Answer to Question #127495 in Mechanics | Relativity for Ayesha Siddiqa

Question

Is hydraulic press against the law of conservation of energy? As we see output is greater than input... energy is equal to work done,, which is equal to the dot product of work and distance...now in case of smaller piston force is smaller while in case of larger piston (having large Cross section area) force is very large conparitively,,, displacement of piston renains same in both cases,,then in this way its violating law of conservation of energy...how could we justify law of conservation of energy in hydraulic press???

Answer 1

The correct answer is:

It doesn't violate the conservation of energy for a very good reason. Energy is not the same as force.

Force and energy are related however, the scalar product of force and displacement (the force measured along a direction) is equal to the work done by that force. This work can be related to the energy leaving or entering the system.

In order to understand hydraulics you have to understand what pressure is. The force F exerted on a cross-sectional area A under a pressure P, is given by F = PA. Remember that for incompressible fluids pressure is the same everywhere. So if you exert a force on a big area, the other side will feel a larger force on a small area.