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

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Homework Help Overview

The discussion revolves around the change in the period of a pendulum due to a temperature-dependent increase in the length of the pendulum's string. The original poster presents a scenario involving a steel wire that lengthens with temperature, leading to questions about the resulting change in the pendulum's period.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to calculate the change in period using the formula for the period of a pendulum, but expresses uncertainty about the correctness of their result. Some participants question whether the period should increase with temperature, while others reflect on the significance of precision in their calculations.

Discussion Status

Participants have shared their calculations and findings, with some expressing confusion about the results. There is a recognition of the need for precision in reporting answers, and the discussion is ongoing with various interpretations being explored.

Contextual Notes

The original poster mentions struggling with the problem for several hours and questions the validity of their calculations, indicating a potential lack of clarity regarding the influence of temperature on the pendulum's period.

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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