Inclined Plane

An inclined plane is an even surface sloping at any angle between vertical and horizontal. An inclined plane produces a mechanical advantage. The amount is determined by the ratio of the length of the inclined plane to the change in elevation. Instead of lifting the entire weight vertically, part of the weight is supported by the inclined plane.

Compare drawings I and II in Figure 4.15. Intuitive reasoning suggests that if the weight being moved and the distance AC are the same in both cases, then less force (ignoring friction) will be required to move the wagon up the inclined plane in the situation represented by drawing I because the change in height is less in I than it is in II for the same length of inclined plane. If we need to know the pounds of force required to pull the wagon, then we must use an equation based on the

FIGURE 4.15. Two inclined planes.

principles of an inclined plane. Expressed mathematically:

where F = Amount of force to pull the wagon (ignoring friction); AC = Length of the inclined plane; W = Weight of the wagon; BC = Height of the inclined plane.

If we analyze drawing I, Figure 4.15, first and assume that the total weight is 100.0 lb, the height (BC) is 2.0 ft, and the length of the inclined plane (AC) is 12.0 ft, then the amount of force that would be required to pull the wagon up the inclined plane is:

Substituting the values gives:

12.0 ft

Now we can see if the conclusion was right about the situation in drawing II. We will use the same equation to calculate the force in this situation. If we assume the length of the plane is the same (AC), then:

12.0 ft

It thus is obvious that an inclined plane with a steeper angle will require more force for the same weight.

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