Mechanical power refers to the rate at which work can be done. It is a power output, as opposed to a power input (how fast the engine can do work, rather than how fast it uses fuel). The rate at which an engine uses fuel is the thermal power. Mechanical power is how fast mechanical energy can be delivered to a system. Recall that power is a transfer of energy in an amount of time.
If mechanical power is attained from an input of thermal power such as in a heat engine or power plant, it is limited by the second law of thermodynamics and the maximum amount of mechanical power is given by the Carnot efficiency. Mechanical power of a wind turbine is also limited, although in a totally different aspect, by the Betz limit.
Simple machines are idealized as lossless, meaning they do not lose any energy in their manipulation of forces. Therefore the mechanical power is conserved throughout the duration of its output, and this allows them to be analyzed easily in terms of mechanical advantage.
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