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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?

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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