# Energy, work and power

A2

Work = force x distance

Energy is the capacity a thing has to do work

Power is the rate of work being done

Power = work / time

The work energy principle:

change in kinetic energy is equal to the net work done

This is derived from the conservation of energy principle.

University

These relationships are expressed more mathematically at university:

(W is work, P is power, t is time, F is force in vector form, p is momentum in vector form, U is potential energy, x is distance)

From Newton’s laws, momentum and impulse  we saw that Newton’s second law states:

We can also write the work equation in terms of potential energy, U. This means that the force in the x direction is equal to the negative of the derivative of potential energy with respect to distance in the x direction:

This can be applied in the y and z directions, so the total force is:

The triangle symbol is the del operator, and means that U is differentiated with respect to x to give the i component, y to give the j component and z to give the k component of the vector.

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