Work and Power

A definition of energy is the ability to do work.

We all know what work is in real life. But in terms of Physics, what is it?

When there is a force F acting upon a body over a distance d, then the force does work W according to the equation:

W = F.d

When a weight is lifted, it gains potential energy. Where does this energy come from?

The Law of Conservation of Energy states that energy cannot be created or destroyed. So when we lift something, we give energy to the object we are lifting, in the form of gravitational potential. We need to use the energy of our muscles to apply a force to counteract gravity in order to lift it up a distance. This force over a distance is called 'work'.

For example, if a man lifts a mass m of 100kg, a height h of 1m, he does work against the acceleration of gravity, g, which we can calculate from:

W = F.d = m.g.h = 100kg . 10m/s2 . 1m = 1000 N.m

The unit of work is N.m (newton-metre), and is equal to the unit of energy J, joule.

1000 J can be written as 1.0 kJ (kilojoule).

When work is done, energy is transformed. When a mass falls, its potential energy is converted to kinetic energy. The work done is the kinetic energy. When the mass hits the ground and all of its kinetic energy is converted to sound and thermal energy, then work is done to convert the kinetic energy to thermal and sound energy.

For example, a mass of 20 kg falls 2 metres. The work done is equal to the loss of potential energy:

W = Ep = mgh = 20.10.2 = 400 J (or N.m)

work done = energy transformed

Another important concept is Power.

Hamster Power: every action of applying a force will do work, and how quickly this is done is the power

When we use electricity, we use electrical power. Power can supply a force and energy to a machine (or any group of objects, which we can call 'a system').

Power is the amount of work done in a certain amount of time:

Power = Work/time, P = W/t

For example, if a man lifts 100kg a height of 1m, he does 1.0 kJ of work.

We can lift very large masses with a carjack because the work is spread over a long time period

If he does this over one second, he applies a Power of 1.0 kJ/s

The unit J/s has another name: watt. So in the above example, the man applies 1.0 kW (kilowatt) of power.

You must be careful not to confuse the symbol for work, W, with the unit for power, W (watt).

We need more power to do work in a shorter time

Even a single human can lift a large mass if the work is done over a long enough time period. To reduce power requirements in lifts and cranes, a system of pulleys ensures the force is applied over a long distance (less work per unit length of cable), and less power is required by extending the time the work is done over a longer time period.

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