Question

A 75 kg box is dropped from the top of a tower. The height of the tower is 35 m. Calculate (i) the initial
potential energy of the box, (ii) its potential energy 15 m above the ground, (iii) the maximum value of
its kinetic energy and (iv) its kinetic energy 20 m below the top of the tower. (g = 9.8 m/s2)
(g = 9.8 m/s2)​

Answer 1

Answer :

• The initial potential energy possessed by the box , PE(initial) = 25725 J.

• The potential energy possessed by the box , when it is 15 m above the ground , PE(at h') = 11025 J

• The maximum value of the kinetic energy possessed by the box , KE(max.) = 25725 J.

• The kinetic energy possessed by the box , when it 20 m below the top of the tower , KE(at h') = 11205 J.

Explanation :

Given :

• Mass of the body , m = 75 kg.
• Height of the tower , h = 35 m.
• Acceleration due to gravity, g = 9.8 m/s².

To find :

• Initial potential energy possessed by the box , PE(initial) = ?

• Potential energy possessed by the box , when it is 15 m above the ground the ground , PE = ?

• Maximum kinetic energy possessed by the body , KE(max.) = ?

• Kinetic energy possessed by the body , when it is 20 m below the top of the tower , KE(at h') = ?

Knowledge required :

By definition , Potential energy is the energy possessed by a particle due to it's state of rest.

Formula for potential energy :

⠀⠀⠀⠀⠀⠀⠀⠀⠀PE = mgh

Where :

• PE = Potential energy
• m = Mass of the object
• g = Acceleration due to gravity
• h = height

By definition , Kinetic energy is the energy possessed by a particle due to it's state of motion.

Formula for Kinetic energy :

⠀⠀⠀⠀⠀⠀⠀⠀⠀KE = ½mv²

Where :

• KE = Kinetic energy
• m = Mass of the body
• v = Velocity of the body

Now ,

According to the law of conversation of energy , "The Potential energy is equal to the kinetic energy just before reaching the ground" i.e,

⠀⠀⠀⠀⠀⠀⠀⠀⠀KE = PE

Hence from here get ,

⠀⠀⠀⠀⠀⠀⠀⠀⠀KE = mgh

Solution :

Initial potential energy of the box :

By using the equation for potential energy and by substituting the values in it , we get :

==> PE = mgh

==> PE = 75 × 9.8 × 35

==> PE = 25725

∴ PE = 25725 J

Potential energy of the box , at h = 15 m :

By using the equation for potential energy and substituting the values in it, we get :

==> PE = mgh

==> PE = 75 × 9.8 × 15

==> PE = 11025

∴ PE = 11025 J

Maximum kinetic energy of the box :

By using the law of conservation of energy and substituting the values in it , we get :

==> KE = PE

==> KE = 25725 ⠀⠀⠀⠀⠀⠀⠀[PE = 25725 J]

∴ KE = 25725 J

Kinetic energy of the box , at h = 20 m below the top of the tower :

By using the law of conservation of energy and substituting the values in it , we get :

==> KE = mgh

==> KE = 75 × 9.8 × (35 - 20)

==> KE = 75 × 9.8 × 15

==> KE = 11205

∴ KE = 11205 J.

Therefore ,

• The initial potential energy possessed by the box , PE(initial) = 25725 J.

• The potential energy possessed by the box , when it is 15 m above the ground , PE(at h') = 11025 J

• The maximum value of the kinetic energy possessed by the box , KE(max.) = 25725 J.

• The kinetic energy possessed by the box , when it 20 m below the top of the tower , KE(at h') = 11205 J.