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Difficulty: EasyWheel and Axle

A mechanic is inspecting a steering mechanism. If the steering wheel has a radius of 14 inches14 \text{ inches} and the attached steering column (axle) has a radius of 2 inches2 \text{ inches}, what is the ideal mechanical advantage of this wheel and axle system?

Answer: 7

Answer

7
The ideal mechanical advantage (IMA) is the ratio of the distance the effort moves to the distance the load moves. In a wheel and axle, this is proportional to their radii. Dividing the wheel's radius (14 inches14 \text{ inches}) by the axle's radius (2 inches2 \text{ inches}) gives an IMA of 77.

Step-by-Step Solution

1
Identify the relevant formula
IMA=Rr\text{IMA} = \frac{R}{r}
The ideal mechanical advantage of a wheel and axle is the ratio of the effort radius (wheel) to the load radius (axle).
2
Substitute the known values
IMA=142\text{IMA} = \frac{14}{2}
The wheel radius RR is 14 inches14 \text{ inches} and the axle radius rr is 2 inches2 \text{ inches}.
3
Perform the division
77
Dividing 1414 by 22 yields an ideal mechanical advantage of 77.

Key Concept

For a wheel and axle system where the input force is applied to the wheel, the ideal mechanical advantage is calculated by dividing the radius of the wheel by the radius of the axle.
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Topics

Wheel and Axle

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