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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

v = 2as or v/2 = as

K.E. gained by the body = work done during acceleration

K.E. = Fs

If we ignore friction and air resistance then, F = ma and so

K.E. = mas

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 earths surface, at constant speed.

At B:

the body possesses more G.P.E. than it did at A because work has been done lifting it.

 

At A:

the body possesses G.P.E. because the force of gravity acts on it.

 

The increase in the G.P.E. is equal to the work done moving the body from A to B.

G.P.E. gained = force distance moved
= mgh

DELTA03 G.P.E. = mgh

This equation

i) only tells us the change in G.P.E. of the body and
ii) is only useful if h is small enough for us to consider that g is constant.

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 (Hookes 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

Therefore

w = Fx = kx

So, the elastic potential energy stored in the spring is given by

E.P.E. = kx

N.B.

Notice that the work done stretching the spring is equal to the area under the graph.

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