Question

A simple pendulum, while oscillating, rises to a
maximum vertical height of 5 cm from its rest
position when it reaches to its extreme position
on one side. If mass of the bob of the simple
pendulum is 500 g and g = 10 ms?, find :
(i) the total energy of simple pendulum at any
instant while oscillating, and
(ii) the velocity of bob at its mean position.
State the assumption made in your
calculation.​

Answer 1

Answer:-

Given, h = 5 cm = 0.05 m, m = 500 g = 0.5 kg,g = 10 m s-2Assumption : There is no loss of energy due to airfriction.(i) Total energy of simple pendulum= potential energy at its extreme position= mgh = 0.5 x 10 x 0.05 = 0·25 J(ii) Kinetic energy at the mean position= potential energy at the extreme positioni.e., 5 mv2 = mghor v = 12gh = 12x10x0:05 = Ji= 1 m s-1

Answer 2

The total energy of simple pendulum and velocity of bob at its mean position are 0.25 J and 1 m/s respectively.

A simple pendulum, While oscillating, rises to a maximum vertical height of 5cm from its rest position when it reaches to its extreme position on one side.

If the mass of the bob of the simple pendulum is 500g and g is 10 m/s², we have to find

1. Total energy of simple pendulum at any instant while oscillating.
2. The velocity of bob at its mean position.

Concepts :

• Total energy of a simple pendulum is the sum of potential energy and kinetic energy at any instant.
• At extreme position, a simple pendulum has only potential energy and hence total energy at extreme position is the potential energy of pendulum.
• At mean position, a simple pendulum has only kinetic energy and hence total energy at mean position is the kinetic energy of pendulum.

1. Total energy = potential energy at extreme position

= mgh

Here, m = 500g = 0.5 kg , g = 10 m/s² and h = 5cm = 0.05 m

∴ total energy = 0.5 kg × 10 m/s² × 0.05 m = 0.25 J

Therefore the total energy of simple pendulum at any instant while oscillating is 0.25 J.

2. kinetic energy at mean position = total energy

⇒ 1/2 mv² = 0.25

⇒ 1/2 × 0.5 × v² = 0.25

⇒ v = 1 m/s

Therefore the velocity of bob at its mean position is 1 m/s.

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