A contractor uses a 15\text{-foot} ramp and a motorized winch to load a 600\text{-lb} gene… — Armed Services Vocational Aptitude Battery (ASVAB)

A contractor uses a $15\text{-foot}$ ramp and a motorized winch to load a $600\text{-lb}$ generator. If the winch can pull with a maximum steady force of $120\text{ lbs}$ , what is the maximum vertical height, in feet, that the ramp can reach assuming a frictionless surface?

Answer: 3 feet

Answer

The maximum vertical height the ramp can reach is 3 feet.

An inclined plane multiplies the applied effort force by spreading the required work over a longer distance. First, determine the Mechanical Advantage needed by dividing the load (

600\text{ lbs}

) by the available effort force (

120\text{ lbs}

), which gives an IMA of

5

. This means the ramp must be

5

times longer than it is high. Given a ramp length of

15\text{ feet}

, divide this length by the IMA of

5

to find the maximum vertical height, which is

3\text{ feet}

Step-by-Step Solution

Determine the required Ideal Mechanical Advantage (IMA).

\text{IMA} = \frac{600}{120} = 5

The IMA represents how many times the machine multiplies the effort force. It is found by dividing the load force by the effort force.

Use the inclined plane IMA formula to set up an equation for the height.

5 = \frac{15}{\text{Height}}

For an inclined plane, the

\text{IMA}

is also equal to the ratio of the

\text{Ramp Length}

to the

\text{Vertical Height}

Solve the equation for the vertical height.

\text{Height} = \frac{15}{5} = 3

Rearrange the equation to isolate the height, dividing the ramp length by the required IMA.

Key Concept

Ideal Mechanical Advantage (IMA) of an inclined plane and determining vertical height from force ratios.

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