Question

The length of a simple pendulum is 1 m. The bob of the pendulum(mass = 0.10 kg) is released when the string is horizontal. Calculate in the lowest point of its path :

(i) its kinetic energy, 

(ii) the tension in the string.

Answer 1

The amplitude θ₀ = π/2 is large. We cannot use SHM equations

(i) When the bob is released from horizontal, the loss in its potential energy at the lowest point = mg l, where l is the length of the pendulum.

Let the velocity of bob at the lowest point is v.Then gain in K.E. = 1/2 mv² 

From conservation of mechanical energy

mg l = 1/2 mv²

Hence, K.E. = 1/2 mv² = mg l

= 1/100 × 9.8 × 1 = 0.098 J

(ii) Tension in the string T –mg = mv² / l

Using (i)