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Mechanics Kinetic Energy A body in motion possesses kinetic energy. The kinetic energy possessed by a body depends on its mass and its speed. Consider a body of mass, m, being given kinetic energy by a force of magnitude F.
If the body starts from rest (as in the example above) then
K.E. gained by the body = work done during acceleration
If we ignore friction and air resistance then, F = ma and so
therefore
Potential Energy If a force acts on a body then the body is said to possess potential energy. Examples A mass in a gravitational field possesses gravitational potential energy. A stretched spring possesses elastic potential energy. A charged body in an electric field possesses electrical potential energy. Gravitational Potential Energy Consider a body of mass m being lifted a short distance near the earth’s surface, at constant speed.
The increase in the G.P.E. is equal to the work done moving the body from A to B.
This equation
Elastic Potential Energy Consider a spring being extended by a steadily increasing force. When the force has a magnitude F, the extension is x.
A graph of force against
extension would be a straight line passing through the origin,
as long as the
elastic limit
of
the spring has not been exceeded (Hooke’s
law).
The slope of the graph is k, the elastic constant of the spring. F = kx The work done increasing the length of the spring by x is given by w = average force × extension
So, the elastic potential energy stored in the spring is given by
N.B. Notice that the work done stretching the spring is equal to the area under the graph. 
