Question

A body of mass $45\,kg$ climbs up $20{\kern 1pt} {\kern 1pt} steps$ in $20{\kern 1pt} \sec$ If each step is $25\\\,cm$ high then calculate the power used in climbing. $(take{\kern 1pt} {\kern 1pt} g = 10\,m{s^{ - 2}})$

Answer 1

In order to solve this question, we need to know about gravitational potential energy. whenever a body displaces against gravity which means when a body displaces from ground level to some height against gravity, the energy possessed by body is called gravitational potential energy, here body displaces from ground level to some height while climbing up, hence we will calculate gravitational potential energy of the body and then will calculate power used by body in climbing the steps.

Formula used:
If $g$ is the acceleration due to gravity, $m$ is the mass of a body and it covers a height $h$ against gravity then gravitational potential energy is calculated as
$P.E = mgh$
Power is defined as rate of change of energy with respect to time hence,
$\text{Power} = \dfrac{\text{Energy}}{\text{time}}$

Complete step by step answer:
According to the question, we have given that
Mass of the body,$m = 45kg$
Height of each step $= 25cm = 0.25m$
Number of steps is $= 20$
Total height of these twenty step will be
$h = 0.25 \times 20$
$\Rightarrow h = 5m$
And $g = 10\,m{s^{ - 2}}$
Using formula of Gravitational potential energy we have,
$P.E = mgh$
$\Rightarrow P.E = 45 \times 5 \times 10$
$\Rightarrow P.E = 2250J$
Now, using formula of power for which $t = 20\sec$
$\text{Power} = \dfrac{\text{Energy}}{\text{time}}$
$\Rightarrow \text{Power} = \dfrac{{2250}}{{20}}$
$\therefore \text{Power} = 112.5\,W$

Hence power used by the body while climbing up is $112.5\,W$.

Note: It should be remembered that, the basic unit of conversion is used as $1\,cm = 0.01m$ and standard SI unit of energy is known as Joule denoted by J whereas, the standard unit for power is known as Watts and denoted by W. Potential energy of a body is always due to the virtue of its position relative to other bodies.