An electric pump is used to raise water from a well, as shown.The pump does work in raising 10 kg of the water through a vertical distance of 8.0 m in 5.0 s. Calculate the power the pump uses to raise the water.
Question
An electric pump is used to raise water from a well, as shown.The pump does work in raising 10 kg of the water through a vertical distance of 8.0 m in 5.0 s. Calculate the power the pump uses to raise the water.
Solution
To calculate the power used by the pump, we first need to calculate the work done by the pump.
Step 1: Calculate the work done Work done is given by the formula: Work = Force x Distance In this case, the force is the weight of the water, which is mass x gravity. Given that the mass of the water is 10 kg and the acceleration due to gravity is approximately 9.8 m/s², the force is 10 kg x 9.8 m/s² = 98 N. The distance is the height the water is lifted, which is 8.0 m. So, the work done = Force x Distance = 98 N x 8.0 m = 784 J (Joules)
Step 2: Calculate the power Power is the rate of doing work or the amount of work done per unit time. It is given by the formula: Power = Work / Time The work done is 784 J and the time is 5.0 s. So, the power = Work / Time = 784 J / 5.0 s = 156.8 W (Watts)
Therefore, the pump uses a power of 156.8 Watts to raise the water.
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