Question

What is the power of a pump which takes 10 seconds to lift 100 kg of water to a water tank situated at a height of 20 m? ($g=10m{s}^{-2}$) [2 MARKS]

Answer 1

Each point: 1 Mark

1. In this problem first of all we have to calculate the work done by the pump in lifting the water against the force of gravity. We know that the work done against gravity is given by the formula:

$W=m\times g\times h$

Here, Mass of water, $m=100kg$

Acceleration due to gravity, $g=10m{s}^{-2}$

And, Height, $h=20m$

So, putting these values in the above formula, we get:

Work done, $W=100\times 10\times 20$

$=20000J$
$=20KJ$

And, Time taken, $t=10s$

2. Now, we know that:

Power, $P=\frac{W}{t}$

$\frac{20000}{10}$

$=2000watts$ (or 2000 W)

Thus, the power of this pump is 2000 watts. This power can be converted from watts into kilowatts by dividing it by 1000.

So, $Power=\frac{2000}{1000}kilowatts$

$=2kilowatts$ (or 2 kW)