Question

The pendulum of a clock consists of a mass of 0.20 kg hanging from a thin rod. The
amplitude of the pendulum swing is 3.0 cm. The clock is driven by a weight of mass
4.5 kg that falls a distance of 0.95 m over a period of 8 days. Assuming the pendulum
to be a simple pendulum of length 0.75 m, show that the Q-value of the clock is
approximately 70.
(Assume g = 9.81 m s−2.)

Answer 1

Solution :

Given :

m = 0.2 kg

L = 0.75 m

A = 3 cm = 0.03 m

g = 9.81 m/s²

^.

The Q value of a pendulum is given by :

The total energy of the pendulum is :

.

The energy per period is given by

Here, M is the mass of falling weight and v is the fall velocity.

M = 4.5 kg

v = 0.95 m / 8 days = 0.95/(8 x 3600 x 24 sec) = 1.37442 x 10^-6 m/s

.

Therefore :