Question

The bob of a simple pendulum dropped from a horizontal position. if the length of the pendulum is 1.5 m. what's is the speed with which the Bob arrives at the lowermost point B given that it dissipates 5 % of its initial energy against air resistance?

Answer 1

length of simple pendulum, l = 1.5 m

let mass of bob attached with simple pendulum is m.

a/c to question,

bob of a simple pendulum dropped from a horizontal position.

means, initial velocity of simple pendulum, u = 0

let velocity at the lowermost point is v.

now, initial energy of simple pendulum = potential energy due to height

= mgl

final energy of simple pendulum = kinetic energy at the lowermost point of circular of the circular path.

= 1/2 mv²

a/c to question,

it dissipates 5 % of its initial energy against air resistance.

so, final energy = initial energy - 5% of initial energy = 95/100 × initial energy

or, 1/2 mv² = 95/100 mgl

or, v = √{1.9gl}

putting, g = 10 m/s² and l = 1.5m

so, v = √{1.9 × 10 × 1.5}

= √{28.5} = 5.3385 m/s