First slide

Power

Question

A crane is used to lift 10,000 kg of coal from a mine 100 meter deep. Time taken by the crane is one hour. Assuming the efficiency of the crane to be 80%, the power of the crane in kW is

Easy

A

0.340
B

3.403
C

34.03
D

4.303

Solution

$Power = \frac{W}{t} = \frac{m g h}{t} = \frac{(10000 \times 9 \cdot 8 \times 100) J}{3600 s e c} = \frac{98 \times 10^{3}}{36} J / s = \frac{98}{36} k W η = \frac{Output}{Input} or Input = \frac{Output}{η} ∴ Input = \frac{98}{36} \times \frac{100}{80} = 3 .403 k W$

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