Answer to Question #322831 in Mechanics | Relativity for Joy

Question

1. What is the power of a 50kg woman in climbing a hill 500m high?
2. How long will a 42kg girl with an average power of 30watts run up a staircase to the second floor of a building 6m high?
3. A sack of cement with a mass of 120kg is lifted by a construction worker in 15m from the ground. Compute the amount of work done by the construction worker and his power after accomplishing the work in 30 minutes?

Answer 1

Explanations & Calculations

1)

• The minimum work done by the person is

$\qquad\qquad \begin{aligned} \small W&=\small Fs=mg.h\\ &=\small 50kg\times9.8\,ms^{-2}\times500\,m\\ &=\small 245\,kJ \end{aligned}$

• To calculate the power she put in, the time she took to climb the hill is needed which is not provided here.

2)

• The minimum work she needs to be done is $\small Fs$

$\qquad\qquad \begin{aligned} \small W&=\small mg.h\\ &=\small 2469.6\,J \end{aligned}$

• Since power is defined as energy per unit time, the time she took can be calculated as follows,

$\qquad\qquad \begin{aligned} \small P&=\small \frac{W}{\Delta t}\\ \small \Delta t&=\small \frac{2469.9\,J}{30\,Js^{-1}}\\ &=\small 82.3\,s[1\,min\,\,22.3\,s] \end{aligned}$

3)

• Work done is

$\qquad\qquad \begin{aligned} \small W&=\small 17640\,J \end{aligned}$

• Then the power is

$\qquad\qquad \begin{aligned} \small P&=\small \frac{17640}{30\times60s}\\ &=\small 9.8\,W \end{aligned}$