Question

Calculate the power of a pump which can lift 100kg of water through a vertical height of 5m in 20s

Answer 1

To calculate the power of the pump, we will use the formula:

Power = (Work done) / (time)

First, we need to calculate the work done by the pump. The work done is given by the equation:

Work = force x distance

The force is the weight of the water being lifted, which is equal to its mass times the acceleration due to gravity:

Force = mass x gravity
Force = 100 kg x 9.8 m/s^2 (approximately)

The distance is the height that the water is lifted:

Distance = 5 m

Now we can calculate the work done:

Work = Force x Distance
Work = (100 kg x 9.8 m/s^2) x 5 m

Next, we need to convert the work to joules. 1 Joule (J) is equal to 1 Newton-meter (N*m). Therefore, the work done will be in Joules.

Work (in joules) = Work (in Newtons) x Distance

To convert from kg.m/s^2 to Newtons (N), we use the equation 1N = 1 kg.m/s^2:

Work (in joules) = (100 kg x 9.8 m/s^2) x 5 m

Finally, we can calculate the power:

Power = Work / (time)
Power = Work / 20s

Substitute the values:

Power = [(100 kg x 9.8 m/s^2) x 5 m] / 20s

Calculating this expression will give you the power of the pump in watts (W).