Pulley: Difference between revisions

Revision as of 06:20, 5 March 2006

Revision as of 16:14, 6 March 2006

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[[Image:Pulley0.png|thumb|right|128px|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.]]

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. It is also assumed that the lines do not stretch. With this assumption, it follows that, in equilibrium, the total force on the pulley must be zero. This means that the force on the axle of the pulley is shared equally by the two lines looping through the pulley. The situation is schematically illustrated in diagram 1. For the case where the lines are not parallel, the tensions in each line are still equal, but now the vector sum of all forces is zero. 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.

[[Image:Pulley1.png|thumb|left|152px|Diagram 2 - A simple pulley system - a single movable pulley lifting a unit weight. The tension in each line is half the unit weight, yielding an advantage of 2]] [[Image:Pulley1a.png|thumb|left|160px|Diagram 2a - Another simple pulley system similar to diagram 2, but in which the lifting force is redirected downward.]] 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. The total force needed is divided between the lifting force (red arrow) and the "ceiling" which is some immovable object (such as the earth). In this simple system, the lifting force is directed in the same direction as the movement of the weight. The advantage of this system is seen to be equal to 2.

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. [[Image:Polispasto2.jpg|thumb|right|A practical compound pulley corresponding to diagram 2a]]