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/s^{2}

^{.}

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 :

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