## Work, Energy and Power

The **energy** of a system is a measure of its capacity to do work.

**Kinetic energy** is the energy a body has by virtue of its motion.

Notice that translational kinetic energy is defined in terms of *speed* rather than velocity, ie it does not depend on direction.

Since mass is kg, and speed is ms^{-1}, the unit for energy is kg x ms^{-1} x ms^{-1}:

1 joule = i J = 1 kg m^{2}s^{-2}

The **work done** on a body by any force is the energy transferred to or from that body by the action of the force.

Notice that work can be *negative*, ie causing the body to slow down.

The equations of uniformly accelerated motion tell us that:

and since

it follows that

Multiplying both sides by m and dividing by 2 we get:

And therefore

Note about units: The joule is kg m

^{2}s^{-2}and the N is 1 kg m s^{-2}. So 1 joule is 1 N m.

The scalar product (dot product) of two vectors **a** and **b** is:

$latex \mathbf{a\cdot b}=ab\cos \theta $

An equivalent expression is:

$latex \mathbf{a\cdot b}=a_{x}b_{x}+a_{y}b_{y}+a_{z}b_{z}$

Which implies that:

$latex \cos \theta=\frac{a_{x}b_{x}+a_{y}b_{y}+a_{z}b_{z}}{ab}$