|The Open Door Web Site|
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
If a force acts on a body then the body is said to possess potential energy.
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.
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
the spring has not been exceeded (Hooke’s
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
Notice that the work done stretching the spring is equal to the area under the graph.