How Does Temperature Affect the Period of a Pendulum?

In summary, the formula for calculating the time period of a pendulum is T = 2π√(L/g). The mass of the pendulum does not affect its time period, which is only dependent on its length and the acceleration due to gravity. A longer pendulum will have a longer time period, while a shorter pendulum will have a shorter time period. The time period of a pendulum remains constant due to the constant acceleration due to gravity, which provides the restoring force for the pendulum's motion. A higher acceleration due to gravity results in a shorter time period, while a lower acceleration due to gravity results in a longer time period.
  • #1
jabbie3
19
0

Homework Statement



A simple pendulum uses a steel wire as the string. The length of this wire is 1.4 m at room temperature. If the temperature is increased by 11.9 degrees C, the length of the wire increases by 1.69 mm . What is the change in period of the pendulum?

Homework Equations



T=2pi*[tex]\sqrt{L/g}[/tex]

The Attempt at a Solution



Lfinal=1.4+.00169=1.40169m
Linitial=1.4m
g=9.8 m/s2

[tex]\Delta[/tex]T=Tfinal-Tinitial

=2pi*[tex]\sqrt{1.40169/9.8}[/tex]-2pi*[tex]\sqrt{1.4/9.8}[/tex]

=2.376253765-2.374820823=.0014329416 s

This is wrong :(. What am I doing wrong?
 
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  • #2
Check the units on your "relevant equation." I think you will find a problem there.
 
  • #3


Your solution looks correct to me. However, there may be a rounding error in your final answer. Make sure to use all significant figures in your calculations and round your final answer to the appropriate number of significant figures. Also, double check that you are using the correct value for g, which may vary slightly depending on location and elevation.
 

FAQ: How Does Temperature Affect the Period of a Pendulum?

What is the formula for calculating the time period of a pendulum?

The formula for calculating the time period of a pendulum is T = 2π√(L/g), where T is the time period in seconds, L is the length of the pendulum in meters, and g is the acceleration due to gravity in m/s².

Does the mass of the pendulum affect its time period?

No, the mass of the pendulum does not affect its time period. The time period of a pendulum only depends on its length and the acceleration due to gravity.

How does the length of the pendulum affect its time period?

The length of the pendulum directly affects its time period. A longer pendulum will have a longer time period, while a shorter pendulum will have a shorter time period.

Why does the time period of a pendulum remain constant?

The time period of a pendulum remains constant because it is independent of the mass of the pendulum. This is due to the fact that the acceleration due to gravity is constant and does not change with mass.

How does the acceleration due to gravity affect the time period of a pendulum?

The acceleration due to gravity affects the time period of a pendulum by providing the restoring force that keeps the pendulum swinging. A higher acceleration due to gravity will result in a shorter time period, while a lower acceleration due to gravity will result in a longer time period.

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