The Inclined Plane
Man's Way of Helping Himself
A man wishes to load the 600-pound bowlder on a wagon, and proceeds to do it by means of a plank. Such an arrangement is called an inclined plane.
The advantage of an inclined plane can be seen by the following experiment. Select a smooth board 4 feet long and prop it so that the end A
is 1 foot above the level of the table; the length of the incline is then 4 times as great as its height. Fasten a metal roller to a spring balance and observe its weight. Then pull the roller uniformly upward along the plank and notice what the pull is on the balance, being careful always to hold the balance parallel to the incline.
When the roller is raised along the incline, the balance registers a pull only one fourth as great as the actual weight of the roller. That is, when the roller weighs 12, a force of 3 suffices to raise it to the height A
along the incline; but the smaller force must be applied throughout the entire length of the incline. In many cases, it is preferable to exert a force of 30 pounds, for example, over the distance CA
than a force of 120 pounds over the shorter distance BA
Prop the board so that the end A
is 2 feet above the table level; that is, arrange the inclined plane in such a way that its length is twice as great as its height. In that case the steady pull on the balance will be one half the weight of the roller; or a force of 6 pounds will suffice to raise the 12-pound roller.
The steeper the incline, the more force necessary to raise a weight; whereas if the incline is small, the necessary lifting force is greatly reduced. On an inclined plane whose length is ten times its height, the lifting force is reduced to one tenth the weight of the load. The advantage of an incline depends upon the relative length and height, or is equal to the ratio of the length to the height.
FIG. - Less force is required to raise the roller along the incline than to raise it to A directly.