It takes 20 s for a person A of mass 50 kg to climb up the stairs, while another person B of same mass does the same in 15 s.Compare the (i) work done, and (ii) power developed by the persons A and B.

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Solution

Let h be the height of the staircase climbed by A and B. Let m_A is the weight of A and m_B is the weight of B.

Work done by A to climb the Staircase, $W_{A} = m_{A} \times g \times$ h Joules

Work done by B to climb the Staircase $W_{B} = m_{B} \times g \times$ h Joules

(a)Hence the ratio $\frac{W_{A}}{W_{B}} = \frac{m_{A}}{m_{B}} = 1$ (Because masses are same)
Power developed by A, $P_{A} = \frac{(m_{A} \times g \times h)}{20}$ watts
Power developed by B, $P_{B} = \frac{(m_{B} \times g \times h)}{15}$ watts

(B)Power ratio $\frac{P_{A}}{P_{B}} = \frac{(15 m_{A})}{(20 m_{B})} = \frac{(3 m_{A})}{(4 m_{B})} = \frac{3}{4}$

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Standard IX Physics

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