If the body starts from rest, its final velocity v and the distance S are related by v=

√2aS.

For freely falling and freely rising bodies the acceleration is designated by g (= 980 cm. per second each second = 32.16 ft. per second each second).

The total distance traversed always equals AVERAGE VELOCITY times the TIME.

Any projectile falls away from its original path in accordance with the laws of freely falling bodies.

An airplane is supported by the vertical component of the force with which rushing air acts upon its surfaces.

QUESTIONS AND PROBLEMS

1. One boy says a whole brick will fall twice as fast as half a brick because the earth pulls twice as much upon it; a second boy says it will fall half as fast because it is twice as hard to set in motion. What is the truth? Give reasons. Try it.

2. a. A boat slid down a shoot-the-chutes, traversing 4 ft. the first second. Without the use of formulas tell the answers to the following: (1) How far did the boat slide in 2 sec.? 3 sec.? 4 sec.? 5 sec.? (2) How far did it go during the fifth second? (3) What was the acceleration in ft./sec.2 (feet per second each second)? (4) What was the velocity at the close of the fifth second? (5) What was the average velocity during the first five seconds? b. Using this average velocity, how far did the boat slide in 5 sec.? Does this answer agree with your answer to the last part of (1)? c. Using the velocities at the beginning and at the end of the fifth second, find the average velocity during the fifth second. Knowing this average, state the distance traversed during the fifth second. Does this agree with your answer to (2)?

3. An automobile starting from rest acquired a velocity of 10 mi./hr. (miles per hour) in 5 sec. Assuming the acceleration to be uniform, what was it in mi./hr./sec. (miles per hour per second)? in mi./min./sec.? in ft./min./sec.? in ft./sec./sec.?

4. A ball thrown across the ice started with a velocity of 80 ft./sec. It was retarded by friction at the rate of 2 ft./sec.2 For how many seconds did it roll? What was its average velocity during this time? On the basis of average velocity, how far did it go? By the use of Sat 2, how far did it go?

5. A skater on reaching a speed of 60 ft./sec. began gliding and came to rest after traversing 600 ft. Find his average velocity during the glide, the time required to traverse the 600 ft., and the acceleration.

6. A bullet was fired with a velocity of 2400 ft./sec. from a rifle having a barrel 2 ft. long. Find (1) the average velocity of the bullet while moving the length of the barrel, (2) the time required to move through the barrel, and (3) the acceleration of the bullet while in the barrel.

7. A boy dropped a stone from a bridge and noticed that it struck the water in just 3 sec. How fast was it going when it struck? What was its average velocity during the 3 sec.? With this average velocity, how far must it have fallen in the 3 sec.? (Take g = 32 ft./sec.2 and as 9.8 m./sec.2 and solve the problem in both English and metric units.)

8. (1) How much additional velocity will the pull of the earth impart each second to a freely falling body? What velocity will it take away each second from a freely rising body? (2) A bullet is fired vertically upward with a velocity of 2400 ft./sec. Assuming no air resistance, find (a) how long it will take the pull of the earth to bring the bullet to rest, (b) the average velocity during the ascent, (c) the height to which the bullet rises, using average velocity and time of ascent, and (d) the height of ascent, using Sgt. (Take g= 32 ft./sec.2)

9. How far will a body fall from rest during the first half second?

10. A baseball was thrown vertically into the air with a velocity of 160 ft./sec. How many seconds did it remain in the air? (Take g= 32 ft. /sec.2)

11. A baseball was thrown upward. It remained in the air for 6 sec. With what velocity did it leave the hand? How high did it go? (Take g= 32 ft./sec.2)

12. With what velocity must a ball be shot upward to rise to the height of the Washington Monument (555 ft.)? How long before it will return? (Take g = 32 ft./sec.2)

13. A ball was batted horizontally with a velocity of 100 ft./sec. from the top of a tower 144 ft. high. Plot its path on the way to the ground, assuming no air resistance.

NEWTON'S LAWS OF MOTION

101. First law: inertia. It is a matter of everyday observation that bodies in a moving train tend to move toward the forward end when the train stops and toward the rear end : when the train starts; that is, bodies in motion tend to keep on moving, and bodies at rest to remain at rest.

Again, a block will go farther when driven with a given blow along a surface of glare ice than when knocked along an asphalt pavement. The reason which everyone will assign for this is that there is more friction between the block and the asphalt than between the block and the ice. But when would the body stop if there were no friction at all?

Astronomical observations furnish the most convincing answer to this question, for we cannot detect any retardation at all in the motions of the planets as they swing round the sun through empty space.

Furthermore, since mud flies off tangentially from a rotating automobile wheel, or water from a whirling grindstone, and since, too, we have to lean inward to prevent ourselves from falling outward in going round a curve, it appears that bodies in motion tend to maintain not only the amount of their motion but also the direction (see gyrocompass opposite page 239).

In view of observations of this sort Sir Isaac Newton in 1686 formulated the following statement and called it the first law of motion:

Every body continues in its state of rest or of uniform motion in a straight line unless impelled by external force to change that

state.

This property, which all matter possesses, of resisting any attempt to start it if at rest, to stop it if in motion, or in any way to change either the direction or the amount of its motion, is called inertia.

102. Centrifugal and centripetal force. It is inertia alone which prevents the planets from falling into the sun, which

The milk is poured into a central tube (see (1) a) at the top of a nest of disks (see (1) and (4)) situated within a steel bowl. The milk passes to the bottom of the central tube, then rises through three series of holes (see (1) b, b, b, etc.) in the nest of disks, and spreads outward into thin sheets between the slightly separated disks. By means of a system of gears (see (3)) the disks and bowl are made to revolve from 6000 to 8000 revolutions per minute. The separation of cream from skim milk is quickly effected in these thin sheets; the heavier skim milk (water, casein, and sugar) is thrown outward by centrifugal force against the under surfaces of the bowl disks (see (5)), then passes downward and outward along these under surfaces to the periphery of the bowl (see (1) d, d, d, etc.), and finally rises to the skim-milk outlet. The lighter cream is thereby at the same time displaced inward and upward along the upper surfaces of the bowl disks (see (5)), then passes over the inner edges of the disks to slots (see (1) c, c, c, etc.) on the outside of the central tube, finally rising to the cream outlet, which is above the outlet for the skim milk (see (1) and (2))