FIG. 103.—Primitive man tried to lighten his task by balancing his burden.
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.
FIG. 104.—Less force is required to raise the roller along the incline than to raise it to A directly.
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.
156. Application. By the use of an inclined plank a strong man can load the 600-pound bowlder on a wagon. Suppose the floor of the wagon is 2 feet above the ground, then if a 6-foot plank is used, 200 pounds of force will suffice to raise the bowlder; but the man will have to push with this force against the bowlder while it moves over the entire length of the plank.
Since work is equal to force multiplied by distance, the man has done work represented by 200 × 6, or 1200. This is exactly the amount of work which would have been necessary to raise the bowlder directly. A man of even enormous strength could not lift such a weight (600 lb.) even an inch directly, but a strong man can furnish the smaller force (200) over a distance of 6 feet; hence, while the machine does not lessen the total amount of work required of a man, it creates a new distribution of work and makes possible, and even easy, results which otherwise would be impossible by human agency.
157. Railroads and Highways. The problem of the incline is an important one to engineers who have under their direction the construction of our highways and the laying of our railroad tracks. It requires tremendous force to pull a load up grade, and most of us are familiar with the struggling horse and the puffing locomotive. For this reason engineers, wherever possible, level down the steep places, and reduce the strain as far as possible.
FIG. 105.—A well-graded railroad bed.