Do all of us work at the same rate? Do machines consume or transfer energy at the same rate? Agents that transfer energy do work at different rates. Let us understand this from the following activity:
♦ Consider two children, say A and B. Let us say they weigh the same. Both start climbing up a rope separately. Both reach a height of `8 m`. Let us say A takes `15 s` while B takes `20 s` to accomplish the task.
♦ What is the work done by each?
♦ The work done is the same. However, A has taken less time than B to do the work.
♦ Who has done more work in a given time, say in `1 s`?
A stronger person may do certain work in relatively less time. A more powerful vehicle would complete a journey in a shorter time than a less powerful one.
We talk of the power of machines like motorbikes and motorcars. The speed with which these vehicles change energy or do work is a basis for their classification.
Power measures the speed of work done, that is, how fast or slow work is done. Power is defined as the rate of doing work or the rate of transfer of energy. If an agent does a work W in time t, then power is given by:
Power = work/time
or ` P = W/t` ..........(11.8)
The unit of power is watt having the symbol `W`. `1` watt is the power of an agent, which does work at the rate of `1` joule per second. We can also say that power is `1` W when the rate of consumption of energy is `1 J s^(–1)`.
`1` watt `= 1` joule/second or `1 W = 1 J s^(–1)`. We express larger rates of energy transfer in kilowatts (kW).
`1` kilowatt `= 1000` watts
`1` kW `= 1000 W`
`1 ` kW `= 1000 J s^(–1)`.
The power of an agent may vary with time. This means that the agent may be doing work at different rates at different intervals of time. Therefore the concept of average power is useful. We obtain average power by dividing the total energy consumed by the total time taken.