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1.1 WORK, ENERGY AND POWER

At the end of this section you should be able to:  Describe and compute work done

 describe potential energy as energy due to position and derive potential energy as mgh

 describe kinetic energy as energy due to motion and derive kinetic energy as mv2

/2

 state conservation of energy laws and solve problems where energy is conserved

 define power as rate of energy transfer

1.1.1 Work done by a constant force

When the point at which a force acts moves, the force is said to have done work.

When the force is constant, the work done is defined as the product of the force and distance moved.

Consider the example in Figure 1, a force F acting at the angle q moves a body from point A to point

B.

Figure 1: Notation for work done by a force

The distance moved in the direction of the force is giveThe distance moved in the direction of the force is given by

So the work done by the force F is

If the body moves in the same direction as the force the angle is

0.0 so

Work done = Fs

Equation 1

When the angle is 90 then the work done is zero.

The SI units for work are Joules J (with force, F, in Newton's N and distance, s, in metres m).

Worked Example 1 : How much work is done when a force of 5 kN moves its point of application

600mm in the direction of the force.

Solution Worked Example 2 : Find the work done in raising 100 kg of water through a vertical distance of 3m.

Solution : The force is the weight of the water, so

1.1.2 Energy

A body which has the capacity to do work is said to possess energy.

For example, water in a reservoir is said to possesses energy as it could be used to drive a turbine

lower down the valley. There are many forms of energy e.g. electrical, chemical heat, nuclear,

mechanical etc.

The SI units are the same as those for work, Joules J. In this module only purely mechanical energy will be considered. This may be of two kinds, potential

and kinetic. 1.1.2.1 Potential Energy

There are different forms of potential energy two examples are: i) a pile driver raised ready to fall on

to its target possesses gravitational potential energy while (ii) a coiled spring which is compressed

possesses an internal potential energy.

Only gravitational potential energy will be considered here. It may be described as energy due to

position relative to a standard position (normally chosen to be the earth's surface.)

Explanation:

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