Question

a girl of mass 40kg climbs a rope 8m long at constant speed in 15s. ‎What power does she expend against gravitational forces during the ‎climb?‎

Answer 1

AnswEr :

From the Question,

• Mass of the girl (M) = 40 Kg

• Height (h) = 8m

• Time taken (t) = 15s

To finD

Power expended by the girl in climbing the rope

Here,

Force acting on the girl is her Weight (mg) and she is displaces vertically for 8m

Power : The rate of doing work

$\sf P = \dfrac{W}{t} \\ \\ \longrightarrow \sf P = \dfrac{Fs}{t} \\ \\ \longrightarrow \sf P = \dfrac{(mg)(h)}{t} \\ \\ \longrightarrow \sf P = \dfrac{40 \times 10 \times 8}{15} \\ \\ \longrightarrow \sf P = \dfrac{640}{3} \\ \\ \longrightarrow \boxed{\boxed{\sf P = 213.33 \ J/s}}$

Power expended by the girl is 213.33 J/s

Answer 2

Answer:

$\large\boxed{\sf{209.06\;J{s}^{-1}}}$

Explanation:

Given that,

• Mass of girl, m = 40 kg
• Displacement, s = 8 m
• Time taken, t = 15 sec.

To find the power expended by the girl in climbing the rope.

We know that, power, p is the work done per unit time or rate of doing work.

And, work done, w is the product of force and displacement.

Here, force, f = mg

Where, g is acceleration due to gravity.

Therefore, we have,

$= > p = \dfrac{w}{t} \\ \\ = > p = \dfrac{f \times s}{t} \\ \\ = > p = \dfrac{mg \times s}{t}$

Substituting the respective values, we get,

$= > p = \dfrac{40 \times 9.8 \times 8}{15} \\ \\ = > p = \dfrac{98 \times 32}{15} \\ \\ = > p = \dfrac{3136}{15} \\ \\ = > p = 209.06$

Hence, power expended is 209.06 J/s.