed in this
manual is equal to one
day's assignment.
Work Problems 1 and 2,
and 7 through 13 on pages
7 and 8 in text, also prob-
lems 1-4 and 7-10 on page
When text assignments and problems have been completed as shown in
the left-hand column, through page 10, the pupils should prepare to make
a thoroughgoing measurement of the motor which they have just torn
down, cleaned up and labeled. As measurements are made they may well
be accompanied by informal discussion of the kind of work done by the
part being measured.
The most important tools in this work
are the ordinary ruler and the inside cal-
iper and the outside caliper. The use of
the calipers and the transfer of their read-
ings to the scale are important skills. The
calipers should be obtained for the labora-
tory or borrowed from some convenient
source such as the school shop, the parent
Inside Outside of a pupil, or a local machinist, supply
calipers calipers
dealer, or hardware merchant.
Pupils may divide up the work in preparing a "List of Specifications of
a (make and model of engine) motor," somewhat as shown below. Have
them write the names of these important parts as training in nomenclature
and spelling.
SPECIFICATIONS
1. Number of cylinders
1. Bore (diameter of cylinder in inches)
3. Stroke (distance in inches which piston moves)
4. Bore/Stroke ratio
5. Displacement in cubic inches (volume of gas drawn in
on intake stroke)
6. Diameter of valve opening
7. Area of piston pin surface which comes in contact (serves
as bearing) with piston
8. Area of piston pin surface which comes in contact (serves
as bearing) with connecting rod
WARTIME COURSE IN PHYSICS
Cylinder and crankcase
sembly.
A bearing assembly a
gear.
ESSENTIA
E S S EQT I A L
CONCEPT
IB
The speed of rotating
Notes
,/ 9. Length of connecting rod (center-to-center)
10. Throw of crankshaft (note this equals vertical travel of
,rk piston)
11. Greatest angle connecting rod makes with vertical (obtain
Tr from diagram)
12. Greatest distance of piston pin center from crankshaft
center
13. Least distance of piston pin center from crankshaft center
14. Bearing surface between connecting rod and crankshaft
(square inches)
15. Surface of a main crankshaft bearing
as-
16. Number of teeth on gear which drives camshaft gear
17. Number of teeth on gear which turns camshaft
18. Ratio of number of turns of crankshaft to number of
turns of camshaft
19. Ratio of number of times any one valve rises to number
of times any one piston rises
nd 20. Distance intake valve is raised (may be measured on
the camshaft)
Speed is rate of motion. It is the ratio of
the number of distance units through which
a body moves to the number of time units
that elapse while this motion is taking place.
bodies is measured by their rate of turn.
TYPICAL PROBLEMS
1. A motorist travels from Miami to Fort Myers, a distance of 160 miles,
in three hours. What is his average speed in miles per hour? Feet per
second?
2. At 100 miles an hour the motor of a light airplane probably "turns
over" about 2500 times each minute. The rate of turn is called "revolu-
tions per minute" and is designated as r.p.m. When the rate of turn of the
crankshaft is 2500 r.p.m. what is the speed of the tip of the propeller as
it travels around its shaft if it has a diameter of 6 feet? Answer:
(2,500 x 67r) feet per minute = 47,100 feet per minute, or
2,500 x 67r x 60
2,50 r x miles per hour = 535.2 miles per hour
5,280
WEIGHTS AND MEASURES
3. If an airplane flies west through the air at an airspeed of 100 miles
per hour, what will be its forward speed with respect to the ground (a) if
the wind blows 30 miles an hour from the west? (Answer: 70 miles an hour.)
(b) the wind blows 30 miles an hour from the east? (Answer: 130 miles
an hour.) Therefore, why do fliers, like ducks and other birds, land against
the wind? (Answer: In this problem the landing speed would be 60 miles
an hour slower against the wind than with the wind.)
4. If the gear on the front of the crankshaft turns 1,000 times each minute,
what is the speed of the outside edge of one of the teeth of this gear in
feet per minute.
(Answer: If D is the diameter of the gear in inches, then
7rD
Speed = 1,000 feet per minute)
12
ESSE TIA I A Density of a body is measured in terms of
C ON CEPTI? units of weight and units of volume. It is
1C weight divided by volume. We can com-
pare the density of different kinds of sub-
stances if we use the same units of measurement for each substance.
Study text from bottom of
page 11 through 14.
Work Problems 2, 6, 9, 10,
11, 12, and 20 on pages 15
and 16, also select a few
review problems on page
17.
How DENSE ARE WE?
(See table, top of page 13 in text)
1. Would milk float on kerosene?
2. Why is aluminum so important for production of airplanes?
3. What are the heaviest metals?
4. Why is it easier to float in Biscayne Bay than in Lake Okeechobee?
5. Why does a firehose usually spread the flames of burning gasoline in-
stead of putting out the fire?
-ES ESJ N' IA There are three types of levers each of which
ON CE PT is a simple machine for doing a certain kind
2A of work. The nature of the work accomp-
lished depends upon the relative position of the three points of contact,
namely, the applied effort, the resistance to this effort, and the fulcrum.
Study text pages 18, 19, 20,
and 21.
Study Figs. 2-1, 2-2, 2-3, 2-4,
2-5, 2-e, and 2-7 in text.
Work Problems 4, 7, 9, page
22 in text.
The instructor will find it advantageous to have diagrams of the three
types of levers on the blackboard for ready reference about as illustrated
here. Demonstrate with a rigid bar.
Explain the relationship between weight
and force, making clear that the weight
of an object is actually a force acting
downward. Show that the formulas on
page 20 are essentially the same, but per-
haps more general in nature, if we sub-
stitute the letter F (for Force) instead
of W. Then show that
Fi x D = F2 x D2
in each of the three types of levers.
Do not leave this important discussion until the full meaning of the above
equation is clear and can be applied by the pupils to a variety of simple
practical situations including those illustrated in the text. Have the pupil!
make a list of levers in which they observe forces in action in their dailI
lives such as leaning back in a chair, opening a door, pushing a typewrite]
key, etc.
Note that in all levers there is movement about a rigid point; that when
ever the leverage increases the force acting on it, it does this because th(
resisting force is not moved as far as the distance through which the effor
acted. On the other hand, the lever may be used to increase the distance<
through which a force acts, but in so doing there is a corresponding decrease
in force.
Demonstrate how a bar will pry a heavy weight and, by merely changing
the position of the fulcrum will also fling a penny across the room when use.
as a catapult. This is an excellent introduction to mechanical advantage
E S S I A L- Mechanical Advantage is the ratio of the
CONCEPT resisting force to the applied force.
28 2B
Study text Article 19, page
24.
Levers and all other machines are designed to do a certain job in a prac
tical way. We have just seen that a ruler or rod can be used as a machine
to lift a heavy load a short distance. By changing the location of the fulcrum
the rod became a machine to flip a light object across the room. Whei
we changed from one purpose to the other we changed the mechanical ad
vantage of the lever. We did this by changing the relative lengths of thi
effort arm and the resistance arm.
SIMPLE MACIINES-LEVERS AND PULLEYS
Resistance (F2) Effort (F,)
Resistance arm (D2) Effort arm (D1)
Fulcrum
By measuring the Resistance Arm and Effort Arm of the crowbar shown
Dl
above we find that the mechanical advantage of this lever is-
Work Problem 1, page 28. D,
If a laborer pushes down on the end of the handle with an effort of F,
pounds he will be able to lift a weight equal to his effort multiplied by
the mechanical advantage of the machine. We can apply this same principle
of mechanical advantage to all machines: the applied force multiplied by
mechanical advantage gives the force that can be exerted by the machine
in doing work.
Be sure to work Problem 1, page 28, in the text.
ESS IN! A- Moments. A moment is a product of force
C ONC EPTj and the distance from its line of action to
2C T the fulcrum. The sum of moments tending
to rotate a lever in one direction is equal to the sum of moments tend-
ing to rotate it in the opposite direction.
It is worthwhile to demonstrate moments in action about a pivot or
fulcrum by measurement of weights and distances, preferably on the common
see-saw. Each member of the class can determine his own weight if the
weight of only one pupil is known. By knowing one's own weight he can
determine the weight of almost any other
heavy object which can be placed on the
other side of the see-saw at whatever dis- 9K
tance is necessary to place the moments of
forces in balance. .
Study text Article 21, page The principle of moments is important to
25. aircraft designers. An airplane is a lever
which is balanced in flight about its center
of weight just as the see-saw is in balance at .
the center of its weight.
WARTIME COURSE IN PHYSICS
Work Problem 5, page 29.
The airplane's center of weight is the fulcrum. The turning effect of
any control surface (the rudder, elevator, or ailerons) is the moment of
the force when wind pressure is exerted on
the control surface. The distance of the
control surface from the point about which
the airplane is balanced is just as important
as the size of the control surface. In other
words, it is force multiplied by the distance
of its action from the fulcrum that produces
the turning effect or the "moment" of force. An airplane (or a model) is a
lever balanced at the center of
gravity.
SsE S S T A Equilibrium. When parallel forces are in
CONCEPTT equilibrium the total forces acting in one
2D direction are equal to the forces in the op-
posite direction. Moments are in equilibrium when the object does
not revolve about a point. It does not revolve because the moments
tending to turn clockwise are equal to the moments tending to turn
counter-clockwise.
Stua'y text pages 25 to 28.
Apply this concept to Fig.
2-12, page 28.
Work Problems 7, 10, page
29.
The demonstration at the right can
readily be made an experimental problem
for each individual. The pupils can take
turns in changing the settings and mak-
ing their own readings. All three spring
balances should be vertical. Each pupil
should draw the apparatus to scale in his
notebook and develop the resulting
equation.
The readings shown above are typical. Some error may occur due to
weight of the bar, therefore use a bar or yardstick of very light weight.
Each pupil should prove conclusively with his own readings that when
three forces act on any object, the point of application of any one of the
three forces can be considered as the center of moments (or fulcrum).
Equations for each of the three types of levers, on the basis of the above
readings, are:
13 x 18 = 26 x 9 fulcrum in center
13 x 27 = 39 x 9 fulcrum at right
39 x 18 = 27 x 26 fulcrum at left
SIMPLE MACHINES-LEVERS AND PULLEYS
ES S EfNT I A L
CONCEPT~
2E
Study text pages 30 to 33.
Work Problems 1, 2, 4, 5,
13, pages 33 to 35.
*
Reference Book Ill Aero-
nautics pages 25, 26. 32, 33.
The force exerted by the weight of a body
may be considered as being exerted down-
ward at the center of weight which is called
the Center of Gravity of the body.
Demonstration: This concept may be illustrated by repeating the foregoing
experiment with a weight hanging at the midpoint (Center of Gravity) of
the yardstick. The weight must exactly equal the weight of a heavier
bar. Then repeat the experiment using the heavier bar in place of the
yardstick and note that all readings are the same as they were when the
weight of the bar was concentrated at the center of gravity.
Applications: Where is the center of gravity of the flywheel of an engine?
of the crankshaft? of an airplane propeller? (Answer: In the center of
motion in the shaft. There would be tremendous vibration if the center of
weight was not also the center of motion.)
Why would an airplane tend to go in a dive if all the passengers walked
forward? (Answer: The center of gravity would be moved forward. The
downward pressure would become greater at the front and less at the back
of the plane. The pilot would offset this, however, by changing the position
of the elevators on the tail of the plane.)
Inasmuch as an airplane in normal flight acts as a lever balanced about
its center of gravity, a study of this part of mechanics is of great importance
to all persons who design or rig airplanes or prepare them for flight. It
is important also to the men who pilot airplanes and need to maneuver
them in any direction as they turn and
Sbank, climb, dive, zoom, and spiral by turn-
\ ing the plane about its center of gravity.
/
A pilot loops his aircraft by swinging it
around its center of gravity as the pro-
peller pulls it forward. The center of
gravity in this maneuver follows the dotted
line as shown in the figure.
SES S ENJT A L The Crank and Axle. The crank is a lever
CONCEPT with the fulcrum at the center of a shaft
2F (or axle). If the effort is supplied by the
turning of the shaft the effort arm is the radius of the shaft. If the
effort is applied by the crank then the radius of the shaft becomes the
resistance arm.
Be certain there is a crank of some kind in the classroom for demon-
stration. The principle of the crank is one of the most important for all
mechanics, engineers, or technicians of any kind.
WARTIME COURSE IN PHYSICS
Study text pages 35 to 37.
Work Problems 2, 4, on
page 39.
24Teeth 2Teeth
O O
D F
The Gear.
In principle the crank and the wheel and axle are just about one and
the same thing, and this should be made clear to the pupils. For instance,
if a door knob were to be placed on a pencil sharpener we would be replacing
a crank by a wheel. The principle is the same but the crank is more
efficient. On a door the circular knob is more efficient but either one would
do the job. The first automobiles were steered by cranks instead of steering
wheels. In each case the steering was done by turning a shaft.
Probably the most important simple machine which uses this principle
is the gear wheel which is a series of cranks in the form of a wheel. Each
gear tooth acts as a crank. It either pushes another gear around or else it
turns a shaft by being pushed around by the other gear.
Note that eacn tooth in either g
unit of the circumference, and
number of teeth is in proportion
diameters of the gears. Also note
these gears were to be separated, s:
inches apart, they could still op
placing a drive chain over them
chain on the sprocket of a bicycle.
the sprockets are replaced by pulle:
same size, and the chain is replace
belt, the shafts will be turned in
the same way.
The foregoing explanation shows
understanding the simple lever we
pared to understand the operation
gears, chains, and belts and pulley
are the principal ways that power
mitted by mechanical means.
The gear teeth which are in contact
actually are on the end of the crank
which has a shaft at the other end. This
is the most common way we transmit
power from one mechanism to another.
How many sets of gears can the pupils
observe in the engine that has been torn
down by the class? What is the me-
chanical advantage of the pair of gears
which cause the camshaft to turn?
(Answer: 1/)
,ear is a
that the
to the
that if /
ay a few >
rate by .-7
like the
Now if
ys of the /9'
ed by a
SThe Chain.
exactly
that by
are pre-
)f shafts,
s. These
is trans-
The Belt.
SIMPLE MACHINES-LEVERS AND PULLEYS
Engine Demonstration. Note that the engine crankshaft is a crank which
turns the straight downward motion of the piston into circular motion in
the main shaft. The gear on this shaft turns the camshaft gear at half
as much speed because the mainshaft gear has only half as many teeth as
the camshaft gear. Note also the belt and pulley which operate the fan.
Drawings and problems may be derived from use of these materials.
SESS E'NoT IAL Block and Tackle is a combination of pulleys
CONCE PT^ and ropes in which a weight is supported by
2G
more than one rope. The mechanical ad-
vantage which multiplies the lifting power is, in general, equal to the
number of ropes which support the weight.
Study text pages 37 to 39
and Figs. 2-22, 2-23, 2-24,
and 2-25.
Work Problems 6, 7, 9, 10,
page 40.
If possible have students use pulleys in
the combinations shown in figure to the
right observing the forces needed to lift
the weights. If no pulleys are available
put drawings on blackboard and apply
the principle of the lever as suggested in
Black and Davis, Fig. 2-22 and Fig. 2-23.
Cheap little pulleys which are suitable
for experiments and demonstrations can
10 cent store.
usually be obtained from a 5 and
Raising a flag on its pole offers an example of use of the fixed pulley.
A single movable pulley is sometimes used to raise a sail on a boat.
A combination of fixed and movable pulleys can be arranged to obtain
the desired mechanical advantage.
Chapter 3. WORK, POWER AND FRICTION
DEMONSTRATION MATERIALS: Spring balances, micrometer caliper, objects to be used as weights, thumb
tacks, smooth board (40" x 6" or 8" wide), gas engine parts, pencil and paper,
model airplane propeller, miscellaneous shop tools.
ESSENTIAIL Work is done whenever force moves some-
CONCEPT3 thing. Work is measured by the product
of the force and the distance through which
the force moves. If there were no friction the work put in the
machine would be the same as the amount of work accomplished
by the machine.
Study pages 43 to 45.
Field trip.
During the work in this
chapter the teacher should
make careful plans for a
trip to a nearby shop where
the pupils will observe the
operation of devices used
for transmission of power
including belts, pu 11 e y,
gears, etc. Pupils should
compute mechanical advan-
tage of chains, of gears,
and of pulleys used on
various machines. They
should recognize clearly
how some speed up the
work while others develop
greater power at slower
speed.
SIt is evident that the work put into
operation of the crowbar shown here
equals the work accomplished. If an
effort of 100 pounds is applied through
20 inches as shown, a weight of 500
pounds will be lifted 4 inches, because
100 x 20 = 500 x 4
The pulleys illustrated below serve identical purposes because in each case
a heavy weight acts on a small pulley to balance a light weight on a large
pulley. The apparatus between the blackboard drawings is made of scrap
lumber with a nail for a shaft or pivot.
The simple problem that follows introduces shop mechanics. The importance
of shopwork both in the war effort and in peacetime living should be made
a topic for class discussion with a view to stimulating interest in the shop
trip being planned for, and by, the class.
WORK, POWER, AND FRICTION
2 Note in the blackboard drawings that forces applied through the belts
S/ "on the pulleys at the right have the same action as the weights hung on
0' the laboratory pulley shown in the center and the weight indicated at left.
Problems: = 2r. See blackboard illustration on previous page.
1. What effort applied to the larger pulley is necessary to overcome the
50-pound resistance on the smaller pulley? (Answer: 25 lbs.)
2. If R = 4" and r = 2", and the work is done by power-driven belts, how
far will the belt move over the larger pulley in overcoming the "pull" or
resistance during each revolution of the smaller pulley?
S- (Answer: 27rR = 25.1)
j 3. A watchmaker uses pulleys the exact size of those pictured at the left.
SMeasure D, and D2. If Pulley A is the driver and has a rate of turn of
500 revolutions per minute, how fast is the belt traveling in feet per minute
What is the rate of turn of Pulley B?
ESS ETIA The Inclined Plane is used for doing work.
CONCEPT The relation of the resisting force and the
3B effort put into the machine is the same as
the relation of the length of the plane and
the height of the plane. The mechanical advantage is length di-
vided by height
Study pages 46 and 47.
Work Problems 1, 2 and 7
on pages 47 and 48.
This concept may be made clear by a demonstration or experiment in
which each pupil makes his own readings. If laboratory equipment illus-
trated in the text is not available the readings may be taken from a spring
balance as shown below. Make due allowance for friction which cannot
be satisfactorily overcome unless the object is rolled on wheels.
Demonstration: Weigh an object (R) with a spring balance as shown
in Fig. A on next page. Record reading on balance as the object is drawn along
horizontally on a board as shown in Fig. B. This reading determines the
approximate force required to overcome friction.
WARTIME COURSE IN PHYSICS
Notes
1<-^--
Run
Pitch of this roof is BD
AC
Set up the inclined plane with the incline about 3 or 4 times as long as
the height. Place the object R on the incline and draw it up with a steady
pull by the spring balance. Call this reading Force F1.
The work done consists of raising the resistance (R) the vertical height
(D2) of the inclined plane. In order to raise the resistance R to this height,
the effort (F,) had to move through distance (D,).
Measure these distances, and the result minus the reading for friction
would be:
30 x 10 = 8 x 40, because
Weight x height of plane = Effort x length of inclined plane.
Mechanical Advantage for the typical readings shown above would be
as follows:
Resistance length of plane 40" 32 oz.
Effort height of plane 10" 8 oz.
PITCH OF A ROOF
The pitch of a roof is the ratio of the rise to the whole width of the
building. For example, if the building is 30 feet wide and the ridge is
to be 10 feet higher than the eaves, then the pitch is 10/30 or 1/3. From
the tables on the framing square used by the carpenter it is possible to
determine the length of the rafters needed for this pitch of roof and for
the particular run involved. Run is half the width of the building. Run,
rise and rafter form a right triangle as shown in the diagram at the left.
E ESS ENT I A L
CONCEPT_ "
3C
WORK, POWER, AND FRICTION
The Wedge is similar to the inclined plane
but is used in a different manner. Instead
of pulling or pushing the load up an in-
cline we push the incline under the load.
2. The Axe
1. The Jack Plane
Study Article 38, page 48.
3. Carpenter's Bit
6. Sawteeth (Timber Saw)
Each Cam is a Wedge.
4. Leveling a floor 5. Stonecutter's
Axe
7. A Gouge
CUTTING TOOLS ARE WEDGES
Obtain a magnifying glass and examine carefully the "teeth" on a nail
file and a metal file. Note how each edge is a wedge. Also examine the
"teeth" of sand paper, emery cloth, and a grinding wheel.
The common carpenter's chisel is a typical wedge. Examine the angle and
pitch of a chisel and of a common sawtooth. Why is this pitch important
in sharpening a chisel, a saw, a jacknife, and all other cutting tools?
WARTIME COURSE IN PHYSICS
E S SE N6T I A L
CONC E P' '
3D D
Study pages 49 and 50.
Work Problem 2, page 5
A Typical Propeller Blad
A Typca -Ppl B
A Typical Propeller Blad
The screw is another form of the inclined
plane. The pitch of the screw is the rise
of the inclined plane for one turn and is
measured by the number of turns or threads
per inch.
Demonstration: The principle of the screw may be clearly demonstrated
as an inclined plane wrapped around a core or cylinder. Cut out a tri-
angular piece of paper and wrap it around a pencil.
i2.
e.
PROPELLERS
The propeller on a boat or an aircraft is a screw. Instead of being turned
in such a way that it draws itself through metal or wood it turns through
the water or air. The geometrical pitch of a propeller is the distance the
blade would move forward in a solid medium in one revolution. The ef-
fective pitch is the percent of the geometric pitch which the propeller ac-
tually moves in air (or water). Slip is the percent of the geometric pitch
which is ineffective.
Lyconumlg-.~mlith ctujtiullkle prup.:lllt.
A controllable propeller in which the pilot can adjust the pitch to the
most effective position for different airplane speeds.
WORK, POWER, AND FRICTION
Assortment of Screws
Self-tapping screws
! c '~
Special Phillips Screw
and screwdriver head
-E S S HJ-A-L
CONCEPT -
a 3E ~E
Study pages 53 and 54.
Notes
Problem: If the geometric pitch of the fan on the automobile engine in
your laboratory is 6 inches and if the fan were used as a boat propeller
and had a slip of 40 percent, how far would it push the boat in 1,000
revolutions ?
.60 x 6" x 1,000 3
(Answer: 12= 300 feet)
12
THE MICROMETER CALIPER
The threads of a screw are used for accurate measurement by an im-
portant device called the micrometer caliper. Examine the threads on
some of the cylinder head bolts on your gas engine. They probably have
about 16 threads per inch. Notice then that the nut moves along the bolt
only 1/16 inch for each turn. Graduations on the circumference of the
caliper show the fraction of the distance between the 1/16 inch threads.
Then, by use of a vernier scale, the fraction may be further reduced and
read with accuracy.
1-8 .125
-8.37 1 .05 12
1-2 .500 5 0937
;-8 .62 7
4. 750 S187
7-8.875
Power always involves the element of time.
1 .0625 1 687
It is the speed with which work is -
complished. 7
11Z6875 AthoLNa-.TS:A. 981812
3 812 N(GLU3. 27.8M3E
5 .9U.75
Power always involves the element of time.
It is the speed with which work is ac-
complished.
Discussion: If a man moves 100 pounds of resistance through a distance
of 10 feet, he does 1000 foot-pounds of work. If it takes him one minute
or even one hour, the work is the same. But if he wants to do the work
in one minute he would have to exert 60 times the power required to do
it in one hour.
Work
Power T
Time
Horsepower is the English unit of power.
Horsepower foot-pounds per minute
Horsepower -
33000
foot-pounds per second
550
See example in text page 54, explaining how to get horsepower of an engine.
Driving or driven machines receive or transmit power by means of shafts,
belts, chains, or gears. See figures 3-11, 3-12. and 3-13.
WARTIME COURSE IN PHYSICS
E S S ETLiA Lj The Horsepower is a unit we use in meas-
CONCEPT during power.
I: C 3F
Study the example on pa,
54.
V ESSENTIAL
_CONCEPT -
3G
Study pages 55 and 5
Article 45.
Work Problems 1, 2, 3,
7, 8, and 10 on pages 5
57. Some pupils may al
work Problems 13, 14, ai
15 on page 58.
Concept of Power and I
Flow Through an Engin
Nearly all machines a
composed of simple m
chine parts. Some do
special job, like the flo
in the carburetor or t]
spark plug; other par
transmit power.
The foot-pound is a unit of work and the minute is a unit of time. If
a machine is capable of doing 33,000 foot-pounds of work in one minute,
ge one horsepower is required to operate the machine.
If we know the number of foot-pounds of work that an engine can ac-
complish in one minute, we find the horsepower of the engine by dividing
the work by 33,000.
Example: A plane weighs 3,960 pounds loaded, and climbs 6,000 feet in
12 minutes. At what rate is the airplane engine doing work?
3,960 x 6,000
(Answer: 3,960 x 6,000 = 60 H.P.)
33,000 x 12
Power is transmitted by any object on
which force is applied in overcoming re-
sistance.
TRACING THE TRANSMISSION OF POWER IN A GASOLINE ENGINE
Name of Machine Kind of Force and Transmitted
Source of Power Part Where Applied to-by
Expanding Gas
Connecting Rod
Driver Pulley
Driver Gear
Cam on Camshaft
Cylinder Head
Crankshaft
Fan Belts and
Pulleys
Camshaft Gears
Intake and
Exhaust valves
Expanding gas
pushes on piston
Connecting rod
pushes and turns
the crankshaft
Driver pulley
pulls belt which
pulls driven
pulley around
Driver gear teeth
push against teeth
of driven gear
Cam pushes up-
ward on valve
stem against
pressure of spring
Piston pushes
against wrist pin
which pushes con-
necting rod down
Turns shaft to
propeller
(on airplane)
Driven pulley
turns shaft which
turns fan
Camshaft gear
teeth are pushed
around
Valve stem
lifted by push
of cam; stem
raises valve
6.
5,
.6,
so
nd
:ts
e
re
a-
a
at
he
*ts
WORK, POWER, AND FRICTION
A good technician can
quickly tell the particular
function of each part of a
machine and because of
this ability he can locate
the source of trouble as it
develops in operation of
the machine.
Pupil ability of this kind
may be discovered by use
of the accompanying table.
The engine parts discussed
in this table should be ex-
amined by the pupils.
Key on Crank-
shaft
Airplane
Propeller
Crankshaft key
pushes hub
around and turns
propeller
Back of propeller
pushes itself for-
ward against air
just as a wood
screw pushes
itself forward
when turned
TRANSMISSION OF POWER IN OTHER MACHINES
Manpower Bicycle Push on crank Axle turns wheel,
turns sprocket rubber on wheel
which pulls chain pushes against
and turns rear ground (traction)
axle
SUMMARY
Note all the devices that were used to transmit power so that useful work
could be accomplished in the least time possible (remember, power involves
time-speed).
rubber traction on ground
wheel and axle
chain and sprocket
crank and axle
propeller traction against air
key in shaft
connecting rod and pin in piston
piston in cylinder
gas confinement in cylinder
gear teeth
camshaft and cams
belt and pulleys
valve stem
E S SEfN)T I A L Friction is resistance which opposes every
OC cONCE PT effort to produce motion.
Materials should be assembled by the pupils to demonstrate each of the
points below.
Study pages 59 to 61
(Article 51 optional)
The Amount of Friction
Depends Upon
Suggested Explanation or
Demonstration
1. Kind of surface in contact Why do we slip on a waxed floor?
Examine the smooth surface of the crank-
shaft bearings in the engine.
2. Amount of Pressure
3. Rate of Motion
Demonstrate increased friction between a
book and the table top when the weight of
more books is added.
At high speed a boy can slide across the
floor; it is difficult to slide at slow speed.
WARTIME COURSE IN PHYSICS
Friction is Reduced by
1. Lubrication
2. Making the surfaces more
smooth
3. Substitute rolling motion
for sliding motion
The film of oil between surfaces may be
considered as composed of minute rollers
which act as roller bearings.
Note that in all parts of the engine where
moving parts are in contact the metal is
highly polished (pistons, cylinder walls,
bearings, etc.)
Examine roller bearings or ball bearings.
Roller skates may be discussed.
ESSENT IAL
CONCEPT
3J
Study page 63 and 64.
Work Problems 1 and 4
page 65. Some pupils ce
work all seven problems
this page.
Review. The extent
which this chapter shou
be reviewed depends up
the clarity of these esse
tial concepts in the min
of the pupils, not upon t
ability to state any fac
or formulas from memory
Simple problems provi
the best tests.
The efficiency of a machine, like the effi-
ciency of a person doing a job, is the ratio
of useful work accomplished to the total
work.
There is considerable advantage in applying the principle of efficiency
to human performance as well as to machine performance. For instance,
if the pupils make an effort to solve all of the seven problems on page 65,
the proportion of the work done correctly may be called a measure of
their efficiency in the performance of this particular job.
Any form of wasted effort decreases efficiency and reduces the usefulness
of a man or a machine.
If a motor can develop 4 H.P. on an input of 5 H.P. the efficiency is:
Work done 4
on Work put in 5
an
o11 What are some of the causes of reduced efficiency that the pupils can
discover, such as the following:
Engine-friction from lack of oil or grease, overheating from lack of
water, low grade fuel, vibration from loose bolts, bad bearings, leaking
valves, etc.
Bicycle-friction from lack of grease, slipping chain, seat too high or
too low for rider, broken pedals, etc.
to Kite-too heavy, improperly balanced, string too heavy, etc.
id Airplane-too heavy, improperly balanced, engine out of order, poorly
on streamlined, flown on wrong course by navigator, controls poorly handled
*n- by pilot, etc.
ds
he Soldier- inadequate training, poor diet, lack of rest, ....................................
t s ............................. ......... .... ...................................................... ................ . ....... ... ...., e t c .
S Stude-poor nutrition, lac of sleep, ... ..............
Student-poor nutrition, lack of sleep, .. .
dtt
................................................ ........................... .................... ................... ......... ... .., e t c .
Ue
Chapter 4. MECHANICS OF LIQUIDS
DEMONSTRATION MATERIALS: Spring balances, objects to be used as weights, tumbler, thumb tacks, glass
tubing (4 mm), test tube (10 mm), small test tube, jar (fruit or pickle),
board (1"x12" x40"), tumbler, tall tin can, spool, cardboard, heavy wrap-
ping paper, quart jars (2), gas engine parts.
"Ships float, anchors sink, and submarines do either at the will of their commanders, in accordance
with certain laws that deal with liquids. Water wheels, hydraulic presses, and hydraulic brakes make
use of liquids. In this chapter we shall see how liquids offer a very convenient medium for the trans-
mission of pressure." (From text, page 72: Study pages 71 and 72.)
E$SE!I.T IA L The pressure of a liquid is independent of
-CONCEPTP the shape of the vessel.
4A
Study pages 73 to 75 with The pressure in your city water system reaches your faucet through a
special emphasis on Article most irregularly shaped container consisting of water mains and small pipes.
57 and Figs. 4-2 and 4-3.
dwlESS IAL- The pressure at any one place in a liquid
CONCEPT_ is the same in all directions.
h4B
Study text pages 75 to 87,
giving special emphasis to
Articles 58 through 60, and
Article 66.
Work Problems 3, 4, 6, and
13, pages 76 to 77; also
problems 3, 5, and 6, page
85.
Demonstrations: 1. If equipment permits show the experiment pictured
in Fig. 4-6 in the text. If equipment is lacking use experiments 2 and 3
below.
2. Upward Pressure. Demonstrate the experiment shown in Fig. 4-4 on
page 75 to show upward pressure. A small lamp chimney or a tin can
with both ends cut out smoothly may be substituted for the glass cylinder,
with a piece of cardboard taking the place of the glass plate.
3. Pressure Sideways. Sideways pressure may be shown in the following
way. Punch 3 holes of equal size in
the side of a tall can (a large grape-
fruit can is ideal) in a staggered (slop-
ing) row from top to bottom. When
the can is filled with water the flow
from the holes shows that liquid pres-
sure is exerted sideways and increases .
with depth. It may be convenient to
plug the holes with match stems while
preparing the demonstration.
WARTIME COURSE IN PHYSICS
This apparatus will show
the principle of the water
turbine. See text page 83.
Some pupils should also
work problems 8, 9, and
10, page 87.
Important Topics for Discussion
1. The kinetic molecular theory of matter explains the three states of matter.
See text page 154, and Chapter 11 of this manual.
2. The downward pressure of a liquid is due to its weight.
3. The upward pressure exerted by a liquid at any depth is equal to the
downward pressure which would be exerted by the same liquid at the same
depth.
4. The sideways pressure of a liquid increases with the depth and density of
the liquid.
5. The force of a liquid is equal to the area times the average pressure.
Supplementary Questions
1. Operating under a weight of a few ounces a phonograph needle may exert
a pressure of several tons per square inch. How is this explained?
Answer: Pressure equals force per unit area. The area involved here is
infinitesimal. If the area here is increased to one square inch and the pressure
increased in proportion, the pressure becomes several tons.
2. Why should a dam be made thicker at the botton than at the top?
Answer: Sideways pressure of liquids increases with depth.
3. Boulder Dam forms a lake 115 miles long. Would the pressure exerted
against the dam be any less if the lake were only 5 miles long? Five feet
long ?
Answer: No. Sideways pressure depends only upon the depth and the density
of the liquid.
4. A ship is sunk where the ocean has a depth of 5 miles. Will the
ship sink to the bottom?
Answer: Yes. As the boat fills with water it sinks when it no longer displaces
its own weight of the water. As it goes down the pressure of the water above
acts equally in all directions.
MEC ANICS OF LIQUIDS
ES EN IA =L When a fluid flows faster it exerts less
SCONCEPT pressure.
4C
Study text pages 87 to 91
with emphasis on Articles
68 and 69.
Develop an especially clear
understanding of principles
explained by the figures
below. (See text pages 89,
90).
Pressure is less where
speed is greater.
Notes
Application in the Engine
Show the class the carburetor of your gas engine and call particular atten-
tion to the throat (venturi) in which the jet is located. Explain the principle
involved in operation of the carburetor, how the intake valve opens, the
piston goes down, and air pressure forces air into the cylinder through the
carburetor and the manifold. The throat
of the carburetor is smaller than the in-
take pipe so the air has greater speed as ThrotU
it goes through the throat. This increased
speed reduces the pressure. The gasoline V ovai\
jet opens right into this area of lower
pressure so gas is drawn out of the jet
in a fine spray. This spray mixes with \- Air Intak
the air that is being drawn into the
cylinder. ol
Inlet
Thus a combustible mixture of about Princille of the Carburetor.
11 parts air and one part gasoline vapor
is drawn into the cylinder by the com-
pression stroke. The mixture is compressed on the up-stroke of the piston,
then is ignited by a spark in the spark plug. The expansion of this burning
gas forces the piston down on the next stroke which is called the power stroke.
The fourth stroke in this four-stroke-cycle engine comes next when the
exhaust valve opens, the piston rises, and the burned gas is forced out of
the cylinder.
Lifting Power of Air Pressure
One reason why the engine operates is that gasoline is raised up in the jet
because of the reduced air pressure in the throat of the carburetor. Put a
straw or glass tube in water and blow across the open end with another
tube. Watch the water rise in the tube. This is the action of a spray gun
and atomizer as well as a carburetor. Paint sprayers work on the same
principle. The fluid is lifted because the pressure upward is greater than
the pressure downward. This is the same kind of "lift" that enables an
airplane to fly.
WARTIME COURSE IN PHYSICS
^j E S ES fNTIA L-EY
CONCEPT
SNotes
Notes
Increased airspeed reduce
pressure above the card.
An airplane is lifted because the air moves
faster across the top than across the bottom
of the wing.
There are several interesting ways in which we can demonstrate that the
airplane wing (or airfoil) is lifted because the air moves faster, and there-
fore reduces the pressure, across the top of the wing.
1. The air travels a greater distance in going over than in going under
the wing, therefore it goes faster. We should prove to ourselves that this is true.
The pupils should draw a typical wing section and note that in going from
A to B across the top the air is deflected much more and travels a greater
distance than across the bottom from A, to B,. Since all of the wing is
moving forward at the same time, the air moves over the longer deflected
course across the top in the same amount of time that it takes to go the
more direct path across the bottom. Therefore, the air speed is greater across
the top, because
Distance
Speed = Time
Time
Since Time is constant, Speed will be greater as Distance is greater.
2. Now we should prove conclusively to ourselves that the increased speed
of air over the top surface actually results in lifting the object. The demon-
stration illustrated at the left is a good home assignment for each pupil
to prove this point to his friends and parents. It calls for a piece of light
cardboard or stiff paper a little bigger than the end of a spool, with a pin
projecting through it in the center. Blow through the spool as shown.
While you are blowing you produce a low-pressure area above the card.
es The harder and steadier you blow the more effective is the normal atmos-
pheric pressure in holding, the card from falling.
MECHANICS OF LIQUIDS
When we blow upward
across the top of a sheet
of paper which extends out
from the pages of a book,
the paper rises and takes
the shape of the top sur-
face of an airplane wing.
Explain.
This lifting force is being measured by putting weights on the
paper "wing section." (See problem below)
In the simple demonstration above a piece of fairly heavy wrapping paper
serves as a section of the upper surface of a small airplane wing. The de-
crease in downward pressure on the wing can be measured by placing ob-
jects on the paper. In the classroom where this manual was prepared it
was found that a /4 H.P. fan supported three piston rings which weighed
2 ounces. The paper surface contained 3 square feet.
Problem: Assume that large airplanes support weight in proportion to the
results of this test. If 1/ H.P. supported 2 ounces with a wing area of 3
square feet, about how much weight could an 800 H.P. motor apparently
be expected to support with wing surface 70 feet long and an average of
10 feet wide. (Answer: 1 H.P. supports 2/3 ounce per square foot so 800
H.P. should support 800 x 8- 3 ounces per square foot = 133 pounds per
square foot. Area = 70 x10 = 700 square feet, therefore total support =
700 x 133 = 93,100 pounds = 46.5 tons.)
We will find many reasons why in actual practice the power of the engine
cannot be used entirely for development of a lifting force.
Problem: A bomber weighs 5 tons, has a crew of four men who average
140 pounds each, and has equipment and fuel load which, at time of take-off,
weigh 4,000 pounds. The wing surface is 80 feet long and has an average
chord (width) of 11 feet. At time of take-off the lifting force is 21 pounds
per square foot. What is the greatest number of 500-pound bombs that
should be loaded into the bomb racks. (Answer: 7 bombs).
WARTIME COURSE IN PHYSICS
.^ ES SE TIA Pressure exerted anywhere on a confined
CON CEPT liquid is transmitted undiminished to every
4E portion of the containing vessel.
Study text pages 91 to 95. This concept is important to future mechanics in all branches of the
service and in industry where hydraulic systems are used to transmit power.
Work Problems 3, 4, and 7,
pages 94 and 95.
ES SSENT IAL A body placed in a liquid is buoyed up by
CONCEPT T a force equal to the weight of the displaced
4F liquid.
Study text pages 95 to 98.
Work Problems 1, 2, 3, 8,
10, pages 98 to 99.
SUGGESTED DISCUSSION OF THE SUBMARINE
Buoyancy of liquids. The science of shipbuilding is based upon Archimedes'
principle and the laws of flotation. Because of the present day need for
ships and interest in them this topie needs careful study.
The submarine sinks if the weight of the water it displaces is less than
the weight of the submarine. If submerged it remains in equilibrium, neither
rising nor sinking, if the weight of the fluid it displaces exactly equals its
own weight. It rises to the top and floats when the weight of water it dis-
places is greater than its own weight.
The submarine operates like the Cartesian diver shown below. When water
is admitted into airtight compartments the vessel sinks because its density
becomes greater than that of the water. Water is blown out of these com-
partments by the use of compressed air to bring the vessel to the surface.
In actual practice the use of elevating fins in connection with the forward
motion of the vessel hastens these operations.
The torpedo is a weapon that carries an explosive charge underneath the
surface of the water for a few miles under propulsion of compressed air.
Automatic devices include a pendulum control to keep it level, a water
pressure control which can be set for a certain depth, usually about 15 feet,
and a gyroscope to keep it from rolling and deflecting.
MECHANICS OF LIQUIDS
A cartesian diver.
Notes
DEMONSTRATIONS
1. The Cartesian diver. Fill a wide-mouth bottle or quart jar with water.
Fill a small test tube or bottle about half full of water. Place the thumb
over the top of the test tube and invert it in the jar of water. The amount
of water in the test tube must be adjusted until the test tube barely floats.
Place the palm of the hand over the top of the jar tightly so that no water
or air can escape.
Press down on the surface of the water. This pressure forces more water
into the test tube thus increasing its density and causing it to sink. When
the pressure is released the compressed air in the top of the test tube forces
out some of the water. The average density of the tube is decreased and
the tube rises again to the surface. Better results may be obtained if the
top is covered with a water-soaked piece of paper towel or newspaper, or
if we use a jar with a flexible top, such as a large mayonnaise jar, and
pressure is applied to the flexible cap.
2. The carburetor float of the gas engine. See text, page 314, Fig. 14-8.
Show the float to the class. As gasoline fills the float chamber the float
rises. When the float chamber is full the float automatically closes the
inlet valve.
3. Solids lighter than water. To show the buoyant effect of liquids weigh
a rectangular block of wood. Place the block in water and measure the sub-
merged portion. Calculate the weight of a volume of water equal in volume
to the submerged portion of the wood. The weight of the water should
equal the weight of the block of wood. This may be used as an experiment
with each pupil making his own measurements and calculations and draw-
ing his own conclusions.
SUPPLEMENTARY QUESTIONS
1. A ship weighs 8000 tons. It can carry a load of 12,000 tons. What
must be the displacement of the ship? (Answer: 20,000 tons).
Some pupils should determine the volume of sea water displaced. (Answer:
20,000 x 2,000 = 622,354 cubic feet)
62.4 x 1.03
2. A battleship is covered with steel plates 10 to 18 inches thick. How
can it float? (Answer: The average density of the ship is less than that
of water because of the large air spaces within the hull.)
WARTIME COURSE IN PHYSICS
$ESSEJ~tIA I Specific gravity is the weight of a body
CONC E PT divided by the weight of an equal volume
4G 3 of water.
Study text pages 100 to
103.
Work Problems 1, 2, 3, 5,
8, and 11, on pages 104 and
105.
Notes
1. Finding specific gravity. Select irregular steel or iron parts of the
gas engine that weigh about three pounds. Weigh the materials in air and
then in water. Divide the weight in air by the loss of weight in water.
The quotient is the specific gravity of the iron weighed. The specific gravity
of iron ranges from 7.1 to 7.9.
Repeat, using material of lower specific gravity such as aluminum, stone,
or glass. Each pupil should take readings and make a record of such an
experiment.
2. Demonstration of the Hydrometer. Fill a two quart jar with water.
Fill a second jar with water in which salt has been dissolved to the point
of saturation. Weight the rubber end of a long pencil with thumb tacks
until it floats upright and place it in the jar of fresh water. Mark the
water line on the pencil with a knife. Now place the pencil in the salt
water and note that more of the pencil floats above the surface of the
liquid. This shows that the salt water is more dense and tnat its specific
gravity is greater than one. The pencil has become a crude hydrometer.
DISCUSSION OF DENSITY AND SPECIFIC GRAVITY
Water is so important in the scheme of life that many times it is useful
to compare the density of a substance with the density of water. Specific
gravity is useful in comparing the densities of any substances.
In the metric system the number expressing the density of any substance
is the same as the specific gravity of that substance. In the English system
the density of a substance expressed in pounds per cubic foot may be
divided by 62.4 to obtain the specific gravity of the substance.
Perhaps the chief reason why the student should learn the concept of
specific gravity is that science and industry insist on using it. Specific
gravity is used in the processes of: identifying rocks and minerals, judging
the purity of substances, and determining the concentration of liquids such
as the acid in the storage battery.
Chapter 5. MECHANICS OF GASES
The greater part of the earth's surface is not solid, but fluid. We spend our existence at the bot-
tom of a vast atmospheric ocean, which is material and has weight. A study of the properties of the
atmosphere is now more important as a preparation for the study of aeronautics, meteorology, and navigation.
While liquids are almost incompressible, gases are very compressible. Keeping this difference in mind
one can apply easily many concepts of liquids and gases.
SESS W j Ij-AL Air has weight and, consequently, exerts
~ 5ONCE PT pressure.
'. 5A y
Study text pages 109 to
113, emphasizing Article 81.
Work Problems 1-4 on
pages 114 to 115.
Notes
WEIGHING THE AIR IN A BULB OR A FOOTBALL
Weigh accurately a large burned-out light globe. Admit air to the in-
side of the bulb by putting a hole in the glass using a flame and a blow
pipe. If a partial vacuum exists the glass which is melted by the blow torch
will be forced into the globe by atmospheric pressure. Discuss with class.
If a metal blowpipe is not at hand blow through the flame with a glass
tube. Weigh the globe a second time.
The globe should now weigh more because air has been admitted to fill
its partial vacuum. The additional weight (in milligrams) is the weight
of the volume of air admitted.
This experiment can be carried out with a football instead of an electric
light globe. Weigh the ball before exhausting the air. A wooden bar sus-
pended by heavy thread can take the place of the balances indicated below.
WARTIME COURSE IN PHYSICS
Notes - r mMm AS SA III-
CHANGING THE WEIGHT OF A SACK OF AIR
lmgrU a~gm mir tmm imB nMullIMM ilm
of air in two sacks. At the same time we show tat a given quantity of
air will lose weight as it is heated. Attach two large paper sacks, bottoms
up, to a very light wooden stick. Suspend this equipment by a string looped
around the middle of the stick and adjust the loop until the stick is bal-
opening of one of the sacks. Within a few moments this sack will rise.
The heated air expanded and therefore the air in the sack lost weight.
Problem: One cubic foot of air weighs about 1.2 ounces. What is the weight
of the air in your classroom?
(Typical answer: 7500 uft x = 562 bs.)
____ A column consisting of the air above one
ESOI
CHANGING THE WEIGHT OF A SACK OF AIm
W se inch of the earthat air has weight by creating a difference in the weight
of air in two sacks. At the same time we show that a given quantity of
air will lose weight as it is heated. Attach two large paper sacks, bottoms
up, to a very light wooden stick. Suspend this equipment by a string looped
around the middle of the stick and adjust the loop until the stick is bal-
anced. Hold a flame, such as a candle or burner or alcohol lamp, in the
opening of one of the sacks. within a few moments this sack will rise.rument
that measure pressure of thhehe air expanded and therefore the air in the sack lost weight.
Problem: One cubic foot of air weighs about 1.2 ounces. What is the weight
of the air in your classroom?
1.2
(Typical answer: 7500 cu.ft. x 16 = 562 lbs.)
What is the approximate weight of the vapor that is consumed in a single
cylinder of your laboratory engine in 1,000 explosions? If about one-eleventh
of this is gasoline vapor, how much gasoline is consumed?
` F $ In- A column consisting of the air above one
SS r. PT A LT square inch of the earth's surface weighs
SB about 14.7 pounds at sea level. This force
is called atmospheric pressure. Instruments
that measure pressure of the atmosphere are called barometers.
MECHANICS OF GASES
Study text from Article 85
on page 113 through page
121.
Work all problems on pages
122 and 123. These prob-
lems will give a foundation
in meteorology.
'DEMONSTRATIONS OF ATMOSPHERIC PRESSURE
1. Fill a tumbler to the brim with
water. Cover the tumbler with a piece
of paper. Place the palm of the hand
on the paper and invert the tumbler
with the other hand. Remove the hand
supporting the paper and water. At-
mospheric pressure will support the
S weight of the water. Explain.
2. Boil a little water in a two gallon oil can. Replace the stopper tightly
and remove the source of heat. Pour cold water on the can. As the steam
condenses the can will be crushed in by the atmospheric pressure.
3. Remove the shell from a hard boiled egg. Light a few small strips of
paper and drop them into a quart milk bottle. Immediately place the egg
in the mouth of the bottle. The oxygen is removed from the air by burn-
ing paper in the bottle, then the heated air cools. This lowers the pressure
in the bottle so the atmospheric pressure on the outside forces the egg
through the opening.
To remove the egg, invert the bottle and blow into it as hard as you can.
The egg acts as a valve in the mouth of the bottle ty holding back the
compressed air until enough air is inside the bottle and the egg is forced out.
Three steps in the demonstration described above.
SE S S E JNT I A L7^
CONCEPT T
5C -
Study text Article 90, pages
118 and 119.
WARTIME COURSE IN PHYSICS
The altimeter is an aneroid barometer with
a scale that indicates altitude above a set
point. It actually measures the weight of
air above the barometer.
Refer to the pupil text on Aeronautics,
Book 3, pages 29 and 30.
The altimeter must be set at zero at the
beginning of any flight because it is change
in atmospheric pressure that causes the hand
to move. This instrument only records the
altitude above the place where pressure is
zero. It is necessary for pilots to make due
allowance also for the corresponding elevation
of landing fields as well as for the day-to-
day changes in atmospheric pressure.
The Principle of the Aneroid
Barometer and Altimeter.
ESSENTALI3 Al
CONCEPT lif
DS lif
ON5D E cr
Study text pages 120 to
128.
Study also pages 29 to 80
of Aeronautics, Book 3.
atmospheric pressure is utilized to provide
ting force on a wing. This pressure de-
eases with ascent above sea level.
I
SUGGESTED DEMONSTRATION
A gas pressure gauge may be used to illustrate the measurement of ai
pressure. Arrange the apparatus as diagrammed. Blow gently into the small
tube. It's water level is lowered. Blow hard and the level is further low
ered. Create a partial vacuum in the tube and the water level rises. Th
water is forced up by the air in the closed tube which expands against
lessened pressure.
The variations of pressure in the open tube may be compared with th
variation of atmospheric pressure at different altitudes. This gauge woul,
be a satisfactory barometer if compensation could be made for temperature
changes. It is called a closed-tube manometer. Some manometers are ope
at each end.
The open-tube manometers illustrated on the next page show that when thi
airplane wing is in flight the pressure on the upper surface is less than atmo!
pheric pressure, whereas the pressure beneath this wing is greater tha
atmospheric pressure.
MECHANICS OF GASES
Notes
Note indication of
ANGLE OF ATTACK I \greater pressure
-. on under surface
+10*
WIND DIRECTION
REGIONS OF REGIONS OF
NEGATIVE POSITIVE
PRESSURE PRESSURE
Pressure distribution on the surface of a typical wing
LIFTING FORCE ON THE WING
The diagram above should be considered carefully because it explains
clearly how airplane wings overcome the force of gravity when they are
in normal flight. Note that the wind strikes beneath the airfoil (wing).
We can therefore assume that the impact of particles of the air produces
some upward force just as a continuous impact of tennis balls will push
over a board. The magnitude of this upward force is measured by the
manometer tubes which lead from the bottom of the wing. Now refer to the
lower diagram which shows the magnitude of pressures on both surfaces
and you will see that the negative pressure, less than atmospheric pressure,
is very great. This means that the atmospheric pressure acts upward on
the airfoil and exerts more of the total lift than does the positive pressure
caused by the impact of air beneath the wing.
This is one theory which appears to explain winglift. Boys and girls
throughout the world are delving into this phenomena, seeking the truth
and complete understanding of nature's forces which have become so vital
in our struggle for freedom.
WARTIME COURSE IN PHYSICS
ES S -TI A L7-- Weather can be predicted by gathering evi-
CONCEPT- dence concerning atmospheric pressures,
V0 5E temperatures, wind velocities and direction,
humidity, and cloud formations.
Re-study Articles 91, 93,
also the weather map on
page 121.
Also study Aeronautics,
Book 3, pages 43 to 46.
When this manual is published in final form it is to include a reprint
from a government bulletin on meteorology, including illustrations. Suitable
text information is available to each pupil in Aeronautics, Elementary Tech-
nology, Book 3, pages 29, 30, 43, 44, 45, and 46. This text is available free
for pupils who are taking this course. Order from State Department of Ed-
ucation, through the County Superintendent.
ESS S E I ~ A Atmospheric pressure can be utilized for
CONCEPT pumping liquids and gases by a suitable
5F arrangement of levers, pistons, and valves.
Study pages 128 through The mechanics of the lift pump, force pump, centrifugal pump, and the
131. syphon are of great importance. Examine carefully, and have the pupils
draw diagrams explaining the operation of the oil pump and water pump
in your gasoline engine. One of them may be the gear pump illustrated below
How To MAKE A SIMPLE FORCE PUMP FOR CLASSROOM USE
To make a cylinder for the pump, heat the closed end of a 6" x %" test
tube. When the end is beginning to melt blow into the open end, forming
a bulb at the other end. Allow the tube to cool a little and break off the
bulb evenly, smoothing the jagged edges in the flame.
To make the plunger, push the sharpened end of a pencil into a No. 0
rubber stopper. At the bottom of the tube use a No. 2 rubber stopper with
,,o>*. k two holes. Uce a one-hole rubber stopper at the outlet valve.
Each of the two valves are made by cutting a small triangle of sheet
rubber from a toy balloon and pinning it over the hole of a rubber stopper
( ourr with three pins. Water is drawn in between the pins of the intake valve
Outlet
v ive and is forced out between the pins of the outlet valve. Arrange the ap-
paratus as shown in the diagram at left.
GEAR PUMP
Examine the gear pump in your laboratory Dseha a
motcr. This is a force pump. Atmospheric
A simple force pump. pressure or gravity feeds the liquid into the
opening at A. The liquid is carried around in
the space between the gear teeth to area B. O O
Here the teeth come together again and the 0
This type of valve may be liquid is "forced" into the outlet pipe.
whittled from wood and
held by a piece of match
and a string. ,
MECHANICS OF GASES
-E E N4-AL s A body placed in a gas is buoyed up by a
CONCEPT- force equal to the weight of the displaced
S5G gas.
Study pages 132 to 134 SENDING UP A HYDROGEN BALLOON
emphasizing Articles 98 to
99. Answer questions or Have the students bring some used-up flashlight batteries. Crush these
work problems 1-3, pages with a hammer, take out the remnants of the zinc cans, and place them in
133 to 134. a bottle or flask. Dilute some sulphuric acid with an equal part of water,
pouring the acid into the water very slowly. (Caution! Do not pour water
into concentrated acid.) Cover the zinc with the acid and collect the
Hydrogen gas in a penny balloon. See diagram. Tie the balloon with thread
(string is too heavy) and send it up. Theoretically this experiment appears
not to be worth the trouble, but actually it is very stimulating to pupils.
They enjoy attaching a return address to find out where the balloon lands.
With a little variation of the equipment soap bubbles may be blown full
of hydrogen. When floating some distance from the generator they may
be exploded quite dramatically with a torch.
Zino strips and sulphuric
acid will send up a balloon
ESS NIA -L When the temperature remains the same,
CONCE PT_ the volume of a given mass of gas varies
.5H inversely as its pressure.
Study pages 134 to 143.
Emphasize Articles 100,
103, 104; 105, 106.
Notes
'Encil
Compressed
Air
THE POP-GUN
Into one end of the cylinder of the force pump described under essential
Concept 5F, insert a No. 2 solid rubber stopper. Stand it upright on a table
with the stopper resting upon the surface of the table. Insert the plunger
in the other end. Push the plunger down, noticing how the pressure in-
creases as the volume of the enclosed air decreases. Remove the pop-gun
from the table and push the plunger in hard. The rubber stopper will
shoot out with a loud pop.
Tl
WARTIME COURSE IN PHYSICS
Work Problems or answer
questions 1, 3, 5, 6, 9, page
141.
Answer the questions on
pages 14a to 144.
Notes
GAS ENGINE PROBLEM
Make necessary measurements and determine the volume of gas in one
of your gas engine cylinders when the piston is (1) at the bottom of the
down stroke, and (2) at the top of the up-stroke. The volume of the upper
part of the cylinder may be measured if it has an irregular shape by filling
with water and measuring the volume of the water. Assuming there is no
leakage past the valves or the piston rings, what pressure does the gas
exert when the piston is at the top of the up-stroke? (Typical answer: If
the volumes were 60 cu. in. and 12 cu. in. respectively, then (see page 138)
P,1V = P2V2, therefore 14.7 x 60 = P2 x 12, thus P2 = 73.5 lbs. per square
inch).
SUPERCHARGING
(Reprint, page 271, Civil Aeronautics Bulletin No. 28)
The power that an airplane engine develops varies approximately with
the pressure of the air entering the cylinders. The pressure of the atmos-
phere varies at different altitudes. The following table gives the readings
as recorded by a barometer:
Pressure, in pounds
Altitude: per square inch
Sea level..
5,000 feet....
7,000 feet
10,000 feet...
20,000 feet .
12.13
11.25
10.00
An unsupercharged engine that will give its maximum horsepower at
sea level will deliver with constant revolutions per minute only 85 percent
power at an altitude of 5,000 feet, 71 percent at 10,000 feet. 58 percent at
15,000 feet, 47 percent at 20,000 feet, and 38 percent at 25,000 feet. This
variation in power is due primarily to the decrease in atmospheric pressure
with altitude. If an engine at any given altitude is supplied with air of
sea level pressure, providing all other factors are normal, it will again
deliver its original sea level horsepower output. This is termed the critical
altitude of an engine.
MECHANICS OF GASES
Generally speaking the supercharger
used on aircraft engines is a mechanical
device for supplying the engine with a
greater weight of charge than would be
induced normally at the prevailing pres-
sure. Supercharging is employed not only
to maintain sea level power at higher al-
titudes, but to increase the power of an
engine at sea level in order to provide
the necessary take-off and climb-power
output of the engine. Some superchargers
are located between the carburetor and
the intake valve while others create the
higher pressure in the line ahead of the
mixing chamber, as shown in the accom-
panying diagrams.
Before leaving this chapter review the con-
cept of lifting force on an airplane wing.
Refer to Article 68, page
89.
Slow
/310' e-
I V
^ ::'4k
V ^
AIR INTAKE' -
Diagram of Supercharger
Locations.
Perform the demonstrations illustrated in the left column. Have the pupils
tell how Bernoulli's general statement that "where speed is great pressure
is small" explains the action of the ping-pong ball in each of the
demonstrations.
(A) The harder we blow in the funnel the more we decrease the pressure
above the ball.
(B) The glass tubing, connected to a faucet, squirts a fountain of water
that has less pressure than the surrounding air. The ball moves
toward the area of least pressure and this holds it in the column
of water.
Conclusion: In this same manner the airplane wing is lifted by atmospheric
pressure because of the reduced pressure above the wing.
Chapter 6. PROPERTIES OF MATTER
ES SE TIAL When an object is under stress it is resist-
CONCEPT ing a force that tends to do one of the
6A following: (1) pull it apart; (2) crush it
by compression; (3) bend it; (4) shear it, or (5) twist it. The ten-
dency to produce twist is called torque.
Study pages 145 to 149.
Notes
A FLASH CONTEST
Discuss the forces acting upon a large number of objects and decide upon
the kind of stress each is under when in use. A brief test or contest can
then be given. Display 15 or 20 of the following objects. Number each
and have the pupils turn in the answer for each number.
1. Leg of chair you sit in......................... ......... .......Compression
2. Lead in pencil you write with ........... ... ........Bending
3. Shaft that turns in pencil sharpener, door knob, or fan Twist
4. W ire that holds up picture frame.................................. ......Tension
5. Sprocket chain in bicycle....................... .......Tension
6. Shaft in bicycle foot pedal ...................... .Bending
7. Cardboard being cut by scissors .......Shear
8. Wire in spring of spring balance..... Bending
The gas engine in operation:
9. P iston pin ...................... ..... ........ .............
10. Connecting rod ................ .. ..........
11. Crankshaft ............ .. ......
12. B hearings .............. .. ..... ..
13. G ear teeth ........... .. ....... .. ............
14. F an b elt .............. ............... .... .... .. ...... ...
15. Cam shaft ........... ........... ........ .....
16. Wire in valve spring ......
Tools in use:
17. Screw driver ..............
18. Hammer ................................
19. Plumb bob string.........
2 0 D rill ............................. .......... ............ ........ ............................
2 1 C r o w b a r ............................ ... ... ............... ......... ....
2 2 W ed g e ........................................ ......... .... .................
23. Monkey wrench.............................................
24. Rivet or bolt at center of pliers
25. Handle of pliers or shears ..........................
...Shear
.Compression
Twist
Compression
.Bending or Shear
...Tension
...Twist
....Bending
.....Twist
.Compression
.Tension
.Twist
....Bending
.Compression
....Bending
.Shear
...Bending
PROPERTIES OF MATTER
Have a pupil draw black-
board sketches of the
bridges shown at right
and below.
Notes
In the bridge above what kind of stress is acting on
26. T h e steel cable B D ....................................................... ................................T pension
27. The steel girders AB and BC.......................... ..................... Compression
28. The girder beneath the man at E Bending
29. The rivets at A and C.........................................................................Shear
30. T h e riv ets at B .......................... .................. ......................................... S h ear
In this suspension bridge what kind of stress is acting on
31. V ertical w ires..................................... .............................. ..............................T pension
32. The main cable..................................................................................................Tension
33. The base to each tower....................................... ...................................Compression
38 WARTIME COURSE IN PHYSICS
AIRPLANE PROPELLER TORQUE
Especially note that stress acting through a crank or a gear in such a
way that it turns a shaft is known as torque. Torque is the turning effect
or twisting effect of a force. It is the moment of the stress or force.
An airplane flies because of the torque or turning moment which is de-
veloped by the engine and transmitted through the propeller shaft to the
propeller. Note that the torque turns the propeller, and the propeller
creates pull or "thrust" forward. The purpose of the propeller is to change
torque into thrust.
ESSEJ1, IHAAL- Whereas stress is force acting on an object
CONCEPT strain is the extent to which the object
6B yields to the stress by changing shape.
Elasticity is the property of a material which enables it to recover its
original size and shape.
Study from bottom of page
149 to 151.
A
,-
Work all five problems on
page 151. Some pupils
should complete problems
on page 152.
EXPERIMENT TO DETERMINE RELATION OF
STRESS AND STRAIN
Use a door spring and set up an experiment similar to diagram at left
so that several equal weights of some kind suspended by the spring can
be recorded on a measuring stick. As each weight is added the amount
of stretch should be the same and after the weights are removed, the spring
should return to its original form.
Elastic Limit. If the spring returns to original form it is said to be
perfectly elastic. If it does not return and was stretched too far, re-
maining permanently distorted, we have exceeded its elastic limit.
Hook's law states that within the limits of perfect elasticity strains are
proportional to the stress.
Every material has a certain range of perfect elasticity through which
it may be distorted before its elastic limit is reached. It takes a great force
to stretch a steel wire but it cannot be stretched very far without becom-
ing permanently distorted. Its elastic constant is high, but its elastic limit
is low.
Liquids and gases are perfectly elastic. The elastic constant in liquids
is high and in gases low.
Chapter 7. FORCES ACTING AT A POINT
When two or more forces act at a single point we may always consider their combined effect as
that of a single force. This force is called the resultant. The single force which will balance the re-
sultant is called the equilibrant. The resultant and equilibrant are always equal in magnitude but op-
posite in direction.
The process of determining the resultant or equilibrant when two or more forces are known is called
composition of forces. The reverse, or finding two or more forces which have the same effect as a single
known force, is called resolution of forces. Pupils should visualize forces of tension, compression, bend-
ing, shear, and twisting, in simple construction, and should see why some construction is weak and
some is strong. Problems of this kind may be solved by trigonometry or graphically by vector diagrams.
Problems in navigation, solved by vector diagrams, are introduced here.
ESS "S I A t.=I Two or more forces acting at a point can
C ONCE PT always be balanced by a single force.
7A
Study pages 167 to 172
emphasizing Article 127.
Work Problems 2, 4, 7,
page 172; 1, 5, 6, page 186.
Demonstration: Attach a spring balance to each of two fasteners placed
above the blackboard. Tie string to these spring balances and fasten the
string together so that the knot will be on the lower half of the board
when the springs have been pulled out to about half scale readings. Label
these spring balances F, and F2. They
represent the two known forces. Hold-
ing the knot, draw the spring balances
down two or three inches, and mark
the spot on the board with chalk, and
also mark along the strings to the
spring balances. Read each balance
and record the reading on the black-
board. Release the knot. Select some
scale such as 1 inch = 4 ounces and
mark off on the chalk line to each
balance equal to the reading of the
balance on that string. With those
two sides known, complete the par-
allelogram and draw the diagonal from
the knot to the opposite corner. This
represents the resultant. If we measure the length of the resultant and
convert it into weights by using the same scale as the other lines, we can
determine the magnitude of the resultant.
WARTIME COURSE I'N PHYSICS
Notes Check your work by attaching a third spring balance to the knot and
by pulling the balance until the knot comes to the same point as before,
as shown in illustration at right. The strings will follow the chalk lines.
Read the balance. Since the third spring balance represents the equilibrant,
it should be equal to the resultant and should be opposite in direction.
Discussion: From the above experi-
ment we see that a resultant and
equilibrant exist for all combinations
of forces and that they may be cal-
culated graphically. Point out that
there are numerous cases where a force
cannot be measured directly with a
spring balance. In a bridge, for ex-
ample, the weight that will be sup-
ported may be known, but it is im-
possible to place a spring balance in
the supports and measure the force
on each girder. The graphic method
allows engineers to calculate the ap-
proximate strain that will be on each
part of the bridge and to select ma-
terials that will stand this force.
Further Activity: Individual pupils may repeat the experiment at the
blackboard. Have them attach the spring balances at different points so
that the forces will vary from the demonstration made by the teacher. Either
the teacher's demonstration, or one of those done by the student should be
recorded as an experiment in the student's notebook.
ESS IAL- A single force may be resolved into two
CONCEPT or more forces acting in given directions.
7B
Sa Discussion: Go over Article 130 as far as middle of page 174 with the
Study pages 173 to 179.
class. Draw the diagram (shown at left) on the board if necessary. Show
that it is simply the reverse of composition of forces.
Practical Applications: Suppose we wish to hang a five pound sign from
the corner of a building. If we attach it as shown in Fig a on the next page
using a board 4 feet long, with three feet projecting beyond the building, let
us see what forces will be acting. Using the law of moments the stress at B
will be the weight of the sign (5 pounds) times the distance to the first
nail (3 feet) or a total moment of 15 foot pounds. This means that the
second nail, at the other end of the board, has to overcome a force of 15
pounds to keep the sign from falling. Even then, the board is likely to
FORCES ACTING AT A POINT
bend unless a heavy board is used. The force at B is being balanced by
only one force-that of the nail at A.
However, a single force may be resolved into two or more forces. By
adding other supports to this sign (Fig b) we have stronger and more
rigid construction. If we attach a wire as shown, the wire will support
part of the weight, since the wire will be under tension. The board will
now be under compression instead of subject to bending. For this reason
the second nail at A is no longed needed.
If, instead of a wire, we wish to
brace the beam from beneath, the con-
struction would be similar to Fig c
The brace is under compression and
a for this reason the wire will be re-
B placed by a bar or a board.
A-.
7.. Experiments: Set up the apparatus
as shown, having some student hold
the end "A". The spring balance will
show the amount of tension in the
b supporting rope. Compare it with the
weight used. Raise the spring balance
to A' and compare the readings. Re-
ODr ,g peat with the rope at A" and compare
the readings. At which position is the
Apparatus to measure tension
tension least? in a brace wire.
D i To determine the amount of compression in the beam, attach a spring
c RFD
No. balance to the end of the beam and pull outward until the beam just leaves
its support. The spring balance will show the amount of compression. How
do both these forces compare with the amount of force if there were no
bracing at all, as in the first sign? What does this show in regard to the
value of triangular bracing?
Explanation: Triangular bracing increases the number of members sup-
porting a weight and none of the members are subjected to bending. The
triangle is rigid. This greatly increases the strength of the entire construction.
The principle of triangular bracing is used in almost all types of wood
and steel construction. The braces in the fuselage and wing of an air-
plane, in bridge construction, truss of the roof, fence post bracing, shelves
on a wall-all frequently use the triangular construction which provides
great strength and requires relatively less material.
When a member is to be subject to tension, wire is preferred because of
its great tensile strength in relation to weight. For this reason large bridges
use steel cables rather than heavy girders. Girders are used to withstand
compression and bending.
WARTIME COURSE IN PHYSICS
ES S EN IA ~4T
CONCEPT
S7C
Fig. 7-16
See Text page 17!9.
Notes
Forces acting on a gliding airplane may be
shown in a vector diagram and used in the
solution of important problems.
In the preceding concepts we have been dealing with forces which were
fixed as to position. We can now discuss forces that are intended to pro-
duce motion, such as the downward glide of an airplane.
Demonstration and discussion: Place a block of wood on a smooth board
and raise one end of the board. The block will start to slide. We know
that friction tends to hold it still, and that gravity pulls the block toward
the earth. Gravity must have overcome friction. Refer to the diagram on
page 179 (Fig. 7-16). The weight of the car (W) acts toward the earth.
OW is the equilibrant of the forces we are considering. OR being the re-
sultant, must be equal in magnitude and opposite in direction to OW. This
upward force may be resolved into two forces. Force OF acts parallel to
the incline and is caused by friction; the other, OP, acts perpendicular to
the incline and is called upward pressure. It is obvious that since OR re-
mains the same, any change in the angle of the incline will change OF
and OP.
In the diagram at the right the auto-
mobile has been replaced by an airplane
in a glide. The same statements above also
apply to the plane. The weight (Wt.)
acts perpendicular to the earth and is the
equilibrant. The resultant R, equal and op-
posite to the equilibrant. is resolved into
two forces. One, air friction or drag, acts ,
parallel to the incline or gliding angle. The ,s
other is the upward pressure or wing lift ... .... ..
which acts perpendicular to the flight path.
The ratio of these two forces is called the lift/drag ratio. This is fairly
constant for each plane but varies according to different types of construe-
tion of different planes.
The Glide: As lift is at right angles to the flight path, it is easily seen
that gliding angle G = angle G, = G2.
Here we have similar right triangles, whose corresponding sides are
proportional,
Glide Distance Lift
Altitude Drag '
Lift x Altitude
Glide Distance = A
Drag
This means that the glide will be some fraction of the altitude, the frac-
tion being the lift/drag ratio. For instance, if the lift were equal to the
FORCES ACTING AT A POINT
Notes drag, the fraction would have a value of 1, the gliding angle would be 45,
and the distance the plane could glide would be equal to the altitude. But
actually the L/D ratio is greater than 1, and the glide is greater than the
altitude. The greater the ratio, the longer will be the glide. Sail planes
are able to glide for hours in gently-rising air currents because the lift/drag
is large, due to careful streamlining and reduction of drag.
If a commercial plane has L/D ratio of 10, the possible landing distance
in still air from an altitude of two miles would be:
Glide = 10(2 miles) = 20 miles.
Aspect Ratio: Soaring gliders are designed for small drag by careful stream-
lining of the fuselage, and by giving the wings a high aspect ratio (span
to chord). The wings of some gliders have a span 22 times the chord. An
airplane must be of stronger construction to support the weight and thrust
(pull) of a power plant; therefore it is impractical for powered planes to
use a wing with such a large aspect ratio.
In aircraft design, reducing the drag 1 pound cuts the required thrust
of the propeller an equal amount. Thus the most perfectly streamlined
plane can utilize more of its power for speed or for climbing ability, or to
carry greater fuel load to extend its range of flight, or perhaps to carry
a heavier load of passengers, or of bombs. Note the resemblance of the
fuselage of most airplanes to fish, which have been streamlined by nature
through the "survival of the fittest" much as airplanes are being developed
today to survive in the bitter competition of war.
SESS TIA The path of an airplane in flight is the
_CONCEPT resultant of wind drift and forward mo-
7D tion of the plane.
NAVIGATION BY DEAD RECKONING
This is a basic concept for later understanding of navigation by dead
reckoning. It is introduced here because navigation is the consideration of
forces acting at a point-a moving point which may be either a boat or an
airplane. In this chapter the pupils have acquired some skill in the use
of vector diagrams and navigation is an activity in which the vector is a
very valuable tool.
The teacher may find pupils interested in taking time out for discussion
of a few aeronautical problems which involve such factors as wind velocity,
wind drift, wind direction, airspeed, groundspeed, heading, and track.
Wind. We live at the bottom of an ocean of air and wind is the move-
ment of this great mass of air across the face of the earth. This moving
mass called wind exerts pressure on objects that are attached to the earth,
WARTIME COURSE IN PHIIYSICS
Such as an airplane standing still on the airfield, or a kite, but it does not
Scale: 1u = 20 miles
exert a pressure upon an object which soars into the wind itself such as
a balloon or a parachute or an airplane in flight. Such an object "drifts
with the wind." In navigating a plane, however, the effect of wind is the
same as though a constant pressure pushed the airplane off its course be-
cause the course is laid out from town to town on the earth beneath and
not from cloud to cloud in the moving mass of air.
SVelocity. The terms velocity and speed mean the same thing. If an air-
I plane travels 60 miles in 30 minutes it has what speed? (120 miles per
] hour.) If the wind blows 30 miles an hour the mass of air will drift how
I far across the earth's surface in one hour? (30 miles.) If this airplane
S I flew at 120 miles an hour against a wind of 30 miles an hour how far would
4 0 the plane go across the earth's surface in one hour? (120-30 = 90 miles.)
"3q4 If it flew in the same direction the wind was blowing? (150 miles.)
SDrift. If the plane above is pointed in another direction which is ex-
D actly across the wind there would be an angle of 90 degrees between the
DI direction of the wind and the heading of the plane. Of course the plane
L > would drift sideways with respect to the direction in which it is pointed
Because it is in a mass of air that is moving at 90 degrees from the pointing
S of the plane.
S Problem 1. How far forward does the plane described above go in one
hour across this moving mass of air? (Airspeed of plane is 120 miles an
S hour.) How far does the plane drift sideways with the air in one hour?
S (30 miles.) How can we find the distance actually flown and the direc-
S tion of the actual path the plane took over the earth's surface during this
S hour? (By drawing the vector diagram shown at the left, then scaling
m e off the distance and measuring the angle between the line of actual flight
u ^miles
( and the known direction.) Assume that the plane is headed north and the
Wind velocity wind is from the west and find the resultant path and velocity of the plane.
I and direction
n (Answer: see diagram).
Note that in this case the results are the same as though we considered
that the plane flew in still air for one hour and then drifted for one hour
with the wind. Actually the plane did fly in the air mass in the direction
it was pointed for one hour. Meanwhile, for one hour, the air mass was
drifting in the other direction. The path of the plane, called the track, is
the resultant of these two independent movements.
F FORCES ACTING AT A POINT
Problem 2. A bombing plane is flying above your school at an altitude of
20,000 feet in an air mass that is moving from the west at that altitude,
at 40 miles on hour. The plane is heading (pointed) southeast and its air-
speed is 200 miles an hour. Locate on a highway map the position of this
plane 6 minutes later. What is its groundspeed? (Answer: see diagram).
Where would the above plane be 10 minutes after it flew over your school
if the wind were blowing 30 miles an hour from the east?
Vector diagram for
Problem 2
Scale, for one hour's flight,
1 inch = 40 miles
The plane is traveling in the
direction shown by the results
track. In six minutes it travE
one-tenth of the resultant.
mtnN
mis
Notes
Chapter 8. ACCELERATED MOTION
DEMONSTRATION MATERIALS: Marbles (5), medicine dropper, gas engine parts, model airplane propeller.
It is recommended that the text be supplemented here with discussion and problems which apply
to wind velocity in aeronautics and angular velocity of shafts, propellers, and moving parts of motor
vehicles. Acceleration should be clearly conceived as gain or loss of speed, but problems in acceleration
may well be confined to the application of formulas for falling bodies and to simple problems in bomb and
bullet trajectories.
ES S iW I A -L Average velocity (speed) is the distance
ECONCE PT traveled in a given unit of time. The same
S8A velocity may be expressed in many different
ways by using different units of distance and time.
EFFECT OF WIND VELOCITY ON FUEL CONSUMPTION
A certain young pilot made his first cross-country flight in his new air-
plane on a day when no wind was blowing. With a full tank of 30 gallons
of gas he flew due north 90 miles to a friend's house where he turned and
flew home. Two hours after he started from home he landed at his home
airport, with his gas tank empty, and noted that the gas consumption for
cruising the new plane was exactly 15 gallons an hour. Later this pilot
started on the same round trip, but this day the wind was blowing from
the south at 30 miles an hour.
Study pages 187 and 188 Why did the gas supply run out on his second trip before he reached
emphasizing the table on
home? How far from home did the pilot have his forced landing?
page 188.
Answers: Airplanes usually cruise at a constant airspeed and therefore
fuel supply is measured in terms of hours. On the second flight the trip
north took 3/4 of an hour because the airspeed was increased by the tail-
wind to a total of 120 miles an hour for the 90 miles. But on the return
flight the groundspeed was lowered by the headwind to 60 miles an hour
for the 90 miles. This made a total of 21/4 hours for the round trip, but the
Work Problems 1-5 on page ( \
189. ,
ACCELERATED MOTION
tank held only a two-hour supply. The landing, therefore, was 15 minutes
short of the destination, which, in this case, was 15 miles from the airport.
This peculiar effect of wind on fuel conservation can be explained by
considering an extreme case in which, if the wind had blown 90 miles an
hour, the flight north would have been very fast. But then the plane
would not have been able to fly at all against the wind on the homeward
flight. All aviators must realize that in making a round-trip flight, a
constant wind from any direction will slow down the plane more than it
will speed it up and will increase fuel consumption.
ANGULAR VELOCITY
One of the pilot's most important instruments is the tachometer. It
measures the angular velocity of the engine at any moment; the speed at
which the engine is "turning over." Measurement is made in terms of
revolutions per minute (r. p. m.). This measurement indicates the torque
(turning moment) that is applied to the propeller shaft by the engine. Pilots
usually "rev up" their motors just before taking off to make certain that
the motor is developing sufficient power
to lift the plane and its load into the air.
Angular velocity is important in all Pon
machines which transmit power through
a shaft. Gears and belts are used to
change angular velocity and in this way
to either increase the speed of the second
shaft or, by slowing it down, to increase
the power. For instance, in a motor ve-
hicle the rear wheels are driven at a
high angular velocity in high gear, but
if greater power is needed the angular
velocity is decreased by shifting gears. .
A similar situation exists in selecting
the propeller of correct size for a motor
boat or a fan or an airplane. With a
given amount of power at the source, the angular velocity will be greatest
when the propeller has a small diameter and small pitch; but there is one
size which develops maximum thrust or pull through the air. Note that
in the radiator fan of your motor and in any electric fan the air is pushed
away whereas the propeller of a boat or airplane pulls itself through
the medium in which it is rotating. Each type has angular motion but
only one type, the propeller, also has linear motion.
/ J
I
e f
' SS
WARTIME COURSE IN PHYSICS
Suggested activity: Urge some of the pupils to carve a propeller suitable
for a model airplane. Any of the pupils who have constructed a model
can show how the propeller acts just like a screw does in pulling itself
forward as it turns; how the forward movement increases according to
the pitch.
Propeller problem: A typical airplane propeller is about 7 feet in diameter
and has an angular velocity of about 3,000 r.p.m. at top speed in flight.
What is the velocity of the tip of the propeller in feet per second and miles
per hour as it revolves at top speed? (Answer: 1099 feet per second or
749.37 miles per hour.)
Gas engine problems: Pupils who volunteer or are appointed to work
this set of problems should assemble the parts of their engine that are
involved, take such necessary measurements as number of gear teeth and
pulley diameters, and draw simple diagrams showing transmission of
power.
1. If the motor turns over 3.14 times for each turn of the rear wheels when
an automobile is in high gear, and the tires are 26.4 inches in diameter,
what is the angular velocity of the crankshaft in r.p.m. when the car is
traveling 60 miles an hour?
Answer: (60 miles) (5,280 feet) (3.14) 2,400 r.p.m.
Answer: = 2,400 r.p.m.
('/12) (r) (26.4 inches) (60 minutes)
2. How many times will any certain valve be actuated in one second when
the crankshaft turns over at the rate of 2,400 r.p.m.?
: 2,400 r.p.m.
Answer: = 20
60 seconds x 2
Note that each cylinder undergoes this same number of explosions each
second at this rate of speed. The "2" is in the denominator because each
valve is actuated on every other rotation of the crankshaft.
3. At this engine speed what is the angular velocity of the radiator fan in
revolutions per second?
4. How many cubic inches of vapor (air-gas mixture) are being drawn
through the carburetor each minute? Cubic feet?
Answer: Piston Area x Stroke x No. of Cylinders x one-half the r.p.m.
A typical 6-cylinder engine would yield about the following answer:
(1/4) (r) (3.5)" (4) (6) ('/2 2,400) = about 276,480 cubic inches,
or 160 cubic feet of gas and air mixture drawn through the carburetor each
minute.
Note that about 1/11 of this mixture is gasoline vapor and the rest is air
ACCELERATED MOTION
ESS EJlT I A Acceleration is change in speed during a
CONCE P T given unit of time
S8B
Study from page 189 Have the pupils discuss changes in speed that take place when we apply
through Article 141 on page
191. pressure to the automobile accelerator and the brake pedal. Note that
"pick-up" or gain in speed is positive acceleration whereas slowing down
is negative acceleration sometimes called deceleration.
The working of problems involving acceleration frequently creates con-
fusion in the pupil's mind and therefore does not clarify the essential concept.
The statement "feet per second per second" is clearer to some pupils
if it is considered as "feet per second during each second."
The slowing down of an automobile, say from 40 miles an hour to 10
miles an hour during one minute of elapsed time, should be expressed in
terms of acceleration-30 miles per hour per minute. 30 miles per hour =
44 feet per second, so the acceleration is -44 feet per second during each
44
minute. The acceleration in one second is therefore = .73 feet per
second per second.
In language that may seem less scientific, but more practical, we could
say that each second the automobile was slowed down it went forward about
nine inches less than during the preceding second.
If the steps involved in the above discussion are not entirely clear to
the pupils, only the simplest acceleration problems should be undertaken at
this point. The class should not be confused with additional problems on
page 195 but should go immediately into the important concepts which con-
cern falling bodies.
Problems involving falling bodies must be solved by bombardiers and by
gunners in the artillery, anti-aircraft, and naval service.
WARTIME COURSE IN PHYSICS
SESS E r I A L- r All freely falling bodies have the same ac-
CONCEPT celebration, but when objects go through
8C V the air their motion is retarded by the drag
of wind resistance.
Study pages 196 through
199.
--
-. .
Work Problems 1, 2, 3, 5,
page 200
A drop of water becomes
streamlined as it falls, thus
reducing wind resistance.
The pupils must realize that a falling body is rarely a freely falling body.
In some cases acceleration is decreased by wind resistance until the speed
of the falling body becomes constant. This occurs when the force of wind
resistance becomes equal to the force of gravity.
When parachute jumpers delay the opening of their "chutes" they reach a
maximum velocity. When the parachute is opened they are subjected to
a sharp negative acceleration and then drop at a steady rate of about 24
feet per second.
Problem: The impact of landing in a parachute which falls at 24 feet
per second is equivalent to jumping from a wall of what height?
(Answer: 242 = 2 x 32 x S,.'. S = 9 ft.)
QUESTIONS AND ANSWERS
Each of the following objects in motion is in positive acceleration,
negative acceleration, or constant speed. Identify each by the correct
symbol: +, -, or 0.
A dive bomber starting down in a dive
A bicycle starting down a steep grade
A person dropping in a parachute...
An automobile coasting on a level road.
A baseball being thrown .................. .
A baseball approaching the bat...........
A baseball bouncing toward shortstop
..(+)
.....(+ )
...(0 )
.....(- )
.... (+ )
.....(- )
.....(- )
ACCELERATED MOTION
O~t
8. A high fly approaching the center fielder... ()
9. An airplane approaching the top of a zoom .............................(-)
10. A plane falling round-and-round in a spin.... ........ .........(0)
11. A plane with 60-mile-an-hour airspeed traveling against a 50-mile-
an h ou r w in d ...... ....... ... ....... ......... .. .. ... .. ......................... ................. ( 0 )
12. A plane with 50-mile-an-hour airspeed traveling against a 60-mile-
a n -h o u r w in d ... . .................................................................................................................................. ( 0 )
13. The same plane going with the wind. .... ............ (0)
14. A train coasting in to the station on a level track as brakes are
app lied .. .... ........................................... ........... .... ......(- )
15. The above train as the brakes are released (before it stops) .. (-)
16. A pendulum on the upswing ...... .............. . (-)
ES SS i r I A L The force of gravity acts upon a projected
o CONCEPT body with the same force and effect it acts
8D s- upon any falling body.
Study pages 201 and 202. If a bullet is fired horizontally and at the same moment another bullet is
dropped from the gun, the bullets will strike the earth at the same instant
although they may be a long distance apart.
Demonstration: The simple apparatus illustrated below may be used to
Work all 5 problems on show future soldiers why the adjustment of the sites on a rifle barrel is a
page 202, also problems 2, matter of serious importance because the bullet starts dropping the moment
3, 4, and 5 on page 203. it leaves the gun barrel.
itl
Sr
p- t - -.-
When the pivot is struck a sharp blow one marble shoots out horizontally
when the other drops. They hit the floor simultaneously.
WARTIME COURSE IN PHYSICS
RIFLE PROBLEMS
1. The front sight on a rifle and a machine gun is -tationary. Does a rifle-
man raise or lower the rear sight when he decreases the range as he approaches
the target? (Answer: By lowering the rear sight the barrel is pointed down-
ward for a shorter range.)
2. If a bullet dropped 14 inches during the first 200 yards, what fraction of
an inch should the rear sight slide be lowered?
A challenging problem:
If these bombs are dropped two sec-
onds apart, and the bomber is flying
240 miles an hour at an elevation of
10,000 feet, find the following facts,
neglecting wind and wind resistance:
1. How far apart will the bombs land?
(Answer: 704 feet)
2. How long will it take the bombs to
reach their target? (Answer: 25
seconds)
3. If the middle bomb hit the target,
hoow far was the plane from a point
over the target when the bomb w'as
released'? (Answer: 8,800 feet)
4 Draw on the blackboard the trajec-
tory of the bomb by finding the
homnb position at the end of each
fourth second. Use S = gt". and
scale of about 1"= 400 feet. (F,-r
instance, at the end of the fourth
second the bomb has moved
240 x 5.280 x 4 feet
horizontally 60 x 60
and vertically x 32 x 42 feet.)
Discuss the effect of wind resistance
in actual situations and the negative
aeceleration, thii prodi.ees on the hori-
zontal movement of the bomb.
Chapter 9. THREE LAWS OF MOTION
Each of these three laws should mean some very definite things to every pupil. Clear concepts of
the application of these laws are important; memorizing them by number is unimportant. All motion is
in accord with these principles and discloses nature's absolute enforcement of these laws. Your class
may discuss movement observed in the classroom, on the playground, the street, and the school shop; in
the engine, airplane, gun, tank, and warship, with assurance that none of these three laws is ever violated.
Demonstrations should be reviewed in analyzing motion and from this point on the laws of motion
should be referred to by name; not by number. All persons living in our mechanical age need clear, every-
day understanding of cause and effect of motion which involves inertia, centrifugal tendency, centripetal
force, acceleration, the interaction of force and reaction, gravitation as attraction between two bodies,
mass as quantity of matter and weight as a force.
The better students may be led as far as they can go into derivation and use of formulas. Ordinarily,
however, this chapter may be completed in two or three lessons. But do not leave Chapter 10 which follows
until all pupils have acquired useful understanding of each of these principles.
.ESS ESNT I A LN"
CONCEPT
9A
Study pages 204-208.
Prest o!
A72\
No Change!
Every body persists in a state of rest or uni-
form motion in a straight line unless com-
pelled by an outside force to change
that state.
Stimulus: Demonstrate how a vaudeville actor can remove the tablecloth
from a table without disturbing the dishes. Place four or five coins in a
stack on a piece of paper. Pull the paper out from under the coins with a
sudden jerk. The coins will remain in place.
Questions: Use the seven questions on pages 208 and 209 as a basis
for class discussion before considering the following:
1. (a) In making a left turn, why does a pilot raise his right wing and
lower his left wing? (b) What would happen if the pilot used his rudder
without using his ailerons? (Answers: (a) to avoid "skidding." (b) the
plane would skid sideways unless it is banked on a turn by its ailerons.)
2. Why is it not necessary to have flywheels on airplane motors? (Answer:
The propeller provides the momentum of a flyweel.)
S 3. A bulldog was struck on the top of his head by a wooden propeller
turning full speed. Why was the propeller and the engine torn to pieces
although the bulldog was not seriously injured? (Answer: When a splinter
at one end of the propeller flew off, the centrifugal force became greater
for one blade than for the other. The propeller became "unbalanced" and
pounded the shaft bearings to pieces. The propeller continued turning
WARTIME COURSE IN PHYSICS
because of its inertia and flew apart when the shaft stopped turning. Note
that when present-day metal propellers strike objects they bend but do not
break.)
CURVILINEAR MOTION
The Gyroscope. Obtain some kind of gyroscope for pupils to observe
in operation: A top spinner or a top, or at least a spinning coin. Note
that any particle on the edge of the spinning object is kept from moving
30 Left Bank in a straight line at a tangent to the spinning circle because it is held in
,^ place as a part of the object. But note also that although the particle is
Held (by centripetal force) from flying off at a tangent, it turns around
in a circle all parts of which are in the same plane.
Now swing a weight around by a string. All points of the path follow-
ed by the weight are in the same plane. To change this path would require
the action of another force. Unless another force acts upon the revolving
object it will continue to move in the same plane. This tendency to continue
30"Riqhi BdnK revolving in the same plane explains the action of the gyroscope.
This is why huge gyroscopes, revolving at high speed, are effective in
keeping ocean liners on an even keel. The flyweels on steamship engines
revolve in a plane that extends fore-and-aft. In this way the gyroscopic
tendency for the flywheel to continue revolving in the same plane opposes
the rolling of the ship.
Climb
The gyroscopic tendency to continue rotating on the same plane has
been used to provide "stability" in airplanes as well as boats.
THE ARTIFICIAL HORIZON
Pilots are assisted in "blind" flying through fog and clouds and at night
by a gyroscope which is set up to act as an artificial horizon. It maintains
S\e. i F1i ht" a constant horizontal position. The horizon is the aviator's most important
instrument to tell him when the plane is flying level, and when the real
horizon is hidden this instrument takes its place. It is mounted on the
instrument panel.
The artificial horizon consists of a horizontal bar maintained in horizontal
position by an air-driven gyroscope, and includes a tiny silhouette of an
airplane which represents the ship of which it is a part. Therefore it tilts
when the airplane tilts, and appears to dive or climb as the plane goes
G d through these maneuvers. Note in the five illustration at the left how the
Five readings of an artifi- pilot can judge with accuracy the position of his plane by looking at this
cial horizon. instrument.
THREE LAWS OF MOTION
Notes
- E S S E Ai L-AC The acceleration of a given body is propor-
-< 9B tional to the force causing it.
Study pages 209-211. The more force applied to an automobile the faster it will go-the harder
the brakes are applied the more quickly the car will come to a stop.
Work Problems 1, 2, 4, 5,
page 211.
THE DIRECTIONAL GYRO
The "Directional Gyro" used in airplanes can be set on any given course.
It provides the pilot a steady reading even when the plane is tossed about
by gusts of wind or when the plane is banked to make a turn.
A gyroscopic compass is used in all submarines and all large seagoing ships.
The torpedo which is launched by fast PT boats, destroyers, and submarines,
must be controlled accurately if it is to reach its target. To accomplish
this the guiding fins are actuated by a pendulum which keeps it from pitch-
ing, and by two gyroscopes set to control ride roll and to keep the torpedo
traveling in a straight line or in a predetermined path.
Centrifugal Force in Action. Have pupils list many examples of cen-
trifugal force in action. Here are a few:
1. The water pump on most automobile engines
2. Mud flying from an automobile or bicycle tire
3. Skidding on a turn
4. The milk in a cream separator goes to the outside of the revolving blades
because, being heavier than cream, it has the greater centrifugal tendency.
5. The governor on a stationary steam engine in which revolving balls fly
outward as their rate of turn increases.
6. The force that holds water in a pail as it is whirled around and upside
down.
7. The force that holds a pilot in his plane when he makes a "loop."
8. The force that drives the blood downward from the head of a pilot of n
dive bomber as he comes out of his dive. For a moment his head exerts a
heavy pressure on his neck, and he may be momentarily blind.
S .. ..... ............. .. ..... ...................... ........... ..... .......
10.
WARTIME COURSE IN PHYSICS
CONCEPTC -
9C 1
Study pages 212-215.
Work all 7 problems pa
215.
For every action there is an equal and op-
posite reaction.
Demonstration: Place two rulers on a table as shown with enough
between them to roll marbles. Place about four marbles in a row, in coi
ge
1. Roll another marble from one end into
the other end. How far does it go?
2. Try it again rolling the marble slowly.
What happens?
3. Now roll two marbles together into the
row. Why is the same number forced off
the other end?
the row. How many com
( 1 /' i 1M I i' i-i i.ir7
4. If possible, use a large marble, equal
in weight to two of the others. How many
come off? This should bring the students to a realization that it ii
mass as well as the speed that determines the reaction to the applied 1
Chapter 10. POTENTIAL AND KINETIC ENERGY
This is the concluding chapter in the section which discusses the mechanics of simple tools and ma-
chines and universal laws of matter in motion. Emphasis should be placed on paragraphs 161, 164 and
165, in developing clear understandings of potential and kinetic energy. But possibly the most important
concept in the entire course is realization of the fact that we transform energy from one kind to another
but we neither create it nor destroy it. For this reason paragraphs 170 and 171 should be expanded to
include discussion of many applications.
ES TSE r I A L Potential energy isstored energy. It may
CON C E PT be stored as electrical, chemical, or mechan-
1OA ical energy. Potential mechanical energy
of a body is due to its position or state of strain.
Study pages 217 and 218. Problems in the text bring out the concept of potential mechanical energy
k P s 1, 4, ad that is due to position. Discussion is needed to draw mental pictures of
Work Problems 1, 2, 4, and
6 on pages 218 and 219. energy due to strain within the object.
Discussion Questions.
1. What kind of a mechanical condition exists within a bomb as the charge
is expanding due to chemical action just prior to the bursting of the con-
tainer? (Answer: Terrific internal compression, similar in nature to the
compression within the cylinder of your gas engine when the piston is at
the top just following ignition of the gasoline vapor. As combusion takes
place the energy of the vapor is due to its state of strain. Likewise, the
state of strain that exists within a gun barrel at the moment following
explosion of the cap is potential energy. This energy due to strain is
transformed into movement of the bullet, and as the bullet goes high into
the air it acquires potential energy due to position.)
2. When enemy airplanes maneuver about for best position before going
into battle, why does each one try to get higher than the other? (Answer:
Because the one which has the advantage of altitude has the greater potential
energy, due to its position. It can dive and pick up greater speed than
the other plane, and in this way can obtain the most advantageous firing
position.)
WARTIME COURSE IN PHYSICS
ES S E'NTI A Lj Kinetic energy is the capacity that a body
CONCE P T has to do work because of its motion.
10B
Discussion Questions
Study pages 219 through 1. Can potential energy utilize its capacity to do work without bc
221. changed to kinetic energy? (Answer: No, the doing of work invo
motion.)
Work Problems 1-5 and No. 2. Does every moving body have kinetic energy? (Answer: Yes.)
7 on page 222.
3. When a bullet is shot into the air does it increase or decrease its kin
energy as it rises? (Answer: Decreases.) While this is taking place is
potential energy increasing or decreasing? (Answer: Increasing.)
4. Does the revolving flywheel of your gasoline engine have kinetic
potential energy? (Answer: Kinetic.)
'-E$SS TIA HA The impulse which is applied to a body is
CONCEPT the force multiplied by the time it acts.
'C 10C The momentum of a moving body is the
mass multiplied by its velocity. Any gain in momentum is equal to
the magnitude of the impulse that is applied to the body.
Study pages 223 and 224. In nature as well as in man-made machines the momentum of mov
bodies is continually being increased or decreased by the action of outb
force. Here are a few examples of this method of transforming energy f]
Work Problems 1-4 on page
Potential to kinetic and back to potential again:
226.
1. The bough of a tree is bent by the impulse of the wind. The str
within the wood increases, thus storing up potential energy. The moment
of the bough carries it to a point where the strain is greater than the fc
of the wind. Then the momentum is overcome by the strain which exi
an impulse opposite and greater than that of the wind and the bougl
swung back until the momentum of the bough is overcome by the fc
of the wind. Thus it swings back and forth in perfect rhythm.
2. Discuss the pendulum, illustrated in the text on page 224.
3. A dive bomber often approaches its target by flying as close to
ground as possible, to avoid anti-aircraft fire. It rises to an elevation
about 1500 feet just before reaching the target, then dives with full po
on before releasing the bombs? Explain. (Answer: Kinetic energy
consumed by climbing thus increasing the potential energy of altitude
that extremely great kinetic energy could be imparted to the bombs ii
downward direction.)
POTENTIAL AND KINETIC ENERGY
'ES i"rlT A L? Energy can neither be created nor destroyed.
SONC E P
IOD
Study pages 225 and 226.
Work Problem 6 on page
226, and problems 2, 4, 6, 7,
and 8 on page 227.
Discussion Problems
1. Trace the energy changes and the forces that are acting when the potential
chemical energy in an aviator's gasoline tank results in the flight of his
plane. (Answer: Chemical combustion in the engine cylinders, kinetic energy
causes compression on the pistons and connecting rods, torque on the crank-
shaft, forward thrust of propeller, movement of plane, lifting force on wings,
and flight.
2. Trace the energy changes when coal is used to generate electricity, and
the current operate a grinder.
3. Similarly, trace energy changes when your gas engine charges a storage
battery which operates a cigar lighter. Note that this problem can be used
to introduce the next section of the course, Heat.
Chapter 11. HEAT AND EXPANSION
DEMONSTRATION MATERIALS: Centigrade thermometer or Fahrenheit thermometer. small piece of ice, tin
can, piece of wire, object to be used as weight, suitable equipment to heat
wire, gas engine parts, hand air pump.
Molecular Theory of Matter. Throughout the study of heat the pupils should keep in mind the
molecular theory of matter. Review Article 53, page 71, and pages 152-155, with special emphasis on
Article 116. The molecular theory explains to the pupils why heat can be defined as "kinetic energy due
to molecular motion."
The class should observe the three states of matter (solids, liquids, and gases) and discuss what is
taking place when, by application or removal of heat, a substance changes from one state to another.
We observe matter in the solid state and it is not difficult to conceive the molecules as having less kinetic
energy than when the matter passes into the liquid state. Molecules which comprise a liquid are more active
and free to move about within their container. Furthermore, we observe that as matter passes into the
gaseous state there are no bounds whatever unless the gas is confined within a closed container. Matter
becomes gaseous because molecular activity has increased to the state where the molecules have broken
their self-contained bounds and are moving about in space.
We see then, how the application of heat causes matter to progressively pass from solid to liquid to gas.
When such changes occur the matter undergoing the change absorbs heat energy from other matter.
The correctness of this assumption is proved by everyday experience. The evaporation of perspiration
from our bodies keeps us cool in warm weather. We experience discomfort when the molecules of the air
about us, as well as those within our bodies, become too active. The evaporation takes part of the kinetic
energy from the molecules (cools them), and we feel better. Ice makes our beverages more refreshing be-
cause, in melting, the slower moving molecules of the ice lowers the molecular activity in the liquid. We
say that the ice, in melting, absorbed heat from the surrounding liquid.
If heat, as we have said, is kinetic energy due to molecular motion, then complete inactivity of mole-
cules means the absence of all heat. This condition is called "Absolute Zero," and is the lowest temper-
ature which can ever possibly be reached.
As the activity of molecules increases (temperature rises), they require more space. This results in
the need for more space for the total matter which the molecules compose, which means expansion. In
practice, nearly every object will expand when heat is applied. This is a fact which requires consideration
in mechanics. Motors must be kept cool to prevent excessive expansion of pistons within cylinders.
Of interest to the student should be the fact Ihat either directly or indirectly, almost all of our heat
may be traced to the sun as its origin. Energy from the sun was stored centuries ago in the coal and
petroleum oils now used for developing heat. Energy is now being stored in plants and trees some of
which will be used later for fuel. Water which is raised to the clouds and deposited in lakes and behind
dams will be utilized by the ingenuity of man in the form of water power.
Chemical action in the form of combustion releases much of the energy which has been stored by the
sun. Energy also can be transformed into heat by friction-that is, by rubbing or sliding one body against
another. The Indians, with their fire-bows and tinder, used friction to start combustion. We can explain
all of these changes in matter by frequent mental reference to the basic idea of matter being composed of
rapidly moving molecules.
HEAT AND EXPANSION
ESS 'IAL L
CONCEPT
Po 11A ;Y
Study introductory matt
on pages 232, 233, an
Article 189 at end of chat
ter.
Answer question
253.
1, pag
Heat is kinetic energy due to molecular
motion.
er
Id If available, Chapter 18, "The Kinetic Theory of Heat" in From Galileo to
S Cosmic Rays, by H. B. Lemon; University of Chicago Press, will prove inter-
esting reading for both teacher and students, and will probably aid in a more
0e thorough understanding of this concept.
' E A SSE AL Temperature is a measure of the degree of
CONCEPT heat. It is commonly measured by ther-
S1 B mometers which are calibrated to show the
expansion and contraction of liquids due to heat changes.
Study pages 234-236.
Work Problems 2, 3, 8, and
9, page 236.
Note that temperature determines- the direction of fow of heat between
two objects of unequal temperature when placed in contact, and that tem-
perature plays the same part in the flow of heat that pressure does in the
flow of liquids.
Remember that temperature is not a measure of the amount of heat,
but of the degree or intensity of heat in any one place at a given time. A
tub of warm water will melt more ice (hence has more heat) than a burning
match. The temperature of the match while burning is much higher than
that of the water, but the amount of heat in the math is less than that in
the water.
Fahrenheit Centigrade Relationship
C = 5/9 (F 32).
When we solve for F we find that the formula becomes
9C
F= +32
5
Experiment: The freezing point' (0C. or 320F.) may be checked on an
ordinary thermometer by placing the bulb of the therinometer in a can of
finely cracked ice in which there is just enough water to fill the spaces
between the particles of ice. Stir the ice, place the bulb of the thermometer
far enough into the ice to completely cover it, and allow to remain until
there is no further drop in the column of liquid. Mark the point on the ther-
mometer scale and compare with the original point indicated on the scale.
The boiling point (1000 C. or 2120 F.) may be checked also if the ther-
mometer is of sufficient range. Hold the bulb in live steam. Most ordinary
thermometers do not have a range sufficient to indicate the boiling point.
If a thermometer with the freezing point boiling point range is available,
have the students take the measurement between these two points. Each
pupil working independently should prepare a Centigrade scale and a
Fahrenheit scale placing them side by side on the same piece of paper. This
should give a clear picture of the relationship between the two scales.
WARTIME COURSE IN PHYSICS
ES SElT I A Most substances expand when heated and
- C NCEPT contract when cooled.
11C
Study pages 237-244.
Work Problems 1, 6, 7, and
9, pages 240 and 241.
Some students should also
work problem 10.
This wire stops swinging
when heated.
Demonstration: Suspend by a piece of light wire some object heavy enough
to keep the wire taut, so the object suspended will barely miss the table as
it swings back and forth. Now heat the wire by moving a flame up and
down its length. The object should strike the table when swung, due to the
expansion of the wire.
Demonstration: Place a cold piston pin in a piston of your laboratory motor.
Observe how loose it is. Heat the piston pin quite hot and try to replace
it while hot into the same piston. Ordinarily it will not go in until it has
cooled.
Discussion: Expansion of solids must be given careful consideration in
construction work and in designing machinery. It is important to under-
stand the tremendous force that is usually exerted by expanding materials.
Consider these situations:
1. Concrete streets and sidewalks have joints filled with tar. Why?
(Answer: To allow for expansion and contraction of the concrete slabs on
hot and cold days.) Similarly, steel rails will buckle on a hot day unless
allowance is made for expansion.
2. Why do telephone wires sag more on a hot day than on a cold day?
(Answer: On a hot day the wires are longer.)
3. The expansion of aluminum is more than twice that of cast iron or steel.
The cylinder blocks of most engines are of cast iron. Some pistons are made
of iron and some of aluminum. Some pistons have split walls below the
rings. Are these pistons more apt to be iron or aluminum? Why? (Answer:
The split in the aluminum piston allows for expansion.) What is an ad-
vantage in aluminum pistons? (Lightness of weight.) What is a disad-
vantage? (Greater expansion in the piston than in the iron cylinder wall
may cause a hot piston to become tight or "freeze" in the cylinder.
HEAT AND EXPANSION
ESS I AIIAL7r There is a temperature below which it is
CONCEPT impossible to cool any matter. This tem-
11D S> perature is called Absolute Zero and is
approximately -27300. At this temperature all molecular motion
ceases.
Study pages 241-245; also Knowledge of how absolute zero was determined will aid in a better
Article 188. understanding of Charles' law. Over a hundred years ago Charles discovered
that when any gas at 100C. is cooled, it loses 1/273 of its volume for each
degree decrease in temperature. He thought if a gas could be cooled to
-273C. it would have no volume and so nothing would be left. It has
since been found that when a gas has been reduced to a certain temperature
Work Problems 1, 2, page it changes to a liquid and no longer obeys the laws of gases.
246, and 4, page 247.
At -273'C. it is believed there is no molecular activity and that that is the
very lowest possible temperature and therefore the absolute zero.
EESI A TIA L In general, when the pressure is kept con-
CONCEPT stant, the volume of a given mass of gas is
11E very nearly proportional to its absolute
temperature.
Re-study Articles 183 and The above principle is considered in the construction of municipal gas
184, and study Article 185. storage tanks which are built in such a way that the volume of the tank
changes according to the expansion and contraction of the gas. This pro-
duces a constant pressure of the gas in the city mains. If no provision were
Work Problems 3, 6, page .
27. made for expansion, the pressure within the tank would vary during the
247.
day with the change in temperature.
S S ESS r L When the volume of a gas is kept constant,
CONCEPT the pressure of a given mass of gas is very
11F nearly proportional to its absolute temper-
ature.
Study Article 186. Emphasize the example of the automobile tire on page 248. Consider the
fact that increase in temperature within the tire is not due to normal heat
of the road alone, but to friction against the pavement and within the tire
Work Problem 2, page 251. itself as it quickly undergoes compression and flexion. Is there much
danger of blowouts on hot days? Would it not be wise, on a hot day, to
check air-pressure within the tires after having driven several miles?
WARTIME COURSE IN PHYSICS
ESSE iTA LS The relation of volume for a given mass of
C N c E P T:: gas to both pressure and temperature is ex-
S11G pressed by the Gas Equation: PV1l P2Va
T1 T2
Study Article 187, page When gases are put under pressure (confined to a smaller volume) there
248, and review Article is a resulting increase in temperature, and when they are released from pres-
104. sure (allowed to expand to greater volume) there is a decrease in temper-
ature. This principle is applied in mechanical refrigeration. Compressed
gas is allowed to expand and the resulting drop in temperature cools the
Work Problems 4, 7, on
page 252 and 3, page 253. coils of the freezing chamber. The gas is again compressed and is cooled
off by a fan or other device, and used again and again. Being confined
where none of the gas can escape, it can be used indefinitely.
Experiment: Using a bicycle or automobile pump, have members of the
class hold their fingers tightly over the end of the air-Lcse and have someone
else operate the pump. The finger held over the hose will get warm. It has
been observed that with the old hand-pump the hose often gets too hot to
hold when pumping up a tire. The same would not be true of an air hose
at a filling station if the air had been compressed for some time, because it
would have had time to cool off after being compressed.
ESS I A Diesel engines utilize the heat generated by
CONCEPT compression of gas to ignite the fuel.
11H
Refer to Elementary Tech- Engines which operate on the Diesel principle do not require an electrical
nology Book 2, Engines, ignition system. Compare the following with the action of your gasoline
pages 25-31, for discussion engine.
and illustrations of the
Diesel type engine. On the intake stroke pure air, without fuel, is drawn into the cylinder of
the Diesel engine. On the compression stroke the air is compressed to a small
fraction of its original volume. When the piston is near the top of the
compression stroke the fuel is forced through an injection nozzle into the
cylinder and is ignited by the heat of the compressed air. The expansion
of the gases within the cylinder because of the combustion then forces the
piston down.
Diesel engines are used extensively where much power is needed. They
are more efficient than gasoline motors because they operate at a higher
temperature. Diesels are heavier than the ordinary gaa engine, and do not
idle smoothly at slow speed. These are the principal reasons they are not
used extensively in this country as automobile and airplane power plants
They have been widely used in Europe because of their low fuel consumption.
ES SE N IAL"
CONCEPT
O 12A .
Chapter 12. TRANSMISSION OF HEAT
Convection is the transfer of heat by cur-
rents within a liquid or gas. The currents are
caused by changes in density within the
fluid. The density change is due to temperature variation.
Study pages 255-260.
Answer questions
page 261. Some
should also work
6.
1, 3, 7,
students
problem
Study and discuss Fig. 12-
3, 12-4. 12-5, 12-7.
'5= SS EWF
SCCONC EPTV
1 2B
Study pages 261-264.
Discuss questions 1, 2, and
3, page 266, and 7, page
267.
One or both of the experiments shown in Fig. 12-3 should be demonstrated.
In Fig. "b," small tin cans with both ends cut out can be used for ventilators
A and B.
Discussion: Many of our weather conditions depend on convection currents
of air. Heated air rises, creating an area of lower pressure. Cooler air flows
in to take the place of the air which is rising, causing wind. In extreme
conditions violent storms and atmospheric disturbances occur.
A cold front is the movement of relatively cold air across the earth. It
is accompanied by strong convection currents of rising warm air, rain squalls,
and severe atmospheric turbulence which makes flying rough and sometimes
dangerous.
Gliders and birds take advantage of rising currents of air which enable
them to soar without effort as long as the rising current continues.
Questions: 1. What is a circulating heater? (Answer: A jacketed heater
in which a strong convection current is generated between the jacket and
the heater.)
2. What is the usual cause of "bumps" in the air? (Answer: A speeding
plane is lifted quickly as it enters a rising current and is as suddenly lowered
when it leaves the current. This explains the sudden drop which many have
said is caused by air pockets.)
Conduction is the transfer of heat within a
substance, or between substances in contact,
by molecular motion within the objects.
Experiment: If possible, obtain a "tin" drinking cup and an aluminum
drinking or measuring cup. Pour boiling water into both cups, nearly
filling them. Have someone hold to the handles of the cups while the water
is poured in. See which gets hot quicker. It should be possible to hold
to the handle of the tin (actually iron) longer, because the iron is not as
good a conductor as aluminum.
A similar test will disclose whether silverware is solid silver or made of
steel with only a silver plate.
Experiment: Perform the experiment illustrated in Fig. 12-9, page 263.
(Heat should never be applied directly to the bottom of a test-tube full of
water unless you shake the tube to keep the temperature of the water in
the tube uniform. Applying heat to the bottom without shaking will usually
WARTIME COURSE IN PHYSICS
SES SEVT A L--
CONCEPT
1 p 2 27.
Study pages 264-267.
Answer questions 4,
page 267.
6,
result in steam being formed in the bottom and blowing the water out of
the tube. This is further proof of the non-conductivity of water. Convection
is acting on the water, but not rapidly enough to keep it uniformly heated.)
Discussion: Why are most automobiles equipped with water pumps? Auto-
mobiles several years ago were not so equipped. Why did the water circulate
through the motor and radiator?
Air-cooled airplane motors have cooling fins of some heat-conducting
metal projecting from the sides of the cylinders and cylinder-heads. What
is the advantage of this? (The fins conduct the heat from the motor and
expose more surface for transfer of this heat to the air.)
The Davy safety lamp makes use of the good conductivity of copper wire
cloth which encloses the flame. If a miner should enter a mine where there
is an explosive mixture of gas and air with an open flame an explosion
would result, but this is avoided by a Davy lamp. The copper conducts the
heat quickly to all parts of the wire, from which it is radiated, so that no
one part gets hot enough to ignite the gas outside. The gas which passes
through the wire will burn gently, but the flame will not pass through the
mesh of the wire.
Demonstration: Bring a piece of fine-mesh copper wire gauze or copper
wire screen down into the flame of an alcohol or gas burner. As the screen
is lowered notice that the flame does not pass through. If a bunsen burner
and gas are available, the gauze may be held a short distance above the top of
the burner and the gas ignited above the gauze without the flame passing
through to the space between the burner and the gauze. Explain the
illustrations in the left-hand column.
Radiation is the transfer of heat through
inter-molecular space.
Heat reaches the earth from the sun by radiation. Beyond the atmosphere
of the earth there is little matter present that absorbs radiant energy,
and it passes unimpeded until it comes in contact with some form of
matter which will absorb it. Different kinds of matter possess different
9, degrees of ability to absorb the radiant energy. Dark objects usually
absorb the energy and become warm more readily than light objects.
The first stratosphere balloonists realized that it would be cold at a high
altitude and they painted the outside of the gondola black. They found that
the black surface absorbed so much heat that the temperature within Ihe
gondola was around 100F. The next ascent was made without the black
paint and the inside of the gondola was uncomfortably cold. Since then
other ascents have been made with part of the gondola black and part white.
Question: Is it likely that radiation enters in as a factor in keeping an
automobile or airplane engine cool? (Answer: Yes. We can feel the heat
radiated by the automobile radiator by placing a hand in front of it but not in
contact with it.)
Chapter 13. ICE, WATER, AND STEAM
E SSE NTIA L- The amount of heat energy stored in fuel is
ONCEPT measured by measuring the rise in temper-
13A 7 ature of a given quantity of water when the
heat from a given amount of the fuel is applied to the water.
Study pages 269-272.
Work Problems 2, 9, 12, 1
pages 272, 273.
E S iNJiT AL-
`_C0 NC EPT.
Sp 13B -7
Study pages 273-279.
Work Problems 1,
page 279.
2,
V ESSEf 'A L
CONCEPT_
7 13C
Study pages 280-287.
Work Problems 5-9, pag
285; 1, 4, and 5, page 288
The British thermal unit and the gram calorie are defined on page 269 and
should be understood by the pupils. The kilogram calorie sometimes called the
large calorie, is one thousand times as great as the gram calorie. Accurat-
3, measurements of these units can be made only if all of the heat generated
by the fuel is absorbed by the water.
1 B.t.u. = 252 gram calories.
The meaning of specific heat, defined on page 270, should be made clear
as well as the method used in measuring it. This is explained on page 271.
Freezing water expands and in a confined
space it exerts enormous pressure. As ice
melts it absorbs heat energy without a raise
in temperature.
The meaning of heat of fusion (Article 207) should be clearly understood.
When the temperature drops a few degrees below freezing there is always
danger of the water in unprotected waterpipes freezing and bursting the
pipes. Likewise there is danger of freezing water bursting the radiator and
the water-jacket around the block of an automobile engine.
Experiment: Fill a small-sized (half-ounce or ounce) screw-cap medicine
bottle full of water. Screw the cap on tightly allowing no air to remain
in the bottle. Submerge in a mixture of cracked ice and salt until the
water within freezes. Observe what has happened and discuss disadvantages
as well as advantages of this property of freezing water. (See Fig. 13-2,
page 275.)
Increasing the pressure upon a liquid raises
the boiling point; decreasing the pressure
lowers it.
If possible, the experiment on vaporization described in the text on page
S280 should be demonstrated. Instead of using the aspirator for decreasing
the pressure, satisfactory results should be obtained by closing the outlet
e valve as soon as the flame is removed from the flask and, after all boiling
. has stopped, pouring cool water over the flask. This lowers the pressure
by condensing the steam within the flask.
Problems 8 and 9 on page 285 should be used as demonstrations. Students
should understand the meaning of heat of vaporization as explained on page
286.
WARTIME COURSE IN PHYSICS
Carburetor and Wing Icing. Why does ice tend to fc-rm in a carburetor
and on the top of the leading edge of an airplane wing in flight at high
altitude. (Answer: Because cold air is further lowered in temperature by
the reduced pressure in the venturi tube of the carburetor and on the
top of the wing.)
Many airplanes are equipped with special carburetor heaters and de-
icing devices for the wings.
ESSEJ T I A L Evaporation lowers the temperature of the
C o 0 E P T_ liquid from which the evaporation takes
13D y place.
Study pages 288-292. Evaporation takes place when the more rapid-moving molecules of a
liquid break through the surface tension and pass off into free space. These
molecules take heat away from the liquid as they pass off and leave the
Answer questions 1-3, page remaining liquid cooler than before. The more rapidly the evaporation takes
292. place the cooler the liquid becomes.
It would be well to demonstrate the experiment described on the bottom of
page 289 if a small quantity of ether can be obtained from a druggist or
doctor. Gasoline may be used in place of ether and the cooling of the
container observed as air is blown through the tube. The water is not likely
to freeze if gasoline is substituted.
Boiling is actually a cooling process. Pure water under normal conditions
cannot be heated to more than 1000C., no matter how much heat is applied.
After boiling begins, increasing the applied heat only speeds up the escape
of the molecules from the water, which keeps the temperature constant.
Will food cook any faster in water when rapidly boiling than when it is
boiling moderately? (Answer: No, because the temperature is not in-
creased.) Consideration of this fact will result in the conservation of fuel.
ESS ENT lA L Relative humidity is the ratio between the
CON CPT amount of water vapor which is actually
13E present in air and the greatest amount which
the air can hold at the same temperature.
Study pages 292-299. Relative Humidity Demonstration: If the wet-and dry-bulb thermometers
are not available as shown on page 294, a satisfactory substitute can be
Answer questions 2, 3, 6, 8, arranged. Wrap a small amount of gauze or other absorbent material
page 297. around the bulb of a thermometer and tie it with a string. Wet the gauze
with water and fan the wet bulb until the temperature has stopped falling.
Note the reading of this thermometer and also of another one which has
been left dry. Use the table on page 693 to find the relative humidity.
This experiment may be performed if only one thermometer is available
by noting its temperature first, then immediately applying gauze, etc., as
explained above.
ICE, WATER AND STEAM
Dew Point Demonstration: Fill a "tin" can which has a shiny outside sur-
face about two-thirds full of water and place the bulb of a thermometer in
the water. Gradually add small pieces of chipped ice, stirring constantly.
As soon as the surface of the can begins to "cloud" over, indicating the
condensation of moisture, read the thermometer. This reading will be the
dew point.
Emphasize the paragraph beginning at middle of page 295, pointing out
how the last demonstration may be of help to farmers in protecting their
crops in cold weather.
SOME HIGH ALTITUDE FLYING PROBLEMS
Because of extremely low temperatures encountered at high altitudes, high-
altitude flying has many hazards in addition to the formation of ice on the
wing and in the carburetor as previously mentioned. Oil in the motor becomes
very "stiff" and the motor becomes sluggish. The movable controls are apt
to freeze and become motionless. The instruments on the instrument panel
may become useless due to the freezing of the oil with which they have been
lubricated or freezing of moisture which has collected on them.
Chapter 14. MECHANICAL EQUIVALENT OF HEAT: HEAT ENGINES
DEMONSTRATION MATERIALS: An old gasoline engine. It is assumed throughout the course that the
laboratory has been equipped with the major parts of an old gasoline motor,
taken down and cleaned up, and that by this time the pupils are quite
familiar with the functioning of the parts and can now concentrate on the
basic principles involved in the transformation of heat energy into mechan-
ical energy and useful work.
ESS IA One British thermal unit (B.t.u.) of heat
CONCEPT energy in fuel is equivalent to 778 Foot-
14A pounds of mechanical work.
Study pages 301 and 302. Discussion: There should be a broad discussion of fuels in general includ-
ing fuels for heating purposes only, fuels for human consumption and human
energy, and fuels for production of mechanical energy in engines.
Work all problems on page
303. Special Lesson on Gasoline. At least one day should be spent here in discussing
and analyzing one particular fuel-gasoline. Pupils should have clear con-
cepts of those properties of gasoline that are important in its refining,
transportation, storage, and use as a fuel in gasoline engines. Some pupils
should make a parallel report concerning the properties and uses of fuel
oil and alcohol.
ESS TIAL Engines are devices which convert heat
CONCEPT energy into mechanical motion and do use-
14B ful work. Some have internal combustion
and others external combustion.
Study pages 304-323. The steam engine is called an external combustion engine because the fuel
is utilized outside the cylinder in the production of heat energy by com-
bustion. In the gas engine in your laboratory the heat energy is released
Work all problems for this by the fuel after the fuel is vaporized at low temperature and drawn into
chapter, pages 323-325. the cylinder. Diesel-type engines also have internal combustion of the fuel.
A rocket and a gun may be considered as internal combustion engines
because heat energy is generated within the cylinder where mechanical
motion is produced.
SUGGESTIONS FOR THE SECOND SEMESTER
Just as the most important wartime applications in the first semester included engine mechanics, shop
mechanics, and principles of flight, so will the second semester's work include study of the weather, compass
navigation, photography, and radio. Pupils will profit by watching out for current newspaper and magazine
articles in all of these fields, and they deserve credit and commendation for any special reports they may turn
in, especially if accompanied by illustrations and drawings.
Special reports should be geared to each pupil's own special preparation for future service. The personal-
vocational rating sheet on page 9 of General Mechanics, Book I of the Elementary Technology Series, is recom-
mended for use in stimulating exploratory work that will direct each pupil's out-of-school activities toward
future usefulness.
Each of the three booklets in the Elementary Technology Series is available free to Florida teachers, and
each is designed for continuous references to the State-adopted text most closely related to the subject matter.
The Series includes Applications of High School Science and Mathematics in:
Book 1, GENERAL MECHANICS
Book 2, INTERNAL COMBUSTION ENGINES
Book 3, AERONAUTICS
Book 4, in this Series has been included as an integral part of this Wartime Course In Physics and com-
prises the sections about radio and photography. It has not been published separate and apart from the course
in physics.
PROPOSED ADJUSTMENT To INDIVIDUAL NEED
It is suggested that pupils make a selection early in the second semester between radio and photography
as an activity for major emphasis. Ordinarily, unless a pupil has exceptional interest in one or the other, the
more capable should be encouraged to master the principles of radio. Virtually all pupils are within the
ability range of the photography section.
RELATED CLUB ACTIVITIES
Radio and photography are suitable activities for school clubs, and teachers should be alert to the pos-
sibility of having clubs organized. It is often preferable to have the organization leadership come from a
local technician in the profession who can work well with boys and girls. Such activities should be recognized
in a school Victory Corps program, and, if possible, should be affiliated with scouting or local aeronautics
club activities. This entire course may be considered as basic to the school's pre-induction training program.
Chapter 15. MAGNETISM
Pupils should work quite independently on such experiments as are necessary to acquire Concepts
15A and 15B below. Iron filing'T may be obtained from a machine shop or direct from filing a piece of
iron. Magnetized needles stuck in cork and floating on water will prove interesting. At least half the class
should complete the work involving principles of navigation; others can prepare special assignments according
to interests and ability, if the study of use of the compass becomes too difficult.
ESSEQNJTIALii
IAL
CONCEPT
15A
- ESS EJNTIAL
- ONC EPT,?
S15B :-
Like poles repel each cther and unlike poles
attract each other.
There is a magnetic field around a magnet
in which lines of force never cross but
stretch from the magnetic poles in the direc-
tion of attraction and repulsion.
S'TIAL The earth is a permanent, natural magnet,
CONCEPT and navigators find direction by means of
15C y compass magnets- which take the direction
of attraction and repulsion in the earth's magnetic field.
Study the entire chapter
and work all problems.
Notes
USE OF THE COMPASS IN NAVIGATION
If America is to survive and prosper in this air age, aerial navigation
must become more generally understood by the youth who are destined to
do the flying. The magnetic compass is a basic instrument in navigation.
The article which follows is the official explanation of the magnetic compass
as provided air pilots in Practical Air Navigation, Civil Aeronautics Bulletin
No. 24. Every pupil interested in aviation should become acquainted with
the construction of the compass, its function, and the terms involved in its use.
An interesting class experiment would be to actually "swing the ship" as
explained here, using an automobile and a laboratory compass instead of an
airplane unless a plane is available. If the compass is of the ordinary
flat type, it should be placed in the center of a compass rose which registers
direction in degrees. A rose is provided at top of next page.
FOUR STEPS IN FINDING COMPASS HEADING
There are four steps to be considered in finding the point on the instrument
toward which the airplane should be headed before the navigator can be certain
that his plane will follow the path indicated on his map:
First, the compass itself must be checked for error. This "compass
deviation" is found by "swinging the ship" and is recorded as part of the
airplane equipment.
Second, the "magnetic variation" must be known for each location. This
is caused by local disturbance of the earth's magnetic field and by the fact
that the compass needle points to the earth's magnetic poles which are seldom
in line with true north and south.
72 WARTIME COURSE IN PHYSICS
Notes
0t 0
o
S0-0
True compass rose
Third, the navigator must determine the amount of drift caused by side
winds and, in the case of ships, by ocean currents. The drift angle is the
angle between the pointing or heading of the craft and the direction the
craft is actually moving. This was discussed in Essential Concept 7D.
The fourth and final step is merely the use of simple arithmetic or drawing
in which each of the above direction angles are added or subtracted from
the direction shown on the map for the true course that must be taken to
reach the desired destination. What we want is the reading on the instru-
ment when the craft is so headed that it will follow the true course. This
can be found by drawing the various angles on the map in such a way that
they increase or decrease the compass reading according to the amount of
(1) compass deviation, (2) magnetic variation, and (3) angle of drift. (4)
The resulting direction angle from true north will be the "Compass Heading."
This heading will lead the craft over the "track" drawn on the chart.
MAGNETISM 73;
Notes 1 These four steps are explained in full detail in the four sections which
follow.
1. The Magnetic Compass: Swinging Ship.
(By Thoburn C. Lyon, U. S. Coast and Geodetic Survey)*
The magnetic compass is the primary instrument for indicating the direction
of flight. It is designed to indicate magnetic directions by utilizing the
directive force of the earth's magnetic field.
The compass appears in a variety of forms. In the compass illustrated
below the markings on the card are in reverse, the N appearing on the south
side of the card, for convenience in reading when it is mounted in front of
Magnetic compass. Bank and turn indicator.
the pilot. The compass card is suspended in liquid, which serves to damp
out, or minimize, oscillations and to reduce the weight on the pivot.
The earth may be considered as a large magnet, with two magnetic poles
at some little distance from the geographic poles. Along the magnetic
Equator (that is, about halfway between the magnetic poles) the lines of
force of the earth's magnetic field are parallel to the surface of the earth.
As the distance from the Equator increases, the lines of force become more
and more inclined until, at the magnetic poles, they are vertical. These
inclined lines of force may be considered as made up of a horizontal com-
ponent and a vertical component.
The magnetic compass takes its directive force from the horizontal com-
ponent of the earth's magnetic field.. As long as the airplane is kept
horizontal, in straight and level flight, the compass is fairly stable and
*Practical Air Navigation, C. A. A. Bulletin No. 24, 245 pp., 1940, $1.00; includes sample
chart, drift grid, and compass rose. Obtainable from Superintendent of Documents, Wash-
ington, D. C.
WARTIME COURSE IN PHYSICS
Notes reliable; with any appreciable degree of bank, the compass card is affected
by the vertical component, and no longer indicates directions correctly.
When the airplane is turned, the compass may even indicate a turn in the
opposite direction, and may turn completely around before taking up the
correct direction again. For this reason a bank and turn indicator is com-
monly used in conjunction with the compass.
Any turn toward the left or right is indicated by a corresponding deflection
of the hand of the turn indicator. If the turn is properly executed, the steel
ball remains centered in its tube; if the controls are not properly coordinated
for the turn, the ball skids outward from the turn, or falls inward.
During construction the iron and steel parts of the airplane acquire a
certain amount of magnetism. The ignition system and other electric cir-
cuits also may be surrounded by magnetic fields when in operation. These
influences affect the magnetic elements of the compass, with the result that
the card does not indicate the magnetic directions correctly on most headings.
This error is known as the deviation of the compass. It is different, of
course, for each compass installation, for each airplane, and for different
headings of the same airplane.
The compass direction may be in error on any particular heading, but the
error on that heading remains the same, except for changes in the ship's
magnetism with the passage of time or from severe landing shocks. The
important thing is to know the amount of deviation on the various headings,
and to allow for it in navigation. This is accomplished by first compensating
the compass, to make the deviation as small as possible: and then "swinging
ship," to determine the deviation on headings for at least every 300.
Before compensating the compass the following tests should be made:
1. See that the bowl is completely filled with liquid.
2. Check the mounting of the compass card for excessive friction by
causing it to deflect through a small angle, with a magnet, and noting
if it returns freely to its original position.
3. Make sure that the lubber line (reference, or index line) is parallel
with the longitudinal axis of the airplane.
4. See that all tools and other equipment are placed in flying position.
5. Raise the tail of the airplane to flying position and see that the wings
are level.
6. Have the engine running.
At some airports, magnetic stations and compass-testing platforms are
available, which greatly simplifies the problem of determining the correct
magnetic directions. In the absence of such facilities, magnetic directions
must first be determined by reference to a master compass of known deviation;
by determining the direction of true north from observations on the sun
MAGNETISM
Notes or stars, and correcting for the magnetic variation of the place; or by other
available means.
Magnetic variation is the angle between true north and magnetic north
at any given place. In engineering and scientific work it is known as
magnetic declination.
SWINGING THE SHIP
After compensating the compass, the airplane is headed toward magnetic
north and the compass reading noted. The airplane is then turned to
magnetic headings for every 300, completely around the compass-testing
platform, and the compass reading for each heading noted. With these
data, a deviation card similar to the table below is prepared, and fastened
up near the compass to which it applies.
If the compass reading is less than it should be, it is clear that compass
north lies to the east of magnetic north, and the deviation is known as
easterly deviation. If the compass reading is greater than it should be,
the deviation is westerly.
For N 330 300 W 240 210
Steer 3 334 298 270 241 209
For S 150 120 E 60 30
Steer 179 147 122 90 61 31
Typical deviation card.
In swinging ship, as just outlined, the engine should be kept running.
Navigation lights and radio should both be turned on at intervals, if not con-
tinuously, to see if their operation affects the deviation. If the compass
card moves when lights are turned on, the wires are too close to the compass.
The electrical field surrounding the wires may be destroyed by twisting
them tightly together in the form of a twisted pair-being careful, of course,
not to break the connections.
QUESTIONS AND PROBLEMS
1. How is a bank and turn indicator of importance in the use of the
magnetic compass?
2. What is meant by deviation of the compass?
3. Does the deviation of the same compass ever change? Why?
4. Why is it advisable to compensate a compass before "swinging ship?"
5. What is meant by "swinging ship?"
6. Why should the engine be running and the lights and radio be on
while swinging ship
7. How would you swing ship in flight?
WARTIME COURSE IN PHYSICS
Notes
Magnetic variation in the United States, 1935.
navigation, and these instruments, of course, refer all directions to magnetic
north. In most localities magnetic north does not coincide with true north,
chiefly because the earth's magnetic poles are at considerable distances
from the true north and south poles. The angular difference between true
north and magnetic north at any place is known in navigation as the
8. Using a compass with deviations as shown in the table above, what
compass course should be flown in order to make good a magnetic course
of 130 ? 215? 315 ? Assuming there is no magnetic variation at the
place where this is done, mark the courses to be flown on the True compass
rose (See figure, page 72). What is the general direction the plane would
be flying on each of these courses?
9. Explain magnetic variation. (Note that the physics text calls this
declination.)
REVIEW QUESTIONS
10. Why does liquid reduce the weight of the moving parts of the
compass? (Review Essential Concept 4F.) Why does the liquid make
the movement more steady? (Review Essential Concept 10C and apply the
principle of momentum to the liquid.) Why does loss in weight on the pivot
make the compass more sensitive? (Note in Essential Concept 3H that the
amount of friction depends upon the amount of pressure.)
2. Finding the Magnetic Course
(C. A. A. Bulletin No. 24)
The true course is measured with reference to a true meridian printed on
the chart, or true north. However, magnetic compasses are used in air
M A GN ET 1 SM
Notes magnetic variation of the place. It is called westerly variation or easterly
variation, depending upon whether magnetic north lies to the west or to the
east of true north.
The figure, page 76, shows the lines of equal magnetic variation in the
United States for 1935, at intervals of 5. These lines, which are also known as
isogonic lines, are shown on the aeronautical charts for each degree of
variation, and in a few cases for each half degree. A chart of the United
States (No. 3077), size 22 by 28 inches, showing lines of equal magnetic
variation at 10 intervals, may be obtained from the Director, Coast and
Geodetic Survey.
At all points along any given isogonic line, the magnetic variation is the
same in direction and amount. Referring to the foregoing map, it may be
seen that in the northeastern part of the United States the magnetic compass
points west of true north (that is, the variation is westrly); in the southern
and western part of the country the magnetic compass points east of true
north (easterly variation). The dividing line between these two areas of
opposite variation, that is, the line of 00 variation, is known as the agonic
line. At all points along the line the direction of magnetic north and true
north is the same. Minor benls and turns in the isogonic lines are chiefly
the result of local attraction.
When a course is referred to magnetic north rather than true north, it is
known as a magnetic course.
A magnetic course has no importance of its own to a pilot; it is simply
a necessary step in converting a true course to a compass heading, and as
such must have some name for reference. It may be defined further as
the true course plus or minus magnetic variation.
There is no other single item in the whole field of navigation as important
as the proper application of magnetic variation. Ships have been piled on
the rocks, and planes have crashed into the sides of mountains or have
been completely lost because of misapplication of this item.
For our present problem just one rule is necessary, but it should be
learned so thoroughly that a wrong application is impossible. To convert a
true course into a magnetic course, add westerly variation.
In the figure at the left, N represents the true geographic meridian, and
N angle 1 is the true course for the route shown.
letic M represents the direction of magnetic north in the vicinity of O and is
ton west of true north as indicated.
Angle NOM is the magnetic variation, which is westerly.
2! Obviously, when magnetic north lies to the west of true north, the angle
NOM must be added to the true course (angle 1) to obtain the magnetic
course (angle 2), or the magnetic direction of the route
If westerly variation is to be added, easterly variation must be subtracted;
but if we can always remember the rule, add westerly variation, there will
Magnetic variation, never be any danger of an erroneous treatment.
WARTIME COURSE IN PHYSICS
At Portland, Maine, magnetic variation is about
170 west, and the magnetic compass reading is 17
greater than the true for any chosen course.
The application of
specific illustrations:
At Portland, Oregon, magnetic variation is a
220 east, and the magnetic compass reading is
less than the true for any chosen course.
magnetic variation may be further clarified by
Near Portland, Maine, the variation is about 170 west, resulting in
condition shown in the figure above (left). Note that in this case
magnetic compass reading is everywhere 170 greater than the correspon
true direction.
Near Portland, Oregon, the variation is about 220 east, as in the fi
above (right), the magnetic compass reading being 220 less than the
for any chosen course.
3. Finding the Compass Course
(C. A. A. Bulletin No. 24)
When a course is referred to compass north rather than true north
magnetic north, it is known as a compass course.
Like a magnetic course, a compass course has no importance of its
since it would be useful in air navigation only in still air or when the
is parallel to the route. (See Compass Heading, following.) It is sil
another step in the process of finding the compass heading, and may be de:
MAGNETISM
Notes N N
c cc cc
westerly variation westerly variation easterly variation easterly variation
westerly deviation easterly deviation easterly deviation westerly deviation
CC= TC+Var+Dev CC = TC+Var-Dev CC =TC Var-Dev CC = TC-Var+Dev
N = True North TC = True Course
M = Magnetic North Var= Variation
C = Compass North Dev= Deviation
CC = Compass Course
Applying variation and deviation to find the compass course.
further as the true course plus or minus magnetic variation and compass
deviation.
By proper adjustments, deviation on the various headings may be greatly
reduced, but a reduction of the deviation is less important than knowing
exactly the amount of deviation on the respective headings. Some pilots,
when they have reduced deviation errors to a maximum of 2' or 30,
ignore this correction altogether, feeling that the uncertainties and variations
of wind alone are likely to produce greater errors. While this may be satis-
factory under some conditions, it is not good navigation and is not recom-
mended. The fact that some errors must be present in a problem is no
justification for introducing another; in fact, the more uncertainties in-
volved, the greater is the need for accuracy in the other factors, lest the
errors become additive and of excessive magnitude.
The correction for compass deviation is exactly similar to the correction
for magnetic variation, and we need change only one word in our rule:
add westerly deviation.
As with magnetic variation, it is obvious that if westerly deviation is to be
added, easterly deviation must be subtracted.
The figures above illustrate the conversion of the true course for different
conditions of variation and deviation.
WARTIME COURSE IN PHYSICS
Review Essential Concept
7D, Navigation by Dead
Reckoning.
Notes
4. Finding the Compass Heading
(C. A. A. Bulletin No. 24)
The compass course is the direction by compass in which an airplane
should be headed in order to reach its destination in still air, or with the
wind parallel to the course; it also was defined as the true course plus or
minus variation and deviation, but with no allowance for wind. In practice,
however, the same term is often applied to the heading of the airplane after
due allowance has been made for wind.
To avoid any confusion at this point, the use of two separate and distinctive
terms is very desirable, and the following formal definitions are given:
Compass course: The true course plus or minus variation and deviation,
but without allowance for wind effect.
Compass heading: The true course plus or minus variation and deviation,
and including allowance for wind; the direction by compass in which the
airplane is pointed.
/
N
M
angle NOM
G
angle MOC
angle 1
angle 2
= True North (geographic meridian)
= Magnetic North
= Magnetic variation (westerly)
= Compass North
=Compass deviation on this heading (westerly)
= True Course
= Magnetic Course
angle 3 = Compass Course
angle 4 = Compass Heading
AB = Track (or intended track)
Graphic definition of terms used in dead reckoning.
M AG NET I SM
Notes QUESTIONS AND PROBLEMS
1. Define magnetic variation.
2. Name some of the causes of compass deviation.
3. The magnetic course is often printed on a chart. Why is the compass
course never given?
4. Distinguish between magnetic course and compass course.
5. Determine the compass heading in each case from the following data,
assuming no wind is blowing or that there is either a headwind or a
tailwind:
(1) (2) (3) (4)
True course 70 3300 1650 400
Variation 70W 170E 40E 120E
Deviation 3E 30E 50W 20E
6. Review Essential Concept 7D and find the compass headings for the
situations shown in Problem 5 above, if the wind correction angle is (1)
8 with wind from right, and (2) 15 with wind from left.
7. Determine the true course in each case from the following data in
which the letters L or R after the drift angle indicate that the airplane is
being drifted toward the left or right respectively:
(1) (2) (3) (4)
Compass heading 140 240 350 900
Deviation 10E 30W 20W lW
Variation 100E 130E 9W 60E
100R 80L 120L 20L
Drift angle
Chapter 16. ELECTRICITY AT REST
Assign the entire chapter for reading, but limit discussion to sections 264, 265, 266, 269, 270, 273, 274, 279.
Schools with elaborate equipment may wish to give a number of demonstrations, but those with almost
no equipment will find that two or three hard rubber or bakelite combs, two glass rods, a piece of wool
and a piece of silk will be sufficient for the demonstrations below.
All pieces of equipment must be thoroughly dry before use, and results will be best if they can be dem-
onstrated on a cool dry day. On moist days the experiment will be a failure because the charge will be
removed by the air as rapidly as it is produced.
SE S SS nr A AL-- Electrification may be produced by friction.
CONCEPT_
16A
Study pages 346-348. Demonstration: Rub a comb with a piece of wool and bring it close to a
small piece of tissue paper. The paper will be attracted. Do the same with
a piece of glass rubbed with silk. The paper will be attracted but not as
strongly. Passing the comb through the hair will also produce the same
effect.
E S S ENT I A L Electricity is of two kinds, positive and
ONCEPT_ negative. Like charges repel and unlike
16B charges attract.
Study pages 348-351. Demonstration: Electrify a comb by rubbing with wool and suspend it by
a piece of silk thread so that it is free to turn. Electrify a second comb
and bring it close to the first. The suspended comb will be repelled. Two
Answer questions 1, 4, 7, 8, pieces of glass will do the same. A suspended electrified comb will, however,
page 351. be attracted to a piece of glass that has been rubbed with silk. This shows
that the type of electrification produced by rubbing gliss with silk differs
from that produced by rubbing rubber with wool. The former was named
positive (+) and the latter negative (-) by Benjamin Franklin and the
names have remained in use to the present day.
ES S IAL A body is negatively or positively charged
o- CONCEPTL depending on whether it contains more or
16C less electrons than normal.
Study pages 351-366. Discussion: After discussing the sections assigned at the left, bring out
the idea that all matter has a certain number of electrons. If this number
is increased, the substance will have more negative charges than positive,
Answer questions 1, 3, 4, 5, hence it will be negatively charged. One theory of static electricity is that
13, page 367. the electrons are rubbed off the glass rod on to the silk. Also electrons are
rubbed off the wool onto the hard rubber comb. This means that some
substances lose electrons more easily than others. Those substances which
lose electrons very easily are called conductors, and are, in general, metals.
Substances which do not lose electrons easily are called non-conductors,
insulators, or dielectrics. It must be realized, however, that even dielectrics
differ in their ease of losing electrons. Emphasize that positive (-) charges
are due to loss of electrons, rather than to a gain of any sort of positive
electricity.
Chapter 17. ELECTRIC CURRENTS AND CIRCUITS
It is expected that each school will secure as minimum equipment for this chapter a small roll of
insulated copper wire, two (preferably three) dry cells, and a door-bell or other similar appliance which
can be operated by use of the cells.
Especially fortunate are the schools already equipped with an ammeter, a voltmeter, and a resistance
box or other types of known resistances, since many demonstrations can be performed with their use which
cannot be done without them. These demonstrations aid in understanding electrical measurements involved
in Ohm's Law.
Some schools which do not have or are unable to secure equipment for the experiments involving
measurements of electrical units can probably get a local radio repair man to give an hour of his time to
the class. He would be glad to know that he was giving his time and the use of his instruments in helping
train boys and girls for their part in the war and the peace that is to follow.
If a radio repair man is not available a local automobile mechanic may have suitable instruments, or it
may be possible to purchase a cheap combination voltmeter-ammeter from the dime-store for fifty cents or
less. The combination instrument is not as satisfactory as separate instruments since voltages and amper-
ages cannot be read simultaneously in the same circuit. Fairly satisfactory results can be obtained,
however.
ESS IAL When an electric current can be made to
CONCEPT flow between two bodies a potential differ-
17A ence is said to exist between the two bodies.
Potential difference, electromotive force (E.M.F. or E.), and voltage
are synonymous terms.
Study pages 368-369.
ESSET IAL
CONCEPT
17B
Study pages 369-370.
There are some advantages, perhaps, in comparing electric currents and
water currents (more thoroughly considered in Article 286), but there are
several ways in which the analogy does not thoroughly hold. Care should
be exercised not to get erroneous ideas through use of this analogy.
Potential difference can be created by
chemical action.
Experiment: If materials are available, build the simple electric cell illus-
trated on page 369. Place a strip of copper and a strip of zinc in a solution
of dilute sulphuric acid (about 20 parts of water to 1 part acid. Be sure
and pour the acid into the water-not the water into the acid.) Attach
wires from the metal strips to an electric bell, flashlight bulb, or other low-
voltage object, and observe that electrical energy is obtained from the cell.
After a time it can be observed that the zinc strip is going into solution
due to the chemical action of the acid upon it.
WARTIME COURSE IN PHYSICS
Vinegar can be substituted for the diluted sulphuric acid, but will not be
as effective. The outside metal covering of flashlight batteries or other dry
cells is zinc and can be used for the zinc strip.
A very simple cell can be made by inserting a zinc strip and a copper
strip in slits cut into opposite sides of a lemon. The amount of electrical
energy obtained from such a cell is very small, but a "tingling" sensation
may be noticed if the tip of the tongue is touched to the ends of the two
strips simultaneously. More definite results will be noticed if wires leading
from the two strips are touched to the wire tips of radio head-phones or a
BrS f telephone receiver, because a click can be heard in the phones each time
Brass /I Copper
1 ithe tips are touched by the wires.
Lemon
A cell.
--E SS e T IAL An electric current consists of a stream of
Co N C E P T electrons moving from a negatively-charged
17C body to a positively-charged one, or between
two bodies with different degrees of electronic charge.
Study Article 284. It should be emphasized here that the conventional definition of the
direction of flow of current is opposite to their actual flow of electrons. This
is apt to cause some confusion in the minds of the pupils. It should be
explained to them that the conventional definition is the result of an effort
on the part of Benjamin Franklin in his early experiments to explain various
electrical phenomena, and it was only after the definition had been widely
accepted and much material written on it that the true nature of the flow
of electrons was discovered.
-ES S NTIA I- A steady electric current will not flow un-
ONCEP T less there is a complete conducting path, or
17D v "closed" circuit.
Study Articles 285 and 286, It is pointed out in the text that there is both an "external" and an "in-
page 371. ternal" circuit, and that the current travels through both circuits. If a
break is made in either circuit the current ceases to flow.
ELECTRIC CURRENTS AND CIRCUITS
SE SS SENjT I A L- Two factors control the amount of electric
_CONCEPT.P current flowing in a circuit. They are
<. 17E potential difference and resistance. The
relationship between current, potential difference, and resistance is
expressed in Ohm's Law, which may be stated thus: In a given
circuit the current equals the voltage divided by the resistance.
Study pages 372-379.
Work Problems 1, 3, 4, 6,
9, pages 379-380.
Mastery of Ohm's Law is
very important.
ESS E IAL
CONCEPT
S17F
Emphasize Article 288.
Unknown Current
S -- ReSi Known
SResistance
E
I-
R
SESS SjTIA L
CONCEPT
17G
Ohm's Law is commonly stated in equation form as follows:
E
I-=
R
where I is the current in amperes, E is the potential difference in volts, and
R is the resistance in ohms. The above equation can be solved for E and for
R in terms of the other terms. We derive
E = IR (Volts = Amperes x Ohms), and
E
R = (Ohms = Volts Amperes).
R -t-
The ampere is the unit used to measure the
rate of flow of electricity, or the number of
electrons per second.
When the resistance and the voltage are known, the current can be calculated
by use of the formula,
E
I-
R
In the figure at left the potential difference across the coil of known resistance
should be measured by a voltmeter in the manner shown.
The ohm is the unit used to measure
resistance to the flow of electricity.
Emphasize Article 289.
Unknown
cDr Resstaonce
Amps Volts
rk 'IN
When the voltage across a piece of apparatus and also the current in a
circuit are known, the resistance can be calculated by use of the formula,
E
R-
The vote and the amerae should be measured in the manner shown at left.
'Hie voltage and the amperage should be measured in the manner shown at left.
E
R-
I
WARTIME COURSE IN PHYSICS
ESSE Nr IAL
CONCEPT
17H
Emphasize Article 290.
HKnpwn
Copper II inc Re.Jstanc
Amps
Unknown
yo I tage
E = IR
CONCEPT
17J
Study pages 380-386.
Work Problems 1, 2, 3,
pages 386, 387.
Testing Maderial
for Resis tance
The volt is the unit used to measure poten-
tial difference, or the force which causes a
current to flow.
When the resistance in a circuit and the amount of current flowing
through it are both known, the voltage can be calculated by using the
formula E = IR. The current should be measured in the manner shown at
left.
If an ammeter, a voltmeter, some known resistances and some dry cells are
available, demonstrations should be prepared showing the relationship be-
tween these units. (Read the last paragraph on page 381 and study Figs.
17-6 and 17-7, as well as those above.) Practical problems should be worked
in which two units are measured with the aid of the instruments and the
third unit calculated.
The resistance of a wire depends on the
material, the length, the cross-section and
the temperature.
Where electrical energy is to be conducted from one place to another
to run motors, burn lights, etc., a conductor with the least possible resistance
S is desired in order that no electrical energy be lost. For filaments in
electric lights, heating elements in toasters, electric irons, etc., conductors
with a great deal of resistance are required in order that the current heat
the wires. This offers some explanation as to why large copper wires are
used for power lines and fine tungsten wires are used for filaments in light
bulbs.
There is a very important practical point on which students are likely to
go astray. They are apt to get the idea: "great resistance, great heating,"
and this is true only in a relative sense, as between parts of a series circuit.
The heat developed is proportional to the square of the current which actually
gets through, times the resistance. (Power = 12R). Since power varies as the
square of the current, and only directly as the resistance, the current magni-
tude is the more influential of the two factors.
A 100-watt lamp uses more current, and develops more light and heat, than
a 50-watt lamp because it has less, not more, resistance than the 50-watt lamp.
If we connected wires from our regular lighting circuit to each end of a
perfectly dry board, there would be practically no current flowing, and hence
no heating effect, although the resistance of the board is almost infinitely great.
It is true that an electric are has a high resistance and produces a very high
temperature. This is not due, however, to the high resistance per se, but
to the concentration of resistance at a single point, thus limiting heat develop-
ment to a very small area and producing a high temperature.
The resistance of different kinds and sizes of conductors can be roughly
compared by inserting the resistances in an electric bell or electric light
circuit (laboratory circuits-not 110-volt house circuits), and comparing
the intensity of the sound or the light after the resistances are inserted
with the intensity before they were inserted.
ELECTRIC CURRENTS AND CIRCUITS
ESSE TJ IALj Electrical apparatus or resistances may be
CONCEPT _~ connected in a circuit in series, in parallel,
S17K -; or in combinations of the two. The choice
is determined by the electrical values desired in the circuit or its parts.
Study pages 387-392.
Emphasize all material in
black print and in italics.
Some extra time may be
necessary on this section of
the book.
This section of electricity is very important, since it has so many appli-
cations in practically all branches of electrical work. It is especially im-
portant in radio. Various arrangements of resistors should be experimented
with if instruments for measurement are available. Students should keep
notes on the results obtained and compare the readings on the instruments
with calculated results.
SESS I A Cells and direct current generators may be
CON'~EPT- arranged in series, in parallel, or in com-
17L binations of the two. The choice is de-
termined by the voltage and amperage desired, and the internal and
external resistances of the circuit.
Study pages 393-396.
Work Problems 1, 2, page
396.
Study pages 396-403 with
emphasis on polarization
(Article 306) and voltage
drop in a line (Article
308).
Various arrangements of cells should also be experimented with if instru-
ments for measurement are available. As suggested above, notes should
be kept and observed readings compared with calculated results.
Chapter 18. EFFECTS OF ELECTRIC CURRENT
E ~I I EPTAL An electric current causes magnetism.
S 1 `18A
Study pages 407-414. Demonstration: 1. Place a compass close to a wire, the ends of which are
connected to the poles of one dry cell. The compass needle will be deflected.
Work Problems 1, 2, 4, Caution: Do not leave the wire attached to the cell except for the instant
page 417. the deflection is to be seen, otherwise the battery will be quickly exhausted.
2. Form the wire into a coil and again notice the deflection. Where is
it greatest, at the ends of the coil or in the center? (Ends.) Which end
of the needle is attracted to the ends of the coil? (Use the thumb rule
shown in italics on page 411.)
e/ 3. Place a large nail or spike in the coil, and again observe the deflection.
Is it greater or less than before? (Greater.) Increase the number of turns
Compass of wire. The deflection of the needle will be greater.
Discussion: From the above experiments the students should realize that
an electric current produces magnetism; that this magnetism is stronger
if the wire is in the form of a coil so that there will be more wire in a smaller
space with the current going the same way, hence the lines of force will be
more concentrated; and that an iron core will concentrate the magnetism
ry even more.
Cc/l
SPractical Applications: The electro-magnet is used in so many ways that
D S the opportunity for finding applications is almost endless. Each student
Corpass should trace the electrical circuit of an ordinary bell and be able to show
why it rings continuously rather than give a single stroke. If a bell is
available, let them use that, otherwise use the diagram on page 412.
Bell
Some students may wish to build a simple telegraph. The key may be
made of a strip of "tin" bent to the shape shown, with a tack and a bolt
Switch as contact points. The sounder may be built of a nail, coil of wire, small
spring, and three or four strips cut from an old tin can. The sketches below
give some idea of the way it can be built. Individual pupils will find
ZDry lr) numerous changes and modifications.
Ce/I/ Cell
The wiring diagram is easily figured out. The number of dry cells will
Electric Bell Circuit vary according to the distance between stations.
Cork '
7j Strip Common Magnet Wire e
kly Sounder n No
key Sounder
EFFECTS OF ELECTRIC CURRENT
ESS
CONCEPT_
1 8B ;
Study pages 418-428.
Testing conductivity
solutions.
ESS E.JTIAL
S CONCEPT
18C
Study pages 429-443.
An electric current will produce chemical
action.
Experiment: 1. Set up the apparatus shown on page 418, Fig. 18-20. The
bulb should be of about 20 watts. The wires which go into the solution
may be only bare copper wire well taped to prevent aiy danger from con-
tact except at the end. Preferably they should be held in some kind of
ret holder. Use the solutions suggested for testing and determine which will
'"P conduct the current.
2. Using the wires from the previous experiment, set up the apparatus as
shown on page 420, Fig. 18-22. This should be connected to two dry cells
for a source of current. Since the previous experiment has shown that
of water is a relatively poor conductor of current it is well to add a little salt
or acid to the water to conduct the current. From this we see that an electric
current will separate some substances into their elements. Similar apparatus
is used to separate sodium and chlorine from salt, and to get copper and
other metals from solution.
An electric current will produce heat.
Demonstrations: 1. Secure an old electric iron or toaster and show the
heating element.
2. Secure an Edison base fuse of five or ten amp rating, screw it into a
light socket, and turn on the current. The fuse "blows." Show that in reality
the wire in the fuse melts. Discuss the reason for fuses, and how the fuse
protects the wiring in a house.
Discussion: We may omit sections 334, 335, 336, 337, 338, except the follow-
ing information:
Electric power is measured in watts.
Watts = amperes x volts.
The electric meter in homes measures the number of kilowatts of current
used. (1 kw. = 1000 watts.)
Demonstrations: Bring in a number of electrical appliances, toasters,
irons, vacuum cleaners, coffee makers, etc. If it is not feasible to bring in
the appliances, have the students copy the data from the name plate on
the machine. How many watts does each use? What will be the cost
of running each appliance for one hour? Discuss local rates.
WARTIME COURSE IN PHYSICS
Work additional problems
of this type based on appli-
ances used in each pupil's
home.
Work Problems 2, 3, page
443-444.
Problems: 1. If an electric iron is rated at 500 watts, what is the cos
running the iron for one hour if the current sells for ten cents a kilo1
hour?
500 watts x 1 hour x 10 cents
1000= 5 cents.
1000
Point out that the number of appliances that can be used on one circu
limited by the size of the fuse and the number of watts that each appli.
uses.
2. If a particular home circuit is protected by a fifteen ampere fuse, i
is the maximum number of watts that can be used?
15 amps x 110 volts = 1650 watts.
3. Could an electric iron (500 watts), a coffee maker
bulbs (100 watts each) and a small radio (25 watts)
circuit at one time safely?
(350 watts), six I
be used on the al
Iron 500
Coffee maker 350
Lights 600
Radio 25
1475 watts.
Since the circuit will take 1650 watts, the appliances may be used sa
Electric Lighting
Use the material in the text for study and discussion.
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