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 m2s-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.

W=\Delta E_{trans}=\frac{1}{2}mv^{2}-\frac{1}{2}mu^{2}

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 m2s-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:

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


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