Question

 A girl of mass 40 kg climbs up stairs by spending 800 joules of energy. How high does the girl climb up?​

Answer 1

Answer:

◇ Given:

$\textsf{Mass of the girl = 40 kg}$

$\textsf{Potential energy used by the girl = 800 J}$

$\textsf{Acceleration due to gravity = 9.8 m/s²}$

◇ To find:

$\textsf{How high does the girl climb up}$

◇ Taken:

Take the formula of potential energy:

$\boxed{\underline{Pe=mgh}}$

Where,

Pe = Potential energy

m = Mass

g = Acceleration due to gravity

h = Height

◇ Concept:

Divide by taking "h" at left hand side and taking "Pe" at right hand side .

◇ Solution:

Height :

$Taken,Pe=mgh$

$\rightarrow{800J=40kg×9.8m/s²×h}$

$\rightarrow{800J=392×h}$

$\rightarrow{h=800J/392}$

$\rightarrow{h=2.04m(approx)}$

◇ Answer:

So , the girl climbed 2.04 m(approx) height.

◇ Extra information:

To find kinetic energy :

$Ke=\frac{1}{2}mv²$

Where,

Ke = Kinetic energy

m = Mass

v = Velocity

To find velocity :

$V=\frac{D}{T}$

Where,

V = Velocity

D = Displacement

T = Time

To find acceleration :

$A=\frac{V1-V}{T}$

Where,

A = Acceleration

V1 = Final velocity

V = Initial velocity

T = Time

Answer 2

☆ To Find :-

The Height which is climbed up by the girl.

☆ We Know :-

Potential Energy :

$\purple{\sf{\underline{\boxed{PE = mgh}}}}$

Where ,

• PE = Potential Energy

• m = Mass of the body

• h = Height above the ground

• g = Acceleration due to Gravity

☆ Solution :

Given :

• PE = 800 J

• Mass of the Body = 40 kg

We Know that the , Acceleration due to gravity on earth is 9.8 m/s².i.e,

• g = 9.8 m/s²

(Note : In Approximation , Acceleration due to gravity is taken as 10m/s²)

Using the formula and substituting the values in it , we get :

$\purple{\bigstar\:\sf{PE = mgh}\:\bigstar} \\ \\ \\ \implies \sf{800 = 40 \times 9.8 \times h} \\ \\ \\ \implies \sf{800 = 392 \times h} \\ \\ \\ \implies \sf{\dfrac{800}{392} = h} \\ \\ \\ \implies \sf{2.041(Approx.) = h} \\ \\ \\ \therefore \purple{\sf{h = 2.041 m}}$

Hence, the Height climbed by the body is 2.041 m

» Additional Information :

• Kinetic energy = ½mv²

• Momentum = mv

• Impulse = m(v - u)