The simplest type of pulley block consists of a wheel, fixed from its center to the ceiling in such a way that it is free to turn. Because it is fixed to the ceiling it is called a fixed pulley. A rope or chain runs over the wheel. The load to be lifted is attached to one end of the rope and the person hauls on the other end. The only advantage here is that of posture. The person can remain standing. But to raise a mass of 20 kilograms (equal to a load of 200 newtons) the effort exerted must be at least 200 N. This machine has a mechanical advantage (force ratio), = load/effort, of 1. The load (resistance) is the same as the effort.
In practice, most pulley systems are designed to have a mechanical advantage of more than one so that much heavier loads can be raised. If, with the aid of a pulley system, a force of 100 N is able to raise a load of 200 N then the pulley system has a mechanical advantage of 2. If an effort of 50 N is able to raise a 250 N load then the mechanical advantage is 5.
A single movable pulley can give a mechanical advantage of 2. This time, one of the ropes is fixed and the pulley itself is cradled in the rope. The load is hung from the pulley block and the effort is used to pull upwards on the free end of the rope. Because the load is now hung from two ropes, each taking half of the strain, the effort needed is only half the size of the load. At first sight, this looks like a way of getting something for nothing, but in fact it is not so. The work done by the effort is never less than the work done on the load. For every meter the rope is raised, the load rises only 0.5 meter. This is because both ropes have to be shortened.
With this movable pulley, the effort moves twice as far as the load moves. The pulley is said to have a velocity ratio, = (distance moved by effort)/(distance moved by load), of 2.
If pulleys had no weight and there were no frictional forces opposing the raising of the load, then the mechanical advantage and the velocity ratio would be equal. But in fact there are frictional forces acting and the pulley does weigh something and so extra effort is needed to overcome these factors. This in practice lessens the mechanical advantage, making it smaller than the velocity ratio.
Here, as a simplification, the pulleys are thought of as being weightless and frictionless.
Usually a pulley system consists of a combination of both fixed and movable pulley blocks, with the "effort rope" arranged so that the person can haul down upon it.
A quick way of finding the mechanical advantage of a perfect pulley system is to count the number of ropes that are bearing the load. If five ropes are bearing it, then the mechanical advantage is 5.
Variable speed can be obtained from a single-speed drive shaft by the use of stepped or cone-shaped pulleys with diameters that give the correct speed ratios and belt tensions.
Related categories CLASSICAL MECHANICS
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