Potential and Kinetic Energy

These pages are going to be looking into specific and mostly understood/used forms of energy.  That of Potential and Kinetic energy.  These two  forms are evident in mechanical energy and are closely linked to each other. 

Potential energy is defined as:

So potential energy is what an object has when it is stationary, such as a  ball in a goal keepers hand.  As this ball is dropped it turns its potential energy into kinetic.

Kinetic energy is defined as:

For the next section the two will be separated and explained in more definite terms.  But to show the relation between the two the definitions are shown together.

Potential Energy

If a body of mass m kg is lifted through a vertical distance of h meters above the ground, work is done because the body being lifted against the gravitational force which acts on the body.  

The work done will be stored in the body as P.E and the body will be capable of doing mgh Joules of work if allowed to fall back to the ground.

This form of energy is often called gravitational potential energy because it is the energy of an object by virtue of moving against a gravitational force.

The unit of potential energy, as in all forms, is the joule.

PE possessed by body = mass x gravity x height 

Example

A body of mass 5kg is supported 12m above the ground.  Determine the potential energy possessed by the body due to its position with respect to the ground.

PE = mgh 

PE = 5 x 9.81 x 12 = 588.6J

Kinetic Energy

The energy a body possesses due to its velocity.

If a constant force F ‘N’ acts on a body of mass ‘m’, initially at rest and displaces it in a straight line through a distance ‘s’ meters, the work done is Fs Joules.

As kinetic energy is down to the velocity of an object it follows from potential.   As an object falls or moves due to a force from stationary then the potential energy transforms into kinetic.  Take this football. Stationary it has potential and no kinetic, as it starts to fall the potential starts to change to kinetic, by the time it hits the floor the potential has completely transformed into kinetic.  It is a sliding exchange.

The equation for Kinetic energy has more to it than potential but is easily remembered.

If ‘a’ m/s2 is the acceleration produced then Newton’s Law can be used.

Accelerating Force = ma

Work done = (ma) x s

If the velocity reached in a distance ‘s’ meters is ‘v’ m/s then from linear motion equation   

( since u=0) w substitute for ‘s’ in the work done equation.

Example


A motor vehicle of mass 2 tonne is travelling at 50.4 kmh.  Determine the kinetic energy of the vehicle at this speed.

V= 50.4/3.6 = 14m/s

KE= 0.5 x 2000x142  

KE=  196000J  

KE=196KJ