Question

A girl of mass 50 kg runs up a flight of 20 States each measuring 15 CM in 25 seconds calculate the energy of girl G equal to 10 metre per second square

Answer 1

Answer:

Work done by girl=force*displacement

force=mass*acceleration due to gravity

force=50*9.8=490

displacement =no.stairs*height of each stairs

displacement=50*20=10

therefore work =f*d=490*10=4900J

power=work /time =4900/20=245J/S

Answer 2

${ \huge \bf { \mid{ \overline{ \underline{Correct \: Question}}} \mid}}$

A girl of mass 50 kg runs up a flight of 20 Stairs each measuring 15 cm in 25 seconds calculate the energy of girl (g = 10 m/s²)?.

$\huge{\bold{\underline{\underline{....Answer....}}}}$

$\huge{\bold{\underline{Given:-}}}$

• Mass of the girl (M) = 50kg.
• Height of Stairs (x) = 15cm.
• No. of stairs (n) = 20.
• Acceleration due to gravity (g) = 10 m/s².
• Time taken (t) = 25 seconds.

$\huge{\bold{\underline{Explanation:-}}}$

$\rule{300}{1.5}$

As we Know,

Work done:-

• Work is defined as the scalar product of Force(F) and displacement(s).
• Its S.I unit is Joules (J).

From, Work done formula,

$\large{\boxed{\tt W = F.s}}$

But, As here Force acting is through by The girl's weight.

• F = W.
• ∴ F = Mg

Substituting it,

$\large{\tt \leadsto W = Mg \times s}$

• And The Displacement will be The Height to which the girl rises,
• ∴ s = h

Now,

$\large{\tt \leadsto W = Mgh \: -----(1)}$

But we know

Energy is Defined as The capacity of Doing work

Therefore,

$\large{\boxed{\tt E = Mgh}}$

$\rule{300}{1.5}$

$\rule{300}{1.5}$

Now, Finding The Height to which the girl rises.

The Height can be Found out Through

$\large{\boxed{\tt h = No. \: of \: stairs \times Height \: of \: Stairs}}$

$\large{\tt \leadsto h = n \times x}$

Substituting the values,

$\large{\tt \leadsto h = 20 \times 15}$

$\large{\tt \leadsto h = 300 \: cm}$

As The obtained Value is in Centimeters

It needs to be converted into Meters.

Therefore,

$\large{\underline{\underline{\tt \leadsto h = 3m}}} \: \: \longrightarrow \tt 1m = 100cm$

Now, Substituting the values in the Energy

$\large{\boxed{\tt E = mgh}}$

Substituting,

$\large{\tt \leadsto E = 50 \times 10 \times 3}$

$\large{\tt \leadsto E = 500 \times 3}$

$\huge{\boxed{\boxed{\tt E = 1500 \: J}}}$

So, the Energy of the girl is 1500 Joules.

$\rule{300}{1.5}$

$\rule{300}{1.5}$

Extra Shots :-

Calculating The power of the Girl?

As we Know,

Power is Defined as rate of doing work.

From Definition we get,

$\large{\boxed{\tt P = \dfrac{W}{t}}}$

As we Know,

Energy = Work done

∴ Work done (W) = 1500 J.

Substituting the values in Power Formula,

$\large{\boxed{\tt P = \dfrac{W}{t}}}$

Now,

$\large{\tt \leadsto P = \dfrac{1500}{25}}$

$\large{\tt \leadsto P = \dfrac{\cancel{1500}}{\cancel{25}}}$

$\huge{\boxed{\boxed{\tt P = 60 \: W}}}$

So, the Power of the Girl is 60 Watts.

$\rule{300}{1.5}$