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Lesson 12 of 13
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# Power

Often it is interesting to know not only the work done on an object, but also the rate at which this work is done. We say a person is physically fit if he not only climbs four floors of a building but climbs them fast. Power is defined as the time rate at which work is done or energy is transferred.

The average power of a force is defined as the ratio of work, W, to the total time t taken

Pav = W/t

The instantaneous power is defined as the limiting value of the average power is defined as the limiting value of the average power as time interval approaches zero.

P = dW/dt ………………………………………………………………….(21)

The work dW done by a force F for a displacement dr is dW = F.dr. The instantaneous power can also be expressed as

P =F.dr/dt

=F.v …………………………………………………………………………………..(22)

where v is the instantaneous velocity when the force is F.

Power, like work and energy, is a scalar quantity. Its dimensions are [ML2T-3]. In the SI, its unit is called watt (W). The watt is 1 J s-1. The unit of power is named after James Watt, one of the innovators of the steam engine in the eighteenth century.

There is another unit of power, namely the horse-power (hp)

1 hp = 746 W

This unit is still used to describe the output of automobiles, motorbikes etc.

We encounter the unit watt when we buy electrical goods such as bulbs, heaters and refrigerators. A 100 watt bulb which is on for 10 hours uses 1 kilowatt hour (kWh) of energy.

100 (watt) × 10 (hour) = 1000 watt hour

= 1 kilowatt hour (kWh)

= 103 (W) × 3600 (s)

=3.6 × 103 J

Our electricity bills carry the energy consumption in kWh. Note that kWh is a unit of energy and not power.

Example 11
An elevator can carry a maximum load of 1800 kg (elevator + passengers) is moving up with a constant speed of 2 m s-1. The frictional force opposing the motion is 4000N. Determine the minimum power delivered by the motor to the elevator in watts as well as in horse power. 