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Difficulty: EasyWheel and Axle

A pipeline technician operates a circular handwheel to control the flow of water through a large valve. The handwheel has an overall diameter of 16 inches16 \text{ inches} and is attached to a central valve stem (the axle) that has a radius of 2 inches2 \text{ inches}. Assuming the effort force is applied to the outside edge of the handwheel, what is the ideal mechanical advantage (IMA) of this mechanism?

  1. A
    0.250.25
  2. B
    22
  3. 44Answer
  4. D
    88

Answer

The ideal mechanical advantage is 44.
The ideal mechanical advantage (IMA) of a wheel and axle system is found by dividing the radius of the input force (the wheel) by the radius of the output force (the axle). Since the handwheel's diameter is 16 inches16 \text{ inches}, its radius is 8 inches8 \text{ inches}. Dividing the wheel radius (8 inches8 \text{ inches}) by the axle radius (2 inches2 \text{ inches}) gives an IMA of 44.

Step-by-Step Solution

1
Convert the handwheel diameter to a radius.
The handwheel radius is 16÷2=8 inches16 \div 2 = 8 \text{ inches}.
To calculate mechanical advantage accurately, both the wheel and the axle must use the same type of measurement (either both radii or both diameters).
2
Divide the wheel radius by the axle radius.
IMA=8 inches2 inches=4\text{IMA} = \frac{8 \text{ inches}}{2 \text{ inches}} = 4.
The formula for the Ideal Mechanical Advantage of a wheel and axle (when force is applied to the wheel) is the radius of the wheel divided by the radius of the axle.

Key Concept

The ideal mechanical advantage of a wheel and axle is the ratio of the radius of the wheel to the radius of the axle.
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Topics

Wheel and Axle

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