Work, energy and power

(a) Work:

When we think of work, we think of jobs, chores, toils. We generally think of something that is hard to do, e.g holding a heavy weight above the ground. However the scientific definiton for work is much more specific and is that work is only done when a force is applied to an object over a specific distance, i.e.

Work is done when a force moves its point of application along the direction of its line of action.

In the simple case, when a constant force F and the displacement s are in the same direction and we define the work W  done by the force on the body by W= Fs

For the above example of holding the weight above the ground, even if it may feel as if a lot of work is being done, because no force is acting on the weight and it isn't being moved; in scientific terms no work whatsover is being done.

If the force does not act in the direction in which the motion occurs but at angle θ to it then the work done is defined as the product of the component of the force in the direction of motion and the displacement in that direction. That is, 'W= (F cos θ)s. 'See animation above: (when it is on the work part!)

When θ= 0, cos θ= 1 and so W= Fs, is at its maximum. When θ= 90, cos θ= 0 and F has no component in the direction of motion and so no work is done. When a body is thrown as a projectile the action of gravity does no work on the horizontal component of the throw, because it is acting at right angles.

If the force varies, the work done can be obtained from a force-displacement graph in which the component of the force in the direction of the displacement is plotted.

'One joule is the work done by a force of 1 newton when its point of application moves through a distance of 1 metre in the direction of the force. 'Thus: 1 joule (J) = 1 newton metre (Nm).

Work is scalar although force and displacement are both vectors. This means work is the same quantity if the same force is acted over the same distance in any direction.

(b) Energy:

If a body is able to do work, it is said to have energy. It requires energy to move a body over a distance, if we had to energy no movement would occur. It is measured in joules like work. When an interchange of energy occurs between two bodies we can consider '''the work done as measuring the quantity of energy transferred between them. '''So if body A does 5 joules of work on body B then the energy transfer from A to B is 5 joules.

(c) Power:

The power of a machine is the rate at which it does work, i.e. the rate at which it transfers energy. The unit of power is the watt (W) and equals a rate of transfer of 1 joule per second, i.e. 1W = 1 Js^-1.

In calculus notation, since power P is the rate at which work W is done or energy transferred, we can write

P = dW/dt

If δw is the energy transferred by a constant force F when a body moves with constant velocity v through a small displacement δs in time δt, then δW = F*δs and P  is given by

P= Fδs/δt = Fv

If F is in N and v in ms^-1, the unit of P is Nms^-1, or Js^-1, or W.