How long will it take? - a matter of power

Power is connected to duration

Suppose an electric motor is being used to lift a heavy load: it might, for example, be a fork-lift truck lifting up a heavy box in a warehouse. If the warehouse is busy, it's not difficult to imagine that it would be useful to know how long it takes to lift each box – too slow and the warehouse is likely to grind to a halt as lots of packages arrive.

This kind of problem is one that can be tackled in terms of energy or, more specifically, in terms of power. If the power supply (in watts) to the electric motor is known, then this gives the maximum rate at which energy can be shifted to lift the box.

For example, supposing that the power supply to the fork-lift lifting motor is 4 kilowatt and that a 200 kilogram box needs to be lifted through 4 metre.

The total energy needed to lift the box through 4 metre: energy = force × distance. Here this is gravity force  ×  height, so (m  ×  g)  ×  h. Put the numbers in, to get: (200 kilogram  ×  10 newton inverse kilogram)  ×  4 m, and do the calculation to get energy as 8000 J.

The lifting motor can supply 4000 joule second^-1.

So, the job of lifting the 200 kilogram box will take: 8000 joule4000 joule second^-1, which is 2 s.

This kind of calculation raises a number of interesting points.

It assumes that all of the power supplied to the motor is made available for lifting the box. In other words, the assumption being made is that the motor is 100 % efficient. This, in practice, won't be the case and, bearing this in mind, the figure of 2 seconds must be the minimum possible time for lifting the box. In practice, the job will take a little longer because some power is switched to heating pathways while the motor is working.

This is a good example of the way in which energy ideas can be used to find out what is possible without getting into the details of the underlying working. Here we have learned that the job can't possibly be done in less than 2 seconds and have arrived at this result without having to consider the detailed mechanism of how the lifting electric motor works. This is one of the strengths of using energy or power ideas in calculations.