A man raises a box of mass 50kg to a height of 2m in 20s, while another man raises the same box to the same height in 50s.

(a) Compare: (i) the work done, (ii) the power developed by them.

(b) Calculate the (i) the work done, (ii) the power developed by each man.

Take g = 10N kg^-1.

(a)

(i) Work done = force x displacement

Hence, work done is same for both men as both carry 50 kg weight to a height of 2m.

Therefore,

Work done by first man : Work done by second man = 1 : 1

(ii)

Let the work done by both men be W.

$\text{Power} = \dfrac{\text{work done}}{\text{time}} \\[1em] \dfrac{\text{Power developed by Man A}}{\text{Power developed by Man B}} \\[1em] = \dfrac{\dfrac{\text{work done by Man A}}{\text{time taken by Man A}}}{\dfrac{\text{work done by Man B}}{\text{time taken by Man B}}} \\[1em] = \dfrac{\dfrac{W}{20}}{\dfrac{W}{50}} \\[1em] = \dfrac{5}{2}$

Power developed by Man A : Power developed by Man B = 5:2

(b)

(i) As we know,

W = F x S = mgh

$W = 50 \times 10 \times 2 = 1000 J \\[0.5em] \Rightarrow W = 1000 J \\[0.5em]$

(ii) Power developed by Man A

$P = \dfrac{1000}{20} \\[0.5em] \Rightarrow P = 50 W\\[0.5em]$

Power developed by Man B

$P = \dfrac{1000}{50} \\[0.5em] \Rightarrow P = 20 W\\[0.5em]$