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Question
An unruly demonstrator lifts a stone of mass 200 g from the ground and throws it at his opponent. At the time of projection, the stone is 150 cm above the ground and has a speed of 3 m/s. Calculate the work done by the demonstrator during the process. If it takes one second for the demonstrator to lift the stone and throw it, what horsepower does he use?
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Solution
\[\text{ Given } , \]
\[\text{ Mass of the stone, m = 200 g = 0 . 2 kg } \]
\[\text{ Heightto which the stoneis lifted, h = 150 cm = 1 . 5 m } \]
\[\text{ Velocity of the projection, } \nu = 3 \text{ m/s } \]
\[\text{ Time, t = 1 s } \]
\[\text{ Total work done, W = K . E . + P . E . } \]
\[\text{ W } = \frac{1}{2}\text{ m } \nu^2 + \text{ mgh } \]
\[ = \left( \frac{1}{2} \right) \times \left( 0 . 2 \right) \times 9 + \left( 0 . 2 \right) \left( 9 . 8 \right) \times \left( 1 . 5 \right)\]
\[ = 3 . 84 \text{ J } \]
1 hp = 764 watt
Horsepower used by demonstrator
\[= \frac{3 . 84}{746} = \left( 5 . 14 \right) \times {10}^{- 3}\]
Therefore, power used by the demonstrator to lift and throw the stone is 5.14 × 10-3 hp.
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