A grandfather pendulum has a simple brass rod of length L. One night, the temper

Question

A grandfather pendulum has a simple brass rod of length L. One night, the temperature in the house is 23.0 oC and the period of the pendulum is 1 second. The clock keeps correct time at this temperature. 1) What is the length of the pendulum's rod? L =__________ cm 2) The temperature in the house quickly drops to 15.0 oC just after 10PM, and stays at that value. By how much does the length of the pendulum change? The coefficient of linear expansion for brass is ? = 1.9E-05 K-1. ?L =________ * 10^-6m 3.)After the temperature drops to 15.0 oC at 10PM, it stays at that value. How much does the period of the pendulum change after the temperature has dropped to 15.0? ?T = ________ * 10^-6s 4) How many cycles does the pendulum make between 10 PM and the next morning when the pendulum indicates 10 AM? N = ________ cycles With respect to the real time, by how many seconds is the pendulum off when it shows 10 AM? t = _________ s

Explanation / Answer

T=2(l/g)

l=0.2456 m

so L=245.6cm

l=c*t*l = 37.33 *10^-6

taking log and differentiating equation of pedulum we get

T/T=0.5*l/l

so T= 607.98 *10^-6 s

no. of cycles = no. of seconds = 3600*12 = 43200 cycles

time lag = 43200*T

=26.26 seconds

so the real time is 9:59:33.74

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