Question

Two girls ,each of weight 400 N climb up a rope through a height of 8m. We name one of girls A and the other B . Girl A takes 20 s while B takes 50 s to accomplish this task. what is the power expended by each girl.​

Answer 1

Solution :

(1) Power expended by girl A :

Weight of the girl, mg = 400 N

Displacement ( height), h = 8 m

Time taken, t = 20 s

From Eq. ( 11.8 ),

Power, P = Work done / time taken

$= \: \frac{mgh}{t} \\ \\ = \: \frac{400 \: N \: \times \: 8 \: m}{20 \: s} \\ \\ = \: 160 \: W.$

(2) Power expended by girl B:

Weight of the girl, mg = 400 N

Displacement ( height ), h = 8 m

Time taken, t = 50 s

$Power, \: P \: = \: \frac{mgh}{t} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{400 \: N \: \times \: 8 \: m}{50s} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 60 \: W.$

Power expended by girl A is 160 W.

Power expended by girl B is 64 W.

Answer 2

Explanation:

Power expended by girl A:

Weight of the girl, mg = 400 N

Displacement (height), h = 8 m

Time taken, t = 20 s

We know,

$\sf{}Power, P = \dfrac{Work\ done}{Time\ taken}$

So,

$\sf{}:\implies \dfrac{mgh}{t}:$

$\sf{}:\implies \dfrac{400\times 8m}{20s}:$

$\sf{}\therefore 160w$

Power expended by girl A is 160 W.

(ii) Power expended by girl B:

Weight of the girl, mg = 400 N

Displacement (height), h = 8 m

Time taken, t = 50 s

So,

$\sf{}:\implies \dfrac{mgh}{t}:$

$\sf{}:\implies \dfrac{400\times 8m}{50s}:$

$\sf{}\therefore 64W$

Power expended by girl B is 64 W.