Since the earth is flattened at the poles, the surface at the equator is farther from the center of the earth than at points north or south. Thus a body weighing 1 lb. at the equator weighs 1.002 lb. at Chicago, or about 1/500 more. The rotation of the earth also affects the weight of a body upon it so that at the equator the weight of a body is 1/289 less than at the pole. Both effects, that of flattening and of rotation, tend to diminish the weight of bodies at the equator, so that a body at the latter place weighs about 1/192 less than at the poles.
In studying the effect of the earth's gravity, the following illustration will be helpful: Imagine an open shaft a mile square extending through the earth. What would happen to a stone thrown into the shaft? At first it would have the attraction of the whole earth drawing it and continually increasing its speed downward. As it descends from the surface, the pull toward the center grows less and less. Halfway to the center the body has lost half its weight. When the stone reaches the center, the pull in all directions is the same, or in other words, it has no weight. It would, however, continue moving rapidly on account of its inertia, and as it continues on from the center, the greater part of the earth being left behind, the attraction pulling toward the center will gradually stop it. It will then fall again toward the center and be stopped again after passing it, and after repeatedly moving up and down will finally come to rest at the center of the earth. At this point it will be found to be a body without weight since it is pulled equally in all directions by the material of the earth. What force brings the body to rest?
90. Center of Gravity.—A body is composed of a great many particles each of which is pulled toward the center of the earth by the force of gravity. A single force that would exactly equal the combined effect of the pull of the earth for all the particles of a body would be their resultant. The magnitude of this resultant is the weight of the body. The direction of this resultant is in a line passing toward the earth's center, while the point of application of this resultant is called the center of gravity of the body. The center of gravity of a body may also be briefly defined as the point about which it may be balanced. As the location of this point depends upon the distribution of matter in the body, the center of gravity is also sometimes called the center of mass of the body.
The earth's attraction for a body is considered for the sake of simplicity, not as a multitude of little forces, but as a single force applied at its center of gravity. To find the center of gravity of a body find two intersecting lines along which it balances, see Fig. 72, and the center of gravity will be at the intersection. A vertical line through this point is sometimes called the line of direction of the weight.
Fig. 72.—The center of gravity is at the intersection of the lines of direction.
91. Equilibrium of Bodies.—Equilibrium means equally balanced. A body at rest or in uniform motion is then in equilibrium. An object is in equilibrium under gravity when a vertical line through its center of gravity passes through the point of support. A trunk is an example of a body in equilibrium since a vertical line from its center of gravity falls within the base formed by the area upon which it rests. Work will be necessary to tip the trunk from its position. The amount of work required will depend upon the weight of the body and the location of the center of gravity.
92. Kinds of Equilibrium.—(a) Stable.—A body is in stable equilibrium under gravity if its center of gravity is raised whenever the body is displaced. It will return to its first position if allowed to fall after being slightly displaced. In Fig. 73, a and b if slightly tipped will return to their first position. They are in stable equilibrium. Other examples are a rocking chair, and the combination shown in Fig. 74.
Fig. 73.—Stable equilibrium.