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 \small ms^{-2}

Answer 1

Given :-

Mass of the girl = 40 kg

Number of steps she climbed = 30 steps

Time taken to climb the steps = 10 sec

Height of each step = 0.1 m

To Find :-

The power developed by the girl.

Analysis :-

Firstly, find the work done by substituting the given values such that work done is equal to mass into gravity into height.

Then you can easily find the power by the formula power is equal to work done divided by the time taken.

Solution :-

We know that,

• p = Power
• g = Gravity
• w = Work done
• h = Height
• m = Mass
• t = Time

Using the formula,

$\underline{\boxed{\sf Work \ done=Mass \times Gravity \times Height}}$

Given that,

Mass (m) = 40 kg

Gravity (g) = 10 m/s

Height (h) = 3 m

Substituting their values,

⇒ w = mgh

⇒ w = 40 × 10 × 3

⇒ w = 1200 J

Using the formula,

$\underline{\boxed{\sf Power=\dfrac{Work \ done}{Time \ taken} }}$

Given that,

Work done (w) = 1200 J

Time (t) = 10 sec

Substituting their values,

⇒ p = w/t

⇒ p = 1200/10

⇒ p = 120 W

Therefore, the power developed by the girl is 120 W.

Answer 2

Answer:

Given :-

• Mass of girl = 40 kg
• Number of steps she climbed = 30 steps
• Time taken to climb the steps = 10 sec
• Height of each step = 0.1 m

To Find :-

Power developed

Solution :-

So, For finding the power developed we will first find work done

$\huge \bf \: {{{W = MGH}}}$

Here,

W denotes Work

M denotes Mass

G denotes Gravitational acceleration

H denotes Height

⟹ W = 40 × 10 × 3

⟹ W = 400 × 3

⟹ W = 1200 J

$\huge \bf \: P = \frac{W}{T}$

Here,

P denotes Power

W denotes Work

T denotes Time

⟹ P = 1200/10

⟹ P = 120/1

⟹ P = 120 W

Hence :-

The power developed by the girl is 120 W.