# How are work and a change in energy related?

##### 1 Answer
May 30, 2015

Work done is equal to the change in energy (kinetic, potential, vibrational or rotational).

This is termed as the work-energy theorem.

The result can be derived very easily for simple cases involving rigid bodies in translational motion.

Try to cook up your own proof on this.
(Hint : Use the notion of time rate of change of kinetic energy $\frac{\mathrm{dK}}{\mathrm{dt}}$, simplify and proceed.You may need to use $F = M a$ once. Finally you should arrive at the integral, ${\int}_{K {\text{_i)^(K}}_{f}} \mathrm{dK} = {\int}_{0}^{x} F \cdot \mathrm{dx}$ . This shall do it.