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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?
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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