First slide

Power

Question

An engine pumps up 100 kg of water through a height of 10 m in 5 s. Given that the efficiency of the engine is 60% . If $g = 10 {ms}^{- 2}$ , the power of the engine is

Moderate

A

3.3 kW
B

0.33 kW
C

0.033 kW
D

33 kW

Solution

Work output of engine = mgh = $100 \times 10 \times 10 = 10^{4} J$
Efficiency ( $η$ ) = $\frac{output}{input}$ $∴$ Input energy = $\frac{output}{η}$
$= \frac{10^{4}}{60} \times 100 = \frac{10^{5}}{6} J$
$∴$ Power = $\frac{input energy}{time} = \frac{10^{5} / 6}{5} = \frac{10^{5}}{30} = 3 .3 kW$

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