# Definition of Power

Question 1: If two people each carry a weight of 50 N up the same hill, which one does more work?

Question 2: What if one of them does it in 1 hour and the other takes 2 hours?

The answer to both of the questions above is that they both do the same amount of work. They both carry the same mass, m, through the same height, h, so both do

Work done = mgh

In the second question, however, the first person completes the work more quickly. They did more work per second. We say that they were more powerful.

Definition: Power is defined as the rate at which work is done.
Power = Work done/Time taken

It can also be defined as the rate at which energy is converted from one form into another.

Power is a scalar quantity and its unit is the watt (W).

From the definition it follows that one watt is equivalent to one joule per second;

1 W = 1 J s-1

Since Power = Work/Time and Work = Fs, another useful equation can be derived:

Time
=> Power = Fs/t But v = s/t
=>  Power = Force × Velocity
remembering that the force and velocity must be in the same direction.

##### Worked examples

Question 1

Dorothy works on a building site. She is lifting a bucket full of cement up to the top of a building using a rope. The cement weighs 200 N and the building is 12 m high:

a) How much energy is needed to lift the bucket?

b) Dorothy takes 10 seconds to lift the bucket - how much power does she develop?

Solution:

a) Energy needed = work done = 200 × 12 = 2400J

b) Power = 2400 ÷ 10 = 240 W

Question 2

Jack is stacking tins of soup onto shelves in the supermarket.
Each tin of soup weighs 5 N. If the shelf is 1.5 m high:

a) How much energy is needed to lift one tin from the floor to the shelf?

b) A case of soup contains 144 tins. How much energy is needed to stack a case full of soup?

c) Jack has to stack three cases of soup. He does this in 10 minutes(600 s). How much power does he develop

Solutions:

a)5 × 1.5 = 7.5 J

b)7.5 × 144 = 1080 J

c)(3 × 1080) ÷ 600 = 5.4 W

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