Energy is the capacity a thing has to do work
Power is the rate of work being done
The work energy principle:
This is derived from the conservation of energy principle.
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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