Question
A clock with a pendulum made of steel has a period of 1.000 s at 20.0°C. The temperature is decreased to 4°C.
By how much does the period change? How much time does the clock gain or lose in one week?
By how much does the period change? How much time does the clock gain or lose in one week?
Answers
drwls
The pendulum length gets shorter and the frequency of oscillation increases.
Compute the new length using the coefficent of thermal expansion of steel, 13*10^-6 C^-1.
Call it the new length L2 and the original length L1.
L2/L1 = 1 -13*10^-6*16 = 0.99979
The new period P2 gets multiplied by sqrt(L2/L1)
P2 = 1.0000*0.999896 = 0.999896 s
One week is 10,080 minutes or 6.04800*10^5 s
The new number of oscillations in one week will be 6.04800*10^5/0.999896 = 6.04863*10^5
63 seconds or about one minute will be gained by the clock.
Compute the new length using the coefficent of thermal expansion of steel, 13*10^-6 C^-1.
Call it the new length L2 and the original length L1.
L2/L1 = 1 -13*10^-6*16 = 0.99979
The new period P2 gets multiplied by sqrt(L2/L1)
P2 = 1.0000*0.999896 = 0.999896 s
One week is 10,080 minutes or 6.04800*10^5 s
The new number of oscillations in one week will be 6.04800*10^5/0.999896 = 6.04863*10^5
63 seconds or about one minute will be gained by the clock.