Kinetic and potential energy

(a) Kinetic energy:



Kinetic energy (k.e.) is the energy a body has because of its motion. For example, in a traffic collision a moving car does work against the resistance of the metal of another car into which it has driven. An expression for kinetic energy can be obtained by calculating the amount of energy transferred from the body while it is being brought to rest.

Consider a body of constant mass m moving with velocity u. Let a constant force F act on it and bring it to rest in a distance s. Since the final velocity is 0, from SUVAT v^2 = u^2 + 2as, therefore ''a = -u^2/2s. The negative sign shows that the acceleration is acting in the opposite direction to u. The acceleration in the direction of F is therefore +u^2/2s. The original kinetic energy of the body equals the work W it does against F, ''that is, the energy transferred in being brought to rest.

Kinetic energy of body = W = Fs = mas (since F=ma) = ms*u^2/2s (since a=u^2/2s)

Therefore k.e. = 0.5mu^2

Conversely, if work is done on a body the gain of kinetic energy when its velocity increases from zero to u can be shown to be ''0.5mu^2. In general, if the velocity of a body of mass m increases from u to v when work is done on it by a force F acting over a distance s, ''then

Fs = 0.5mv^2 - 0.5mu^2

This is the work-energy equation and may be stated as work done by forces acting on the body = change in kinetic energy of the body.

(b) Potential energy:

Potential energy (p.e.) is the energy a system of bodies has due to its position in a field. It arises when a body experiences a force in a field such as the earth's gravitational field. In that case the body occupies a position with respect to the earth and the potential energy is regarded as a joint property of the body-earth system and not of either body separately. The relative positions of the parts of the system, i.e. of the body and earth, determine its potential energy; the greater the separation the greater the potential energy.

Gravitational potential energy-

Work done by external force against gravity = Fs.

s can be represented by h, signifying the height a body is above the earth. The force follows Newton's 2nd law F=ma, where m is the mass of the body and a=g, see acceleration due to gravity. Therefore:

Gravitational potential energy = mgh

On returning to gorund level an amount of potential energy equal to mgh would be transferred. A good example of this occurs when the water in a mountain resevoir falls to a lower level and does work by driving a power station turbine.