Question

A girl of mass 40 kg runs up a staircase of 30 steps in 10 s. If the height of each step is 0.1 m, find the power developed by her. Take g = 10ms^-2

Answer 1

Explanation:

Given, mass of the boy, m=40kg ;

total height gained, h=50×10cm

=500cm=5m

time taken to climb, t=5s

Work done by the boy,

W=mgh=(40)(10)(5)=2000J

Power developed, P=

t

W

=

5

2000

=400W

Answer 2

Given -

Mass = 40 kg

Number of steps = 30

Time = 10 sec

Height of each step = 0.1 m

To find -

• Power developed by her.

Solution -

Here we will first find the Work done by the girl.

$\longmapsto$ Work = Potential Energy

$\longmapsto$ Work = mgh

where,

m = Mass

g = acceleration due to gravity

h = Height

On substituting the values -

m = 40 kg

g = 10 m/s²

h = 0.1 × 30 = 3 m

$\longmapsto$ Work = 40 × 10 × 3

$\longmapsto$ Work = 1200 J

Now,

We have the work done, so we will find the power developed by her.

$\longmapsto$ Power = $\sf\dfrac{Work}{Time}$

$\longmapsto$ Power = $\sf\cancel\dfrac{1200}{10}$

$\longmapsto$ Power = 120 W

∴ The power in this case is 120 W

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