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Difficulty: MediumWheel and Axle

Match each wheel and axle concept to its correct definition or mechanical characteristic.

  • Wheel and Axle SystemA simple machine consisting of two rigidly attached circular objects of different radii that rotate together.
  • Ideal Mechanical Advantage (IMA)Calculated by dividing the radius of the input component by the radius of the output component.
  • Force Multiplier Setup (MA > 1)Occurs when the input effort is applied to the larger wheel, yielding a greater output force at the smaller axle.
  • Distance/Speed Multiplier Setup (MA < 1)Occurs when the input effort is applied to the smaller axle, yielding a greater output speed at the larger wheel.

Answer

The correct matches are: Wheel and Axle System pairs with its definition of two rotating circular objects; Ideal Mechanical Advantage (IMA) pairs with the ratio of input radius to output radius; Force Multiplier Setup pairs with effort applied to the larger wheel; and Distance/Speed Multiplier Setup pairs with effort applied to the smaller axle.
Each concept describes a specific operational mode or structural property of the wheel and axle. The fundamental physical relationship dictates that applying effort to the larger diameter (wheel) multiplies force at the expense of distance, while applying effort to the smaller diameter (axle) multiplies speed and distance at the expense of force. The mathematical ratio of these radii determines the exact Ideal Mechanical Advantage.

Step-by-Step Solution

1
Identify the basic definition of the wheel and axle system.
It is matched as a simple machine with two connected circular objects of different radii rotating together.
Establishes the structural baseline for the mechanism.
2
Determine how Ideal Mechanical Advantage (IMA) is calculated for rotational machines.
IMA is matched to the ratio of the input component's radius to the output component's radius.
IMA represents the theoretical multiplication factor of the machine based on lever arms.
3
Analyze the conditions for a force multiplier setup.
It is matched to the scenario where effort is on the larger wheel, resulting in greater output force at the smaller axle (MA > 1).
A larger input radius creates a longer effective lever arm for the effort.
4
Analyze the conditions for a distance/speed multiplier setup.
It is matched to the scenario where effort is on the smaller axle, resulting in greater output speed at the larger wheel (MA < 1).
One rotation of the small input axle forces the large outer wheel to travel a much larger circumference in the same amount of time.

Key Concept

Mechanical principles and force-distance trade-offs of the wheel and axle simple machine.
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Topics

Wheel and Axle

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