The Golden Rule of Mechanics
From Thermal-FluidsPedia
The “golden rule” of mechanics essentially states that whatever you lose in power you gain in displacement. We commonly use pulleys and ramps to lift things which would otherwise be too heavy for muscle alone. In both cases, a smaller force achieves the necessary work, but over a greater distance.
Question: Consider a bottle opener. In lifting the handle, you do work on the opener, which in turn does work on the cap it is lifting. Which one is greater, your work or the work of the bottle opener? Answer: Because the opener cannot be a source of energy, the output work (work of opener) can never exceed the input work (your work). The opener simply aids in the transfer of energy from you to the bottle cap. In fact, nearly all of your work will go into deforming rather than into lifting the bottle cap. Of course, energy was not really lost; it was just not used in the way you intended.
Although the output work is always less than the input work, output force does not have to be smaller than input force. This is exactly what a machine is supposed to do - transform part of the energy (work) into a form most convenient -- that requiring less force.
References
(1) Toossi Reza, "Energy and the Environment:Sources, technologies, and impacts", Verve Publishers, 2005