Kinetic Energy 

A body in motion possesses energy. This is called kinetic energy. 



This statement is supported by the fact that the body can do
work at the expense of its motion. 

Wind passing through a wind turbine slows down and as a result
we can obtain electrical energy from the generator driven by the
turbine. 



Remember that "motion" is a relative concept; see the
relativity section for
more discussion of this idea. In what follows here we will assume that any
speeds are measured relative to some local reference body, usually the earth. 

In order to find the quantity of energy possessed by a moving body, we find
how much work we have to do to get the body moving at the speed it
has. 



Consider a car being accelerated from rest to speed v in a distance s, as shown
below . 



For a body starting from rest we have: 





Kinetic energy (KE) gained by the body = work done causing it to accelerate. 

work done = force × displacement 

If the force used to acceleration the car was (on average) of magnitude F then
(if we ignore friction and air resistance) we can say that F = ma. So, we have 



Therefore 



Potential Energy 

If a force acts on a body then the body is said to possess potential energy. 

For example: 

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. 

The potential energy possessed by a body is equal to the work done putting it
into its "energetic state". 



Gravitational Potential Energy 

Consider a body of mass m being lifted a short distance, h,
near the earth's surface, at constant speed. 







At position B the body possesses
more GPE because work has been done (against the force of gravity)
lifting it from A to B 
At position A the body possesses GPE (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. 

If, as stated, the body is lifted at constant speed through the height
h then, the force needed to do the work against gravity must be exactly equal in
magnitude (and opposite in sense) to mg. 

Work done = force × displacement 

Therefore the change in GPE (written ∆ GPE) is simply given by 





This equation is, of course, only useful if the distance h is small enough to
consider that the magnitude of the gravitational field strength, g does not
significantly change. 
