Timekeeping Changes with Temperature: Pendulum Clock at 1°C

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SUMMARY

The discussion focuses on the timekeeping changes of an aluminum pendulum clock when the temperature drops from 20.0°C to 1°C. The original period of the pendulum is 1.20 seconds, calculated using the formula T=2π√(L/g). The user calculated the change in length due to temperature using the coefficient of linear expansion and found a new period of approximately 1.199726369 seconds. The user seeks clarification on how to convert the difference in period to a time gain over one hour, indicating a misunderstanding in the final calculation.

PREREQUISITES
  • Understanding of pendulum motion and period calculation
  • Familiarity with the coefficient of linear expansion
  • Knowledge of basic physics formulas, specifically T=2π√(L/g)
  • Ability to perform unit conversions and time calculations
NEXT STEPS
  • Learn how to calculate time gain from period differences over extended durations
  • Study the effects of temperature on material properties, specifically for aluminum
  • Explore the concept of oscillation frequency and its relation to pendulum length
  • Investigate the impact of environmental factors on precision timekeeping devices
USEFUL FOR

Physics students, mechanical engineers, and anyone interested in the effects of temperature on pendulum clocks and timekeeping accuracy.

starfish794
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An aluminum clock pendulum having a period of 1.20 s keeps perfect time at 20.0°C. When placed in a room at a temperature of 1°C, how much time will it gain every hour?

I used T=2pi*squareroot(x/9.8) and solved for x to be .357823847 as the length of the pendulum. Then I plugged that into delta L = (alpha)(Lo)(delta T) and found the change in L to be 0.000163168. I subtracted 0.000163168 from .357823847. Then I used T=2pi*squareroot(L/g) to find the period with the new length and got 1.199726369 so that the difference between the original period and the new period would be .000273631.

I don't understand why this is the wrong answer. Did I do it correctly and just make a math error?
 
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What is your answer to the question? You have computed the difference in time for 1 oscillation of the pendulum. Now you need to find the error over 1 hour.
 

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