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# The Wheel, Axle and the Pulley Study Guide for McGraw-Hill's Firefighter Exams

By — McGraw-Hill Professional
Updated on Jun 25, 2011

### The Wheel and Axle

The wheel and axle is another type of simple machine that moves objects across distances. Wheels help move objects along the ground by decreasing the amount of friction between what is being moved and the surface. The work of this simple machine can result from the larger wheel being utilized to turn a smaller axle wheel. (Example: The steering wheel and shaft of a car enhances effort (force) with the trade-off, once again, having to apply effort (force) over a greater distance). Movement is created as the steering wheel turns, thereby applying a rotating force to its cylindrical axle post. The bigger the wheel, the greater the twisting force (torque) that can be applied to the axle.

Work can also result when an axle is used to rotate wheels, such as the example of a rear axle and wheels of a truck. The effort (force) is applied to the axle at a point close to where the axle turns. This can be equated as the effort (force) distance. When effort (force) is applied to the axle, the mechanical advantage will be less than one but the speed is enhanced. The distance between the point where the wheel touches the ground and the point where the wheel turns can be called the resistance force (load) distance. These two distances are equal to the radius of the axle and the radius of the wheel, respectively.

To calculate the mechanical advantage of a wheel and axle assembly divide the radius of the wheel by the radius of the axle.

Example: What is the mechanical advantage provided by a car's steering wheel assembly when the radius of the steering wheel is 6 inches and the radius of the axle is 1 inch?

Effort (force) is being applied to the steering wheel and therefore multiplied, providing torque on the axle six times greater than the effort (force) applied to the wheel. The trade-off, however, is that the steering wheel travels six times farther than the axle does during one full rotation.

Use the formula below to calculate the amount of effort (force) required when using this simple machine.

Effort × Circumference = Resistance Force×Circumference

(Force) × (Wheel) = (Load) × (Axle)

Example: In the drawing below of a well crank (windlass), the handle is attached to a 2-inch radius axle. The turning circumference of the crank is 16 inches. How much effort (force) is required to lift a bucket of water weighing 40 pounds?

### The Pulley

A pulley can be considered as a circular lever. It is a wheel with a grooved rim and axle with a rope, belt, or chain attached to it in order to change the direction of the pull and lift a load. The effort (force) distance is the radius of the pulley (length from the axle to the side of the rope being pulled). The resistance force (load) distance is the radius of the pulley from the axle to the load-carrying side of the rope. Pulleys are used to lift heavy loads and can be found in block and tackles, cranes, hydraulic systems, and chain hoists. They change the direction of effort (force) making it easier to lift the object or they enhance the effort (force).

Mechanical advantage for pulley systems can be found using the following formulas:

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