How is the work output of a machine related to its work input?

Answer 1

Note: This answer addresses simple machines, such as levers, pulleys, and ramps - it does not address complex machines, such as engines.

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Machines affect work by applying one or more of the following principles:

1. altering the amount of force applied in order to do the work;
2. altering the amount of time over which the force is applied; and/or
3. altering the direction that the force is applied.

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A simple pulley, or a balanced lever, does not change the amount of force required to lift an object, or the time during which the force is applied, but they do change the direction of the force. A balanced lever (a teeter totter) makes it easier to lift another object (your friend on the other end of the teeter totter) because you can use your own weight to help lift that object (your friend). Such simple, balanced machines do not decrease the force, nor increase the amount of time during which the force is applied - they merely redirect the force, which is often helpful.

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Ramps, pulleys, and levers can also reduce the required force, in addition to changing the direction of the applied force, making the work easier in two ways. For example, a compound pulley reduces the amount of force required to lift a heavy object, but it now takes more time of that applied force to lift the weight. When this occurs, the machine does not actually change the amount of work done, but the machine makes it easier to do the same amount of work by spreading that work done over a longer period of time at a reduced force.

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Some machines use the opposite principle - they require more force than normal, but the force is applied over a reduced period of time. A catapult is an example of this principle - it is a lever in which more work is required to lift an object than without the catapult lever, but the object is lifted so quickly that, by the time the object is lifted, it is travelling fast enough to become a ballistic object.A machine affects work done by magnifying human's physical capabilities which reduces the intensity of the work.

Answer 2

In an ideal universe, where there are no friction or heat transfer losses, work out = work in.

In our universe, however, work output is always less than input. How much less depends on the efficiency of the machine's design.