A pump is required to raise 600 litres of fresh water a vertical distance of 120 m. If the efficiency of the pump is 45%, how much work must be done on the pump to raise the water?

To determine the amount of work that needs to be done on the pump to raise 600 litres of water a vertical distance of 120 meters with an efficiency of 45%, we first need to calculate the potential energy required to lift the water.

The potential energy (PE) required can be calculated using the formula:

[ PE = m \cdot g \cdot h ]

where:

• ( m ) is the mass of the water in kilograms,

• ( g ) is the acceleration due to gravity (approximately 9.81 m/s²),

• ( h ) is the height in meters.

Since 1 litre of water has a mass of approximately 1 kg, 600 litres of water will have a mass of 600 kg. We can now plug in the values:

[ PE = 600 , \text{kg} \cdot 9.81 , \text{m/s}^2 \cdot 120 , \text{m} ]

[ PE = 600 \cdot 9.81 \cdot 120 = 705720 , \text{J} = 705.72 , \text{kJ} ]

However,