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 = 10 \ ms-²

Answer 1

Given :

A girl of mass 40kg runs up a staircase of 30 steps in 10s.

Height of each staircase = 0.1m

To Find :

Power developed by her.

Solution :

❖ Power is defined as the rate of work done per unit time.

• It is a scalar quantity having only magnitude.
• SI unit : W (watt)
• Dimension formula : [M¹L²T‾³]

Formula : $\underline{\boxed{\bf{\red{Power=\dfrac{Work}{Time}}}}}$

We know that work done is measured as the product of force (mg) and displacement.

$\sf:\implies\:P=\dfrac{W}{t}=\dfrac{F\cdot d}{t}$

$\sf:\implies\:P=\dfrac{mg\cdot nx}{t}$

• n denotes number of steps
• x denotes height of each step

By substituting the given values;

$\sf:\implies\:P=\dfrac{(40\times 10)\cdot(30\times 0.1)}{10}$

$\sf:\implies\:P=\dfrac{400\times3}{10}$

$\sf:\implies\:P=1200/10$

$:\implies\:\underline{\boxed{\bf{\gray{P=120\:W}}}}$

Answer 2

$\huge{\boxed{\bold{Question}}}$

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 = 10 \ ms-²

Given :

A girl of mass 40kg runs up a staircase of 30 steps in 10s.

Height of each staircase = 0.1m

To Find :

Power developed by her.

Solution :

❖ Power is defined as the rate of work done per unit time.

It is a scalar quantity having only magnitude.

SI unit : W (watt)

Dimension formula : [M¹L²T‾³]

Power= TimeWork

We know that work done is measured as the product of force (mg) and displacement.

⟹P= W t

= F⋅d t

⟹P= t mg⋅nxn denotes number of steps

x denotes height of each step

By substituting the given values;

⟹P= 10(40×10)⋅(30×0.1)

⟹P= 400×3/10

⟹P=1200/10

⟹P=120W