8. Would an electric fan in motion on the rear of a light boat move it?

Would it move the boat if revolving under water? Explain.

9. What turns a rotary lawn sprinkler?

10. Why, when you are standing erect against a wall and a coin is placed between your feet, can you not stoop and pick it up unless you shift your feet or fall over?

11. What would become of a ball dropped into a large hole bored through the center of the earth?

12. When an apple falls to the ground, does the earth rise to meet it?

13. How far from the earth does the force of gravity extend?

14. Why in walking up a flight of stairs does the body bend forward?

15. In walking down a steep hill why do people frequently bend backward?

16. Why is it so difficult for a child to learn to walk, while a kitten or a puppy has no such difficulty?

17. Explain why the use of a cane by old people makes it easier for them to walk?

(6) FALLING BODIES

=94. Falling Bodies.=--One of the earliest physical facts learned by a child is that a body unsupported falls toward the earth. When a child lets go of a toy, he soon learns to look for it on the floor. It is also of common observation that light objects, as feathers and paper, fall much slower than a stone. The information, therefore, that all bodies actually fall at the same rate in a vacuum or when removed from the r.e.t.a.r.ding influence of the air is received with surprise.

This fact may be shown by using what is called a coin and feather tube.

On exhausting the air from this tube, the feather and coin within are seen to fall at the same rate. (See Fig. 78.) when air is again admitted, the feather flutters along behind.

[Ill.u.s.tration: FIG. 78.--Bodies fall alike in a vacuum.]

=95. Galileo's Experiment.=--The fact that bodies of different weight tend to fall at the same rate was first experimentally shown by Galileo by dropping a 1-lb. and a 100-lb. ball from the top of the leaning tower of Pisa in Italy (represented in Fig. 79). Both starting at the same time struck the ground together. Galileo inferred from this that feathers and other light objects would fall at the same rate as iron or lead were it not for the resistance of the air. After the invention of the air pump this supposition was verified as just explained.

[Ill.u.s.tration: FIG. 79.--Leaning tower of Pisa.]

=96. Acceleration Due to Gravity.=--If a body falls freely, that is without meeting a resistance or a r.e.t.a.r.ding influence, its motion will continually increase. The _increase_ in motion is found to be constant or uniform during each second. This uniform increase in motion or in velocity of a falling body gives one of the best ill.u.s.trations that we have of uniformly accelerated motion. (Art. 75.) On the other hand, a body thrown upward has uniformly r.e.t.a.r.ded motion, that is, its acceleration is downward. The velocity acquired by a falling body in unit time is called its _acceleration_, or the _acceleration due to gravity_, and is equal to 32.16 ft. (980 cm.) per second, downward, each second of time. In one second, therefore, a falling body gains a velocity of 32.16 ft. (980 cm.) per second, downward. In two seconds it gains twice this, and so on.

In formulas, the acceleration of gravity is represented by "_g_" and the number of seconds by _t_, therefore the formula for finding the velocity, _V_,[F] of a falling body starting from rest is _V_ = _gt_. In studying gravity (Art. 89) we learned that its force varies as one moves toward or away from the equator. (How?) In lat.i.tude 38 the acceleration of gravity is 980 cm. per second each second of time.

[F] _V_ represents the velocity of a falling body at the end of _t_ seconds.

=97. Experimental Study of Falling Bodies.=--To study falling bodies experimentally by observing the fall of un.o.bstructed bodies is a difficult matter. Many devices have been used to reduce the motion so that the action of a falling body may be observed within the limits of a laboratory or lecture room. The simplest of these, and in some respects the most satisfactory, was used by Galileo. It consists of an inclined plane which reduces the effective component of the force of gravity so that the motion of a body rolling down the plane may be observed for several seconds. For ill.u.s.trating this principle a steel piano wire has been selected as being the simplest and the most easily understood. This wire is stretched taut across a room by a turn-buckle so that its slope is about one in sixteen. (See Fig. 80.) Down this wire a weighted pulley is allowed to run and the distance it travels in 1, 2, 3, and 4 seconds is observed. From these observations we can compute the distance covered each second and the velocity at the end of each second.

[Ill.u.s.tration: FIG. 80.--Apparatus to ill.u.s.trate uniformly accelerated motion.]

In Fig. 63, if _OG_ represents the weight of the body or the pull of gravity, then the line _OR_ will represent the effective component along the wire, and _OS_ the non-effective component against the wire. Since the ratio of the height of the plane to its length is as one to sixteen, then the motion along the wire in Fig. 80 will be one-sixteenth that of a falling body.

=98. Summary of Results.=--The following table gives the results that have been obtained with an apparatus arranged as shown above.

In this table, column 2 is the one which contains the results directly observed by the use of the apparatus. Columns, 3, 4, and 5 are computed from preceding columns.

(1) (2) (3) (4) (5) No. of Total Distance Velocity at Acceleration seconds distance each second end of second each second moved

Per second Per second 1 30 cm. 30 cm. 60 cm. 60 cm.

2 120 cm. 90 cm. 120 cm. 60 cm.

3 270 cm. 150 cm. 180 cm. 60 cm.

4 480 cm. 210 cm. 240 cm. 60 cm.

Column 5 shows that the acceleration is uniform, or the same each second. Column 4 shows that the velocity increases with the number of seconds or that _V_ = _at_. Column 3 shows that the increase in motion from 1 second to the next is just equal to the acceleration or 60 cm.

This is represented by the following formula: _s_ = 1/2 _a_(2_t_ - 1).

The results of the second column, it may be seen, increase as 1:4:9:16, while the number of seconds vary as 1:2:3:4. That is, _the total distance covered is proportional to the square of the number of seconds_.

This fact expressed as a formula gives: _S_ = 1/2_at_.

Subst.i.tuting _g_, the symbol for the acceleration of gravity, for _a_ in the above formulas, we have: (1) _V_ = _gt_, (2) _S_ = 1/2_gt_, (3) _s_ = 1/2_g_(2_t_ - 1).

=99. Laws of Falling Bodies.=--These formulas may be stated as follows for a body which falls from rest:

1. The velocity of a freely falling body at the end of any second is equal to 32.16 ft. per sec. or 980 cm. per second multiplied by the number of the second.

2. The distance pa.s.sed through by a freely falling body during any number of seconds is equal to the square of the number of seconds multiplied by 16.08 ft. or 490 cm.

3. The distance pa.s.sed through by a freely falling body during any second is equal to 16.08 feet or 490 cm. multiplied by one less than twice the number of the second.

Important Topics

1. Falling bodies.

2. Galileo's experiment.

3. Acceleration due to gravity.

4. Laws of falling bodies.

Exercises

1. How far does a body fall during the first second? Account for the fact that this distance is numerically equal to half the acceleration.

2. (a) What is the velocity of a falling body at the end of the first second? (b) How far does it fall during the second second? (c) Account for the difference between these numbers.

3. What is the velocity of a falling body at the end of the fifth second?

4. How far does a body fall (a) in 5 seconds (b) in 6 seconds (c) during the sixth second?

5. (a) What is the difference between the average velocity during the sixth second and the velocity at the beginning of that second?