Cuckoo clock weight falls

Asked by maham237 @ in Physics viewed by 365 People

A small cuckoo clock has a pendulum 25cm long with a mass of 10g and a period of 1s. the clock is powered by a 200gram weight which falls 2m between the daily windings. the amplitude of the swing is 0.2rad. what is the q value of the clock?

Answered by maham237 @


Q factor is defined as the ratio of the total amount of energy stored in the pendulum and total amount of energy lost per one cycle.
Q=2\pi f \frac{energy\ stored}{power\ loss}
We will need to figure out power loss and energy stored.
Power loss is happening due to friction. It is equal to power that the weight is supplying to the clock:
P_l=\frac{mg\Delta h}{\Delta t}=\frac{0.2\cdot 9.81 \cdot 2}{24\cdot 60 \cdot 60}=0.000045W
Now we need to figure out the energy stored in one the pendulum. We can think of this as potential energy of the pendulum:
E_s=m_pgh_p=m_pgL(1-cos(\theta))=0.01\cdot 9.81 \cdot 0.25 \cdot (1-\cos(0.2))
E_s=0.0004888J
Please see the attachment for clarification.
Now we can calculate the Q factor:
Q=2\pi f \frac{E_s}{P_l}=2\pi \frac{0.0004888}{0.000045}=68.2

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