Simple Pendulum Problem: Finding Coefficient of Linear Expansion

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SUMMARY

The discussion focuses on calculating the coefficient of linear expansion (α) for a pendulum string material based on its time period changes at different temperatures. The pendulum loses 5 seconds per day at 15 degrees Celsius and gains 10 seconds at 30 degrees Celsius. The relationship between the time period and the length of the pendulum is crucial for solving this problem. The solution involves using the ratio of time periods to the ratio of lengths to derive the coefficient of linear expansion.

PREREQUISITES
  • Understanding of simple harmonic motion and pendulum mechanics.
  • Knowledge of the coefficient of linear expansion and its significance.
  • Familiarity with temperature effects on physical properties of materials.
  • Basic algebra for manipulating equations and ratios.
NEXT STEPS
  • Study the relationship between the time period of a pendulum and its length.
  • Learn about the derivation and application of the coefficient of linear expansion.
  • Explore temperature effects on pendulum performance in various materials.
  • Investigate practical experiments to measure time period changes with temperature variations.
USEFUL FOR

Physics students, educators, and anyone interested in the thermal properties of materials and their effects on mechanical systems.

amal
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Homework Statement



A simple pendulum whose string is made of some unknown material loses 5 seconds per day at 15 deg and gains 10 seconds at 30 deg. What is the alpha i.e. coefficient of linear expansion of this material?

Homework Equations





3. The Attempt at a Solution [/b

I assumed the length where the pendulum has correct period to be L. Then,

L15(Length at 15 deg)= L-(L*alpha*delta T) where delta T is the fall in temperature but since I do not know both L and delta T, I got stuck. Something similar happens for T =30 deg.

Please guide me.
 
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How is the time period related to the length of the pendulum?
Calculate with the ratio of the time periods and that of the lengths.

ehild
 
Thanks. I got it.
 

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