Power is the Rate of Change of Energy

There are two booklets available on physbang.com to help you revise the equations that you are expected to know by the end of Y10. These booklets were posted a few months ago (click here to read that post and download the booklets) but it has since been pointed out that one equation is missing: sorry about that!

I will update the booklets shortly but, for now, here is the extra piece of information that you need to answer some of the revision questions…

Power is the rate of change of energy.

What does that mean?

When we talk about the “rate” of something, we mean how it changes with time. For example, the rate of change of distance tells you how the distance (travelled by an object) changes with time. You may spot that this is the same thing as speed, which we calculate by taking the change in distance and dividing that number by the change in time. If the object moves ten metres in five seconds then we say that its speed is two metres-per-second (2 m/s). And that also means its rate of change of distance is 2 m/s.

Although this may sound like confusing words, the rate of change concept is a really important idea in physics – so it would be good to go back and read that explanation again if you aren’t sure about the speed example given above.

All this talk about change may also make you think of gravitational potential energy, where we even introduced the delta symbol to emphasise the importance of change (there is a separate post about that too: click here to read it).

Now let’s go back to power… it is defined as the rate of change of energy so that means we calculate it by taking the amount of energy transferred and divide that by the time taken to transfer the energy. As an equation, we would write the following;

Power ( W ) = Energy ( J ) / Time ( s )

Note the correct SI units; power is measured in watts (although sometimes you might see it written as joules-per-second, or J/s). Obviously, to get an answer in watts (or J/s) you must make sure that the energy transferred is measured in joules (J) and the time taken is converted (if necessary) into seconds (s).

A very important aspect of this equation is tested in exam questions that ask something like; “Explain whether the amount of energy required to lift a pile of bricks through a certain height depends on the time taken to complete the lift.”

The answer should refer to the fact that the energy required to lift an object depends only on the height change and the weight of the object (in newtons, remember – NOT in kilograms as that’s a mass, not a weight). There is no mention of time in that sentence so clearly the time does not matter. But if you were pulling the object up on a rope and you tried to do it quicker, you know it would be harder – so surely time does matter after all… doesn’t it?

No.

The time taken does not affect the energy transferred but it does affect the power needed.

• Energy tells you what happened.
• Power tells you how quickly it happened.

There is another post about this idea if you want to read all of this explained in a slightly different way. Click here to see the alternative version!