Answer to Question #222354 in Electric Circuits for Jason

Question

A girl whose mass is 150 kg walks up a flight of 12 steps each 20 cm high in 2 second. Find the power she developed in Watts assume g = 10 m/s2

Answer 1

Explanations & Calculations

• The power, as it is defined can be written as $\small P = \large \frac{\Delta \text{Work done}}{\Delta \text{time}}$.
• Then it is about finding the work done by the girl during the given time of $\small \it2s$.

• What happens here is that her mass actually, her center of mass travels a verticle distance of $\small 12\times20cm$ up during that time. So the minimum work she needs to done (as she just reaches that height without any significant speed at that height: $\small E_{kinetic} = 0$) can be calculated to be,

$\qquad\qquad \begin{aligned} \small w&=\small mg\Delta h\\ &=\small 150kg\times10ms^{-2}\times(12\times0.20m)\\ &=\small 3600\,J \end{aligned}$

• Then the power she generates would be,

$\qquad\qquad \begin{aligned} \small P&=\small \frac{w}{t}=\frac{3600\,J}{2\,s}\\ &=\small \bold{1800\,W\approx1.8\,kW} \end{aligned}$

• Actually, we should appreciate that she has such mobility with that much of mass, amazing!!