Question

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

Answer 1

Hint: Recall that the work done is the displacement of any object under the influence of a force. Here, the force under consideration is the gravitational force, and the work done is against the acceleration due to gravity. Using this, determine the work done by both A and B. Following this, we know that the power is the rate at which this work is done and is dependent on the time taken to do this work. Using this determine the power of both A and B used in climbing the stairs and obtain a suitable comparison from their numerical values.

Formula used: Work done $W = mgs$
Power $P = \dfrac{W}{t}$

Complete step by step answer:
We have two persons A and B with masses $m_A = 50\;kg = m_B$, and the time they take to climb up the stairs is $t_A = 20\;s$ and $t_B = 15\;s$
(i)The work done by both the persons is against the gravitational force arising from their weight to climb up the stairs of height say h.
$W_A = F_{gravitational}h = m_A gh = 50gh\;Nm$, where g is the acceleration due to gravity.
$W_B = F_{gravitational}h = m_B gh = 50gh\;Nm$
Therefore, the work done by both A and B in climbing the stairs is the same.
(ii)The power developed by A and B in climbing up the stairs is defined as the rate at which the work is done.
$P_A = \dfrac{W_A}{t_A} = \dfrac{500gh}{20} = 25gh\;W$
$P_B = \dfrac{W_B}{t_B} = \dfrac{500gh}{15} = 33.33gh\;W$
Therefore, the power developed by B is more than the power developed by A since B climbs up the stairs quicker than A.

Note: Do not get confused between work, energy and power.
Work is said to be done when a force applied changes the state of rest or motion of an object. The SI unit of work is joules (J). It is usually given as:
$W = F.d$, where F is the force applied and d is the resulting displacement produced.
Energy of a body is defined as its capacity to do work or bring about a change in the state of the body. Its SI unit is joules (J).
Finally, power is defined as the rate at which the work is done or the rate at which the energy conversion from one form to the other takes place. Its SI unit is watts (W), and is usually defined as:
$P = \dfrac{W}{t}$, where t is the time taken to do the work.