# Episode 218: Mechanical power

Power is the rate at which work is done, i.e. the rate at which energy is transferred by a force. It is likely that your students will be familiar with this definition. They may also have studied power in an electrical context.

Many of the practical activities suggested earlier in this topic could readily be adapted to relate to power; simply measure the time during which a force acts, and calculate:

Power = work done / time taken.

**Summary**

- Discussion: The meaning of power (10 minutes)
- Worked example: A sample calculation; power = force × velocity (10 minutes)
- Student experiment: Simple measurements of human power (20 minutes)
- Student questions: Practice calculations (20 minutes)

**Discussion: The meaning of power**Give the definition of power – this will probably be revision for your students. Ask for the unit (watt, W) and its relationship to SI base units

(1 W = 1 kg m^{2} s^{-3}).

**Worked example: A sample calculation; power = force × velocity.**

A car engine provides a forward force of 1000 N. If the car is travelling at 20 m s^{-1}, what power is developed?

In 1 s, the car travels 20 m. Hence we can calculate:

Work done in 1 s = force × distance = 1000 N × 20 m = 20 000 J = 20 kJ

Power = work done / time taken = 20 kJ / 1 s = 20 kW.

From this example, you can point out that we could equally have used an alternative form of the equation for power:

Power = force × velocity

e.g. Power = work done / time taken = (force × distance (in direction of the force))/ time taken

Distance (in the direction of the force) / time taken = velocity

so power = force × velocity.

(However, this only works if the velocity is steady, i.e. the ‘force’ is NOT the resultant force on the moving object.)

**Student experiment: Simple measurements of human power**

Students can perform various physical activities, for example lifting measured weights, and deduce their useful output power, using a stop watch. (Note that the human body is not very efficient in these activities, so the actual power dissipated by the student will be considerably greater than deduced here.)

This is included as it is possible that some of your students are less than confident in this area. It is expected that the majority of students will have already covered this ground.

Episode 218-1: Power of a pupil - running upstairs (Word, 39 KB)

**Student questions: Practice calculations**

The first questions are warm–up exercises which should give students confidence. Note that the first question makes the connection between power, force and velocity (power = force × velocity).

Episode 218-2: Mechanical power (Word, 26 KB)

Episode 218-3: Work out with a cycle (Word, 114 KB)

**Download this episode**

Episode 218: Mechanical power (Word, 164 KB)