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Question
In a factory, 2000 kg of metal needs to be lifted by an engine through a distance of 12 m in 1 minute. Find the minimum horsepower of the engine to be used.
Solution
Given:
Mass of the metal,
m = 2000 kg
Distance, s = 12 m
Time taken, t = 1 minute = 60 s
Force applied by the engine to lift the metal,
F = mg
\[\text{ So, work done by the engine, } \]
\[\text{ W = F } \times \text{ s} \times \cos \theta = \text{ mgs } \times \cos 0^\circ[ \theta = 0^\circ \text{ for minimum force } ]\]
\[ = 2000 \times 10 \times 12\]
\[ = 240000\text{ J } \]
\[\text{ So, power exerted by the engine, }\]
\[\text{ P } = \frac{\text{ W }}{\text{ t } }\]
\[ = \frac{240000}{60} = 4000 \text{ watt } \]
\[\text{ Power in hp, } \]
\[\text{ P} = \frac{4000}{746} = 5 . 3 \text{ hp } \]
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