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?

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?

• A. 1570 GJ
• B. 1570 MJ
• C. 1570 kJ
• D. 1570 J

Answer: (C)

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,

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,