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# Inclined Planes Study Guide for McGraw-Hill's Firefighter Exams (page 2)

By — McGraw-Hill Professional
Updated on Jun 25, 2011

The inclined plane—a slanted surface raised at one end—is a simple machine that does not move. It is used to lift heavy loads by providing the worker with a mechanical advantage. The inclined plane provides for less effort, not for less work, to lift the object. Getting heavy boxes or barrels onto a loading dock is much easier if you slide the objects up a ramp rather than lift them up. The trade-off is the greater distance to travel. Stairs and ramps provide examples of inclined planes.

The mathematical formula for the mechanical advantage of an inclined plane is the length of the inclined plane—the effort (force) distance—divided by the height—the resistance force (load) distance. The length of the inclined plane can never be less than the height; therefore, the MA can never be less than 1.

Example: A ramp 20 feet in length is 5 feet in height. What is the mechanical advantage of this simple machine?

The trade-off is that the length of the slope (effort distance) is 4 times greater than the resistance force (load) distance, or height of the slope.

Example: Select the inclined plane diagram below that gives the best mechanical advantage in lifting a heavy barrel to the height of the platform.

The correct choice is answer B. Using the MA formula for the four inclined planes shown reveals that choice B has the greatest MA, 3, compared to 1.25 for A, 2 for C, and l.5 for D. However, B would require the longest effort (force) distance, 12 feet.

Example: Determine the amount of force, or effort, required to move a 400-pound load to a height of 3 feet, using a 12-foot ramp.

Use the following formula:

Effort × Effort Distance = Resistance Force × Resistance Distance

OR

Force Length of Inclined Plane = Load × Height

To solve: effort (force) × 12 = 400 pounds 3 feet

The inclined plane with a MA of 4 allows a 400-pound object to be raised 3 feet with a 100-pound force.