Question

The bob of a pendulum is released from a horizontal position. If the length of the pendulum is 1.5 m, what is the speed with which the bob arrives at the lowermost point, given that it dissipated 5% of its initial energy against air resistance?

Answer 1

Length of the pendulum, l = 1.5 m

Mass of the bob = m
Energy dissipated = 5%
According to the law of conservation of energy, the total energy of the system remains constant.

At the horizontal position:

Potential energy of the bob, E_P = mgl
Kinetic energy of the bob, EK = 0
Total energy = mgl … (i)

At the lowermost point (mean position):

Potential energy of the bob, E_P = 0

As the bob moves from the horizontal position to the lowermost point, 5% of its energy gets dissipated.

The total energy at the lowermost point is equal to 95% of the total energy at the horizontal point, i.e.,

=5.28 m/s