Consider a small cuckoo clock in which the length of the pendulum is L, suspendi
ID: 2057272 • Letter: C
Question
Consider a small cuckoo clock in which the length of the pendulum is L, suspending a mass m with a period of oscillation T. The clock is powered by a falling weight (mass = M) which falls 2 m between the daily windings. The amplitude of the swing is 0.2 radians.(A) Determine the quality factor Q of the clock.
Data: m = 51 g; T = 1.0 s; M = 938 g.
(B) How many days would the clock run if it were powered by a 1.5 volt battery with charge capacity equal to 1800 mAh?
DO NOT COPY OTHERS ANSWER AND PASTE!
Explanation / Answer
(a)
T = 1 sec
L=T2g2/42
= 2.433 m
M=938*10^-3 kg
= 0.2
Velocity=2/(24*60*60)
m=51*10^-3 kg
Gain in potential energy:
E=mgl(1-cos)
=51*10^-3*9.8*2.433*(1-cos0.2)
=0.02424 J
Rate of work:
W=MgV
=938*10^-3*9.8*2/(24*60*60)
=0.2128*10^-3
Energy lost per period:
E1=0.2128*10^-3*1=0.2128*10^-3 J
(A)
Quality factor=E/E1
=0.02424 /0.2128*10^-3
=113.9135