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Difficulty: EasyWheel and Axle

A worker operates a well crank (a wheel and axle mechanism) to lift a heavy bucket of water. The crank handle travels in a circle with a radius of 12 inches12 \text{ inches}. The lifting rope is wound around an axle that has a diameter of 6 inches6 \text{ inches}. What is the Ideal Mechanical Advantage (IMA) of this system?

  1. 44Answer
  2. B
    22
  3. C
    11
  4. D
    0.50.5

Answer

The correct Ideal Mechanical Advantage (IMA) is 44.
The correct answer is calculated by finding the ratio of the wheel's radius to the axle's radius. The wheel radius is given as 12 inches12 \text{ inches}. The axle diameter is 6 inches6 \text{ inches}, meaning its radius is 3 inches3 \text{ inches}. Dividing 1212 by 33 yields an IMA of 44.

Step-by-Step Solution

1
Identify the radius of the wheel (input distance).
The radius of the crank handle circle is 12 inches12 \text{ inches}.
The IMA formula requires the radius of the wheel.
2
Calculate the radius of the axle (output distance).
The diameter is 6 inches6 \text{ inches}, so the radius is 6÷2=3 inches6 \div 2 = 3 \text{ inches}.
The IMA formula requires the radius of the axle, not the diameter.
3
Calculate the Ideal Mechanical Advantage (IMA).
IMA=Radius of WheelRadius of Axle=123=4IMA = \frac{\text{Radius of Wheel}}{\text{Radius of Axle}} = \frac{12}{3} = 4
This ratio shows the mechanical advantage gained by applying force to the larger wheel to turn the smaller axle.

Key Concept

Ideal Mechanical Advantage of a Wheel and Axle
Estimated Time:45s
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Topics

Wheel and Axle

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