Energy is not Power!

Suppose that two identical twins decide to go upstairs in their house: one twin runs up the stairs whereas the other twin walks up the stairs. Which twin transfers the greatest amount of energy?

Almost everybody says the twin who runs transfers more energy because she goes faster. This is a common misconception.

In fact, both twins transfer exactly the same amount of energy. The reason can be explained in two ways;

1. The running twin expends energy at a faster rate but for less time (because it takes less time to run up the stairs) whereas the walking twin expends less energy for a longer time. So the total amount of energy transferred is the same.
2. The change in the system is exactly the same for both twins: they both started at the foot of the stairs and they both finished at the top of the stairs. As such, they both gained the same amount of gravitational potential energy.

However, there is an important and measurable difference between running and walking up a flight of stairs. The difference is power, which is defined by the equation;

power ( W ) = energy transferred ( J ) / time taken ( s )

Let’s say that the twins both have a mass of 50 kg and that we can take the gravitational field strength to be 10 N/kg. This means each twin has a weight of 500 N.

If the height change when climbing the stairs is 3 m then the change in gravitational energy is 1500 J. (Remember that you can also carry out this calculation using the equation for work done. To remind yourself about that approach, click here.)

The twin who runs might take 5.0 s and the twin who walks might take 7.5 s.

The power for the running twin is therefore 300 W (1500 / 5.0) whereas the power for the walking twin is 200 W (1500 / 7.5).

It is important to realise that the energy transferred is dependent on the initial and final states of the object whereas the power is dependent on the time taken for the transition between the states.