Pulleys can make work easier in a few different ways. You may have seen block and tackle hoists on ships that double up rope to gain mechanical advantage. Or you may have seen a pulley hoist at a mechanic's garage that lifts engines out of cars. In both cases, the input force needed is less than would required without the pulleys. Pulleys can even ease work simply by changing the direction of a pulling force.
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The most basic way in which a pulley can make work easier is by redirecting a force. For example, a pulley hanging from above allows your pulling down on a rope convert into an upward force on the load. You can therefore use your full weight as a pulling force.
Using multiple pulleys, you can obtain what is called "mechanical advantage." For example, one pulley attaches to the load; another pulley attaches to a support above. Threading the lifting rope over the hanging pulley, under the load's pulley and back up to the hanging pulley to be tied off will cut the required input force in half.
Why It Works
If you want to lift the load one foot, the distance between the two pulleys in the multi-pulley example has to shorten by one foot. This means the two stretches of rope between the two pulleys has to shorten by a foot. So the person pulling the free end of the rope has to pull two feet, not one. While pulling is needed over a greater distance, the trade-off is less force required over that longer distance.
Analogy to Lever
This trade-off between force and the distance over which it is applied is the same benefit seen in the lever, which most people know from riding see-saws as children. For a more work-related example, you can move a big rock with reduced effort if given a long lever and a fulcrum placed very close to the rock. You'll need to move the free end of the lever a long distance downward compared to how little the opposite end rises, but the input force required is reduced as well.
To understand the variables at work, the product of the force and the distance over which the force is applied is a measure of the energy required to do a job. The famous formula for this phenomenon is work equals force times distance. So though the product "work" is constant for a given task, force and distance can vary inversely. The pulleys increase the distance. Because of the constancy of energy required, the input force required diminishes.
Auto mechanics use differential pulleys, or chain hoists, to hoist car engines. The differential pulley consists of two pulleys on the same axis. An engine can hang off the pulleys without dropping because the chain hooking onto the engine wraps around the two pulleys on opposite sides. Because the pulleys differ slightly in size, the mechanic's pulling the closed-loop chain a long distance lifts the engine a small distance.
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