8.2 Power

Power

Now that we understand the relationship between work and energy, we are ready to look at a quantity that defines how long it takes for a certain amount of work to be done. For example, a mother pushing a trolley full of groceries can take 30 s or 60 s to push the trolley down an aisle. She does the same amount of work, but takes a different length of time. We use the idea of power to describe the rate at which work is done.

Power

Power is defined as the rate at which work is done or the rate at which energy is expended. The mathematical definition for power is:

$$P=F·v$$

[link] is easily derived from the definition of work. We know that:

However, power is defined as the rate at which work is done. Therefore,

This can be written as:

The unit of power is watt (symbol W).

Investigation : watt

Show that the W is equivalent to $\mathrm{J}·{\mathrm{s}}^{-1}$ .

Research project : james watt

Write a short report 5 pages on the life of James Watt describing his many other inventions.

Machines are designed and built to do work on objects. All machines usually have a power rating. The power rating indicates the rate at which that machine can do work upon other objects.

A car engine is an example of a machine which is given a power rating. The power rating relates to how rapidly the car can accelerate. Suppose that a 50 kW engine could accelerate the car from 0  $\mathrm{km}·{\mathrm{hr}}^{-1}$ to 60 $\mathrm{km}·{\mathrm{hr}}^{-1}$ in 16 s. Then a car with four times the power rating (i.e. 200 kW) could do the same amount of work in a quarter of the time. That is, a 200 kW engine could accelerate the same car from 0  $\mathrm{km}·{\mathrm{hr}}^{-1}$ to 60 $\mathrm{km}·{\mathrm{hr}}^{-1}$ in 4 s.