You wish to lift a 12,000 lb stone by a vertical distance of 15 ft. Unfortunately, you can only generate a maximum pushing force of 2,000 lb.

a. What is the amount of work you must input in order to move the stone?

b. What is the actual mechanical advantage (AMA) required by a machine to complete the work above?

c. You build a ramp to create the ideal mechanical advantage. What is the length of the ramp in feet?

a. 180,000 ft·lbf

b. AMA = 6

c. 90 ft

Explanation:

Here we have;

a. The amount of work one must put in is given by the following relation;

Work = Force × Distance = 12,000 × 15 = 180,000 ft·lbf

b. Ideal mechanical advantage IMA given by the following relation;

In the absence of friction IMA = AMA (Actual Mechanical Advantage) = 6

c.

Therefore, Y = 15×6 = 90

Therefore, X = √(90² - 15²) = 88.74 ft

The distance moved by the load is the  length of the ramp = 90 ft.

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