Question

6. A girl of mass 50 kg runs up a flight of 40 stairs, each measuring 20 cm, in 50 seconds.
Calculate the work done against gravity.​

Answer 1

Explanation:

$work \: done \: by \: girl = fore \times displacement \\ force = mass \times acceleration \: due \: to \: gravity \\ 50 \times 9.8 = 490 \\ displacement = no.stairs \times height \: of \: each \: stair \\ displacement = 50 \times 20 = 100 \\ therefore \: work = f \times d = 490 \times 100 = 49000j$

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Answer 2

Given :

Mass of the girl = 60 kg

Total Number of stairs = 50

Height of each one = 20 cm

Time taken = 60 sec

To Find :

Power of the girl

Solution :

Height of each stair = 20 cm = 0.2 m

Total height of the staircase = Number of stairs × height of each stair = 50 × 0.2 = 10 m

Expression for Power is given by ,

$\begin{gathered} \\ : \implies \sf \: P = \frac{mgh}{t} \end{gathered}$

We have ,

m = 60 kg

g = 9.8 m/s²

t = 60 sec

h = 10 m

Now by substituting the values we get ;

$\begin{gathered} \\ : \implies \sf \: P = \frac{(60 \: kg)(9.8 \: ms {}^{ - 2} )(10 \: m)}{(60 \: s)} \\ \end{gathered}$

$\begin{gathered} \\ : \implies \sf \: P = \frac{600 \: kgm {}^{2} (9.8)}{60 \: s {}^{ - 3} } \\ \end{gathered}$

$\begin{gathered} \\ : \implies \sf \: P = \frac{5800}{60} \: kgm {}^{2} {s}^{ - 3} \\ \end{gathered}$

$\begin{gathered} \\ : \implies{\underline{\boxed{\sf { \: P = \:98 \: W }}}}\end{gathered} </h3><h3>$

Hence , The Power of the girl is 98 W.