A simple machine: a wheel with a grooved rim in which a rope can run. This changes the direction of force applied to the rope, and so can be used to raise heavy weights by pulling downwards.
Pulleys are usually used in sets designed to reduce the amount of force needed to lift a load.Types of pulleys
Fixed A fixed or class 1 pulley has a fixed axle. Block and tackle - A block and tackle is a compound pulley where several pulleys are mounted on each axle, further increasing the mechanical advantage.Theory of operation
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Diagram 1 - A basic equation for a pulley: In equilibrium, the force F on the pulley axle is equal and opposite to the sum of the tensions in each line leaving the pulley, and these tensions are equal. |
Diagram 2 - A simple pulley system - a single movable pulley lifting a unit weight. |
Diagram 2a - Another simple pulley system similar to diagram 2, but in which the lifting force is redirected downward. |
The simplest theory of operation for a pulley system assumes that the pulleys and lines are weightless, and that there is no energy loss due to friction. This means that the force on the axle of the pulley is shared equally by the two lines looping through the pulley. A second basic equation for the pulley follows from the conservation of energy: The product of the weight lifted times the distance it is moved is equal to the product of the lifting force (the tension in the lifting line) times the distance the lifting line is moved. The weight lifted divided by the lifting force is defined as the advantage of the pulley system.
In diagram 2, a single movable pulley allows a unit weight to be lifted with only half the force needed to lift the weight without assistance. Although the force needed to lift the unit weight is only half of the unit weight, we will need to draw a length of rope that is twice the distance that the weight is lifted, so that the total amount of work done (Force x distance) remains the same.
A second pulley may be added as in diagram 2a, which simply serves to redirect the lifting force downward, it does not change the advantage of the system.
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Diagram 3 - A simple compound pulley system - a movable pulley and a fixed pulley lifting a unit weight. |
Diagram 3a - A simple compound pulley system - a movable pulley and a fixed pulley lifting a unit weight, with an additional pulley redirecting the lifting force downward. |
Diagram 4a - A more complicated compound pulley system. An additional pulley redirecting the lifting force has been added. |
Figure 4b - A practical block and tackle pulley system corresponding to diagram 4a. |
The addition of a fixed pulley to the single pulley system can yield an increase of advantage. In diagram 3, the addition of a fixed pulley yields a lifting advantage of 3. The tension in each
line is ⅓ the unit weight, and the force on the axles of each pulley is ⅔ of a unit weight. As in the case of diagram 2a, another pulley may be added to reverse the direction of the lifting
force, but with no increase in advantage. This situation is shown in diagram 3a.
This process can be continued indefinitely for ideal pulleys with each additional pulley yielding a unit increase in advantage. For real pulleys friction among rope and pulleys will increase as more pulleys are added to the point that no advantage is possible. The above pulley systems are known collectively as block and tackle pulley systems.
Other pulley systems are possible, and some can deliver an increased advantage with fewer pulleys than the block and tackle system. The advantage of the block and tackle system is that each pulley and line is subjected to equal tensions and forces. Other pulley designs will require different strengths of line and pulleys depending on their position in the system, but a block and tackle system can use the same line size throughout, and can mount the fixed and movable pulleys on a common axle.
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