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Difficulty: EasyWheel and Axle

Match each wheel and axle configuration to its resulting Ideal Mechanical Advantage (IMA).

  • Effort is applied to a wheel with a 10 cm10 \text{ cm} radius to turn an axle with a 2 cm2 \text{ cm} radius.IMA=5\text{IMA} = 5
  • Effort is applied to a wheel with a 12 cm12 \text{ cm} radius to turn an axle with a 3 cm3 \text{ cm} radius.IMA=4\text{IMA} = 4
  • Effort is applied to an axle with a 4 cm4 \text{ cm} radius to turn a wheel with an 8 cm8 \text{ cm} radius.IMA=0.5\text{IMA} = 0.5
  • Effort is applied to an axle with a 2 cm2 \text{ cm} radius to turn a wheel with a 10 cm10 \text{ cm} radius.IMA=0.2\text{IMA} = 0.2

Answer

Match each configuration by correctly dividing the effort radius by the load radius.
The correct matches are found by calculating the ratio of the input (effort) distance to the output (load) distance. For a wheel and axle, this is equivalent to Effort RadiusLoad Radius\frac{\text{Effort Radius}}{\text{Load Radius}}. When the effort is on the wheel, the IMA is greater than 1. When the effort is on the axle, the IMA is less than 1.

Step-by-Step Solution

1
Identify the effort radius and the load radius for each given configuration.
You determine whether the force is applied to the wheel (larger radius) or the axle (smaller radius).
The location of the applied force dictates which radius is the numerator in the IMA formula.
2
Apply the Ideal Mechanical Advantage formula: IMA=Effort RadiusLoad Radius\text{IMA} = \frac{\text{Effort Radius}}{\text{Load Radius}}.
Calculations yield 55, 44, 0.50.5, and 0.20.2 for the respective configurations.
This formula provides the theoretical multiplication of force for a wheel and axle mechanism.

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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