An agitated protester lifts a stone of mass 200 g from the ground...

An agitated protester lifts a stone of mass

200 \text{ g}

from the ground and throws it at an opponent. At the instant of projection, the stone is

150 \text{ cm}

above the ground and possesses a speed of

3.00 \text{ m/s}

. Determine the work done by the protester during this process. If the protester takes one second to lift and throw the stone, what horsepower is utilized?

Options

A $3.84 \text{ J}$ , $3.84 \text{ hp}$
B $3.84 \text{ J}$ , $5.14 \times 10^{-3} \text{ hp}$
C $0.90 \text{ J}$ , $1.21 \times 10^{-3} \text{ hp}$
D $2.94 \text{ J}$ , $3.94 \times 10^{-3} \text{ hp}$

Correct answer

B. $3.84 \text{ J}$ , $5.14 \times 10^{-3} \text{ hp}$

Step-by-step solution

Mass of the stone,

m = 200 \text{ g} = 0.2 \text{ kg}

Height of projection,

h = 150 \text{ cm} = 1.5 \text{ m}

Speed of projection,

v = 3.00 \text{ m/s}

Time taken,

t = 1 \text{ s}

The work done by the protester is equal to the total mechanical energy imparted to the stone.

W = \Delta K + \Delta U

W = \dfrac{1}{2}mv^2 + mgh

W = \dfrac{1}{2}(0.2)(3.00)^2 + (0.2)(9.8)(1.5)

W = 0.9 + 2.94 = 3.84 \text{ J}

Power utilized is the work done per unit time.

P = \dfrac{W}{t} = \dfrac{3.84}{1} = 3.84 \text{ W}

Since

1 \text{ hp} = 746 \text{ W}

, the power in horsepower is:

P = \dfrac{3.84}{746} \text{ hp} \approx 5.14 \times 10^{-3} \text{ hp}

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