Question

A simple pendulum of mass 300 g is shown in the figure. The pendulum bob is displaced from the mean position A to the extreme position B. The potential energy at position A is zero. At the position B, the pendulum bob is raised by 10 m.

1. Calculate the potential energy of the pendulum at position B.
2. Calculate the total mechanical energy at position С.
3. Determine the speed of the pendulum bob at position A when released from position B.

Consider g = 10 m/s² and there is no loss of energy.

Answer 1

Given Data:

Mass of the bob (m) = 300 g = `300/1000` kg = 0.3 kg

Height at extreme position B (h) = 10 m

Acceleration due to gravity (g) = 10 m/s²

(i) At the extreme position B, the bob is at a height of 10 m relative to position A.

PE_B = m × g × h

= 0.3 kg × 10 m/s² × 10 m

= 30 J

(ii) According to the Law of Conservation of Energy, the total mechanical energy remains constant at every point in the path if there is no air resistance or energy loss.

At point B, the bob is momentarily at rest, so Kinetic Energy (KE_B) = 0.

Total Mechanical Energy at B = PE_B + KE_B

= 30 J + 0

= 30 J

Therefore, the total mechanical energy at position C is exactly the same:

Total Mechanical Energy at C = 30 J

(iii) When the bob swings back to the mean position A, its height becomes 0, meaning all its Potential Energy converts completely into Kinetic Energy (KE).

KE_A = Total Mechanical Energy = 30 J

Using the Kinetic Energy formula:

KE = `1/2 mv^2`

`30 = 1/2 xx 0.3 xx v^2`

30 = 0.15 × v²

`v^2 = 30/0.15`

`v^2 = 200`

v = `sqrt200`

v = 14.14 m/s