Question

A body weighing 20 kg climbs up a vertical height of 50 m. Calculate the amount of work done by it. How much potential energy does it gain in the process? (g = 9.8 m/s²). *​

Answer 1

Answer :

• Amount of word done by the body is 9800 J.
• Potential energy gained by the body is 9800 J.

Explanation :

Given :

• Mass of the body , m = 20 kg.
• Height climbed by the body, h = 50 m.
• Acceleration due to gravity, g = 9.8 m/s².

To find :

• Work done by the body, W = ?
• Potential energy of the body, P.E. = ?

Knowledge required :

• Work done by a body is the product of the force applied on the body and the distance covered in the direction of force.i.e,

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀W = Fs

⠀⠀⠀⠀⠀⠀⠀⠀⠀● W = Work Done

⠀⠀⠀⠀⠀⠀⠀⠀⠀● F = Force applied

⠀⠀⠀⠀⠀⠀⠀⠀⠀● s = Displacement

But we know that, Force is the product of the acceleration and the mass of the body.i.e,

F = ma

⠀⠀⠀⠀⠀⠀⠀ ⠀⠀● F = Force applied

⠀⠀⠀⠀⠀⠀⠀⠀⠀ ● m = Mass

⠀⠀⠀⠀⠀⠀⠀⠀⠀ ● a = Acceleration

By substituting the equation for force and substituting it in the equation for work done ,we get :

⠀=> W = Fs

⠀=> W = ma s

Since the body is vertically displacing , the displacement of the body will be h , by substituting it in the above equation , we get :

⠀∴ W = mgh

But the above equation is the potential energy possessed by a body.

So in this case , we get that :

⠀⠀⠀⠀⠀⠀⠀Work done = Potential energy or/

=> W = P.E. = mgh

Hence work done of the body will be equal to the potential energy of the body.

Solution :

By using the formula for work done or potential energy and substituting the values in it, we get :

⠀=> W = P.E. = mgh

⠀=> W = P.E. = 50 × 9.8 × 20

⠀=> W = P.E. = 50 × 98/10 × 20

⠀=> W = P.E. = 50 × 98 × 2

⠀=> W = P.E. = 9800

⠀⠀⠀∴ W = P.E. = 9800 J

Therefore,

• Work done by the body, W = 9800 J
• Potential energy of the body, P.E. = 9800 J

Answer 2

Given :

• A body weighing 20 kg climbs up a vertical height of 50 m.

• Calculate the amount of work done by it.

To Find :

1. Calculate the amount of work done by it.
2. How much potential energy does it gain in the process?

Solution :

To be Calculated :

• (i)Calculate the amount of work done by him.
• (ii)How much potential energy does he gain?

Formula Used :

• Force ,F = m × g

• Work ,W = F × d

• Potential energy, P.E = m × g × h

$: \implies \: \: \: \: \boxed{\sf F = m \times g }$

• Substitute all Values :

$: \implies \: \: \: \: \sf \: \: \: \: \: F = 20\times 9.8 \\ \\ \\ : \implies \: \: \: \: \sf \: \: \: \: \: F = 196$

Now Find The Value of Work :

$: \implies \: \: \: \: \boxed{\sf W = F \times d }$

• Substitute all Values :

$: \implies \: \: \: \: \sf W = 196\times 50 \\ \\ \\ : \implies \: \: \: \: \sf W = 9800$

Now Find The Value of potential energy :

$: \implies \: \: \: \: \boxed{\sf P.E = m \times g \times h }$

• Substitute all Values :

$: \implies \: \: \: \: \sf P.E = 20\times 9.8\times 50 \\ \\ \\ : \implies \: \: \: \: \sf P.E =1000 \times 9.8 \\ \\ \\ : \implies \: \: \: \: \sf P.E =9800$

Hence ,

• The amount of work 9800

• The potential energy is 9800