Question

A man has power of 90 W and mass 60 kg runs up a staircase in 40 seconds. If each step of staircase is 20 cm high, calculate the number of steps.

Explain with complete calculations & justifications.

Points : 20 ☺

Answer 1

a man has power = 90 w
masss = 60 kg
weight of man in staircase = mg
=60 x 10 =600N
( we assume g =10m/s^2 )

now ,
power = energy /time
energy =power x time
=90 x 40 = 3600 Joule

we know potential energy =mgh

here we use potential energy because man goes above the ground hence they have potential energy .

now,
potential energy = 3600 Joule
600 x h =3600
h =6m
now,
no of steps = h/ height of each staircase
=6/(20/100) =30

hence,
no of steps =30

Answer 2

Given,

Power=90w

Mass=60kg

Time=40seconds

Hight=20cm

g=10m/s^2

Let's think the number of stairs are x

Power = work /time

or,90=work /40

or,Work =90×40

or,Work=3600j

We can also say,

Work = Mgh

or,Work=60×10×0.2×X [20cm=0.2m]

or,Work=120×X

or,3600=120×X

or,X=3600/120

or,X=30

So the number of stairs are 30

Hope it helps.