Power can be defined as the time rate of doing work. This means that how much power expended by a body depends on how much work is done and how fast it is done.
If two men of the same weight are to lift a load of 50kg up a flight of stairs of the same height, the man who gets to the top of the stairs first has the greater power. This is because
he was able to lift the load (doing work) through the flight of stairs at a shorter time than the other man. Power explains how fast or slow work is done.Mathematically,
Power = work done or energy utilized / time taken to do work
The unit of Power is the Watts when work done is measured in
Joules and the time taken is measured in seconds.
Note: 1 Watt is the same as 1 Joule per second. Other units
of power commonly used are the Kilowatts (kW), the megawatt (MW) and the horse
power (h.p.).
Examples:
1. A man of mass 40kg ascends a flight of stairs 5m high in
5 seconds. If acceleration due to gravity is 10m/s2, calculate the
power expended?
Solution: Power = Energy expended/ time
=
m x g x h / time
=
40 x 10 x 5 / 5
=
2000/5
=
400 Watts
2. A boy weighing 300N runs up a flight of stairs consisting
of 20 steps each 10cm high in 10 seconds. What is his power?
Solution: Force
= 300N Distance =
20steps x 10cm
= 20 x 0.1m = 2m
Power = Work done / time
= Force x
distance / time
= 300 x 2
/ 10
= 600 / 10
= 60
Watts
3. Find the electrical energy expended by an electric lamp
labelled 100W in 8 seconds.
Solution:
Power = Energy expended / time
100W = Energy expended / 8secs
Energy expended = 100W x 8secs
= 800Joules
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