CHAPTER II

FORCE AND ENERGY

18. Gravity. Many of our most common phenomena are simply changes in the position of bodies. The falling of an apple, the movement of water in waves and tides, the flight of a stone or a bullet through the air, all illustrate this. So do the turning of a magnetic needle toward the poles and the vibrating of a violin string. Now, why does a stone or an apple "fall"? Sir Isaac Newton gave the reason when he said that the earth pulls the apple and all other falling bodies. We do not find it easy to picture to ourselves just how the earth's "pull" is applied. A horse pulling a wagon is attached to the wagon, and the strength of his muscles overcomes the tendency of the wagon to remain at rest. Similarly, an engine is attached to the cars it pulls. But the earth's attraction acts through space, without visible or invisible attachment.

We can illustrate the earth's attraction, on a small scale, by the action of a magnet upon an iron nail. The magnet is a piece of steel which has been “magnetized,” so that it has the power of drawing to itself bodies consisting of steel, iron, nickel, etc. There is no connection between the magnet and the attracted object, yet we know that there is action between them.

It is just as necessary for us to assume that the apple attracts the earth as that the earth attracts the apple. It is also just as reasonable to suppose that the earth falls

toward the apple as that the apple falls toward the earth. But the distance that the earth moves before they meet must, of course, be very small, owing to the much greater size of the earth. This earth-pull we call gravity.

19. Gravitation. The attraction which exists between the earth and bodies near its surface exists also between all bodies of matter on the earth and between the earth and the sun, moon, and other heavenly bodies. It is called gravitation. Gravity is merely a particular case of gravitation.

The gravitation, or attraction, between two bodies on the earth, as, for example, between two suspended balls (Fig. 14), is not easily observed, because the great attraction of the earth for both of them holds them in a vertical position. By means of a celebrated experiment first carried out in the latter part of the 18th century this attraction was made visible. A large ball of lead and a small one of copper were suspended side by side, with the result that the copper ball was drawn aside from a vertical position.

FIG. 14.

The two balls attract each other.

20. Mass and Weight. We need to distinguish between the mass of a body and the weight of a body. Newton saw that the earth's attraction for a body depends on the quantity of matter in the body, and not upon its kind. A pound of feathers is attracted with the same force as a pound of lead. The quantity of matter in a body is called

MASS AND WEIGHT

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the mass of the body. The weight of the body is the result of the earth's pull upon the mass of the body. If, in some way, the pull upon a given body is increased, the weight will be in

creased; but if the pull is weakened, the weight will be decreased. Now, how can we change the effect of gravity, that is, the attraction of the earth for a certain mass? We can do it by changing the distance between the earth and the body. In other words, the attraction between two bodies depends not only on their

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masses, but also on the distance they are apart. The distance between two bodies is taken to be the distance between their centers.

Suppose we have two balls weighing, say, 10 grams each, and 1 inch apart. If we place them 2 inches apart, the force of the attraction between them will be only 14 as great as at 1 inch. If the distance between them is made 1/2 an inch, the attraction will be 4 times what it was originally. Now, we have learned that the earth is not a perfect sphere, but is flattened at the poles. An object at the poles is about 13 miles nearer the earth's center than if it were at the equator. As a result of this difference a body weighing 589 pounds at the equator would weigh 590 pounds at the poles.

If we remove a body from the earth at any given place, that is, if we take it "up in the air," or on a mountain top, it will also lose in weight. The mass of the body will, of course, remain the same everywhere.

21. Falling Bodies. We know that if we drop a stone it falls "straight down." We have also seen bricklayers using a string with a weight attached

a plumbline to be sure that they were making a wall vertical. The position taken by the plumbline, like the path of the falling ball, shows that gravity pulls vertically downward.

But objects that are very light, like feathers, seem to fall more slowly than heavy objects. Why is this? Galileo, dropping balls of different sizes and different materials from the "leaning tower" of Pisa (Fig. 15), insisted that all objects, heavy and light, if let fall from the same Bodies Falling in a height, should reach the ground at the same time. A feather and a bullet would fall at the same rate were it not for the air, which resists being pushed out of the way. In a tube free from air, that is, in a vacuum (Fig. 16) they do fall at the same rate.

FIG. 16.

Vacuum.

On a very windy day even a heavy body may not fall straight down. Thus an apple blown off the tree by a sudden gust will go in the direction of the wind (horizontally) and also downward. It cannot go in either of these directions alone, so it goes down in a curved path. But it will reach the ground by the longer, curved path in the same time as if it fell vertically to the ground. This fact may be illustrated by two marbles (Fig. 17) one of which is given a horizontal blow, while the other is permitted to fall vertically.

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22. Exercises.

1. Name five phenomena, besides those of § 18, that are "changes in the position of bodies."

2. Suppose that the moon and the earth were of exactly the same mass, and that a ball weighing a ton were placed half-way between them. What would its weight be?

Why?

3. If you dropped wooden, iron, and lead balls from an upper window, which would reach the ground first?

4. Suppose the wind were blowing hard down the street, and you dropped a tennis ball from an upper window. Where would it strike the ground? Why?

5. Draw a diagram to show the kind of a path a ball takes if you throw it horizontally. If you throw it upward

FIG. 17.

The Marbles Reach the Floor at the
Same Instant.

at an angle of 45 degrees (half a right angle). In which case would the ball have the greater range?

6. Who was Sir Isaac Newton? When did he live, and where? What did he add to our knowledge?

Answer the same questions regarding Galileo.

23. Force. Let us imagine we are at a baseball game. The pitcher throws a "fair" ball, the batter strikes at it but makes a "foul" hit, and the catcher catches the ball. Three persons were concerned in the flight of that ball: the pitcher, who set it in motion; the batter, who changed the direction of its motion; and the catcher, who stopped its motion. We say that all three exerted force upon the ball.

Besides the players, two other bodies exerted force upon the pitched ball: (1) the air, which resisted being pushed