- #1
Nathan B
Homework Statement
A pendulum shortens due to a change in temperature, decreasing the length L and therefore period T. How many seconds ahead does the clock get in 24 hours? We assume that the grandfather clock is completely accurate at a normal pendulum length.
Li = 1.3 m
ΔT = -10°C
Homework Equations
Equation for the period of a pendulum, T = 2π√(L/G)
Equation for change in length due to temperature. ΔL = αLiΔT
The Attempt at a Solution
The new and old periods are relatively easy to calculate.
I've gotten all sorts of approximate values for time off, but I need to be exact. One of several methods that I've tried:
T2 / T1 = time given by the shortened pendulum/actual time
If we want to examine the results of 24 hours of time passing, we take the number of seconds in 24 hours to be our actual time = 84600 seconds.
Time given by shortened pendulum = 84600*T2 / T1
subtract actual time and we know how far off we are:
Time off in seconds = 84600*T2 / T1 - 84600
This seems like it should work, but it's always a little bit off.
What can I do to make this more accurate?