A manual boat winch is used to pull a small boat onto a trailer. The crank handle travels … — Armed Services Vocational Aptitude Battery (ASVAB)

A manual boat winch is used to pull a small boat onto a trailer. The crank handle travels in a circle with a radius of $15 \text{ inches}$ , turning a central spool (the axle) with a radius of $3 \text{ inches}$ .

What is the Ideal Mechanical Advantage (IMA) of this winch?

Answer: 5

Answer

The Ideal Mechanical Advantage is 5.

The Ideal Mechanical Advantage of a wheel and axle is calculated by dividing the radius of the wheel by the radius of the axle. Here, the wheel's radius is

15 \text{ inches}

and the axle's radius is

3 \text{ inches}

, which gives

15 \div 3 = 5

Step-by-Step Solution

Identify the given dimensions of the wheel and the axle.

R_{wheel} = 15 \text{ inches}

R_{axle} = 3 \text{ inches}

These are the required variables for the IMA equation.

Apply the Ideal Mechanical Advantage formula for a wheel and axle.

IMA = \frac{R_{wheel}}{R_{axle}}

IMA represents the ratio of the effort distance to the resistance distance.

Calculate the final value.

IMA = \frac{15}{3} = 5

Dividing the wheel radius by the axle radius yields the mechanical advantage.

Key Concept

Ideal Mechanical Advantage (IMA) of a Wheel and Axle

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