What is the change in period of a pendulum with a temperature-dependent length?

AI Thread Summary
The discussion revolves around calculating the change in the period of a pendulum when the length of the steel wire increases due to a temperature rise. The initial length of the wire is 1.1m, and a temperature increase of 10.8 degrees Celsius causes a length increase of 1.58mm. The calculations show that the initial period is approximately 2.10505 seconds, and the final period is about 2.10656 seconds, resulting in a change of approximately 0.0015 seconds. However, it was noted that using more significant figures in the final answer is necessary for online systems to accept the response as correct. The conclusion emphasizes the importance of precision in calculations when dealing with temperature-dependent changes in pendulum length.
Roxanne
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Homework Statement



A simple pendulum uses a steel wire as the string. The length of this wire is 1.1m at room temperature. If the temperature is increased by 10.8 degrees Celsius, the length of the wire increases by 1.58 mm. What is the change in period of the pendulum?

Homework Equations


T=2*pi*(sqrt(L/g))


The Attempt at a Solution


First I converted 1.58mm to meter = .00158m
I then tried subtracting T initial from T final in order to get the change in period.
T initial = 2*pi* (sqrt(1.1/9.8)) = 2.10505 sec.
T final = 2*pi* (sqrt (1.1+.00158))/9.8) = 2.10656 sec.
getting the change in period to be = .0015 seconds...which is incorrect.
I don't know of a formula that takes into consideration the temperature change.
Please help, I have been trying to figure this out for 5 hrs now.
 
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Welcome to PF, Roxanne.
I ran the problem through and got exactly the same answer as you did!
It sure looks right. Could the computer be wrong? I don't know how you handle situations like this - write out the solution and hand it to your prof?
 
Hmm I'm pretty sure that when you increase temperature actually the period of a pendulum is supposed to get longer.
 
Last edited:
I figured out why I kept getting the problem wrong. I needed to include more significant figures in my answer. The answer should have been = 0.0015112693 seconds in order for the on-line system to accept it as correct.

Thank you for your prompt replies.
 

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