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# The Wheel, Axle and the Pulley Study Guide for McGraw-Hill's Firefighter Exams (page 2)

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

#### Types of Pulleys

There are three types of pulleys: fixed, moveable, and compound. The mechanical advantage of pulley systems depends on the number of ropes, chains, etc. supporting the load. For example, using two supporting ropes to lift a resistance force (load) of 40 pounds would give you a mechanical advantage of 2.

#### Fixed (Single) Pulley

A fixed (single) pulley is attached to a stationary object like a wall or ceiling. It acts as a first-class lever having the fulcrum at the axis and the rope acting as the bar. Fixed (single) pulleys only change effort (force) direction (you can pull down on the rope to lift the load instead of pushing up on it). They do not enhance the effort (force). Effort (force) distance equals resistance force (load) distance and, therefore, each foot of pull on the rope will lift the load one foot. It provides no mechanical advantage (MA = 1).

Example: The fixed (single) pulley has a resistance force (load) at one end of the rope (see diagram). The other end must have effort (force) applied downward to raise the load. The effort (force) is equal to the load in this pulley system and there is no mechanical advantage, with the MA equal to 1.

#### Movable Pulley

A movable pulley moves up and down with the effort (force). It acts as a second-class lever having the resistance force (load) between the fulcrum and the effort (force). Unlike the fixed (single) pulley, it cannot change the direction of the effort (force). Moveable pulleys, however, enhance effort (force). Their mechanical advantage is greater than 1. The trade-off is that the effort (force) distance is greater than the resistance force (load) distance.

The moveable pulley (see diagram) has the resistance force (load) supported by both the rope ends (the rope end attached to the upper bar and the rope end to be pulled effort [force] in the upward direction). The two upward tensions are equal and opposite in direction to the load. The mechanical advantage is 2.

#### Compound Pulley

A compound pulley utilizes both a fixed (single) pulley and a movable pulley. Compound pulleys provide both a change in the direction of the effort (force) as well as dramatically decreasing the effort (force) required to lift the resistance force (load). The mechanical advantage of this type of pulley is 2. The effort (force) distance, however, like with the moveable pulley, will be greater than the resistance force (load) distance.

Note: The mechanical advantage of pulley systems can also be calculated visually by counting the number of ropes, chains, etc. supporting the load. For example, in the illustration of the compound pulley above, there are two supporting ropes to lift the resistance force (load), giving the pulley system a mechanical advantage of 2.

A T of several fixed and moveable pulleys is known as a block and tackle. Archimedes showed that by using multiple pulleys, a large ship fully loaded with men could be pulled by a single man's effort.

#### Efficiency of a Pulley System

To calculate the efficiency of a pulley system, first determine the mechanical advantage. Next, determine the velocity ratio by dividing the distance moved by effort (force) by the distance moved by the resistance force (load). Finally, divide the mechanical advantage by the velocity ratio and multiply this number by 100 percent.

Example: A pulley system can lift an object weighing 50 N with an effort (force) of 10 N. The input distance is 5 m and the output distance is 0.5 m. What is the efficiency of the pulley system?