Period of a Pendulum: Calculate New Period & 24h Loss

In summary: I will surely guide the students to the concept rather than just providing the answers.Thank you for the prompt reminder.In summary, the clock pendulum has a period of 1.222 seconds with a gravitational acceleration of 9.812 m/s^2. When the gravitational acceleration changes to 9.797 m/s^2, the new period of the pendulum is 1.222935 seconds. In 24 hours, the clock using this pendulum will lose 8812.8 seconds due to the change in gravitational acceleration, resulting in a longer period of 1.324 seconds.
  • #1
jdeakons
3
0
A clock pendulum has a period of 1.222 seconds where g = 9.812 m/s^2.

1. What is the new period of the pendulum when g = 9.797 m/s^2?

2. How many seconds will a clock using this pendulum lose in 24 hours?

For the first one, using 7 significant figures, the new period comes out to 1.222935 seconds. I'm not sure how to do the second part. Any suggestions?

Thanks.
 
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  • #2
Thanks for the post, but how did you arrive at the resulting numbers? I also don't understand how .102 seconds are lost for every 1 second...
 
  • #3
...start with the equation for period

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

(This has the initial data for T and g)

What you want is

[tex]T'=2\pi \sqrt{l}{g'}[/tex]

and so

[tex]\frac{T'}{T}= \sqrt{\frac{g}{g'}}[/tex]
 
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  • #4
physixguru said:
Welcome to PF>

New time period is 1.324 seconds


Since it loses 0.102 second in 1 second
Time lost in 24 hrs will be = 0.102*60*60*24 = 8812.8 seconds
Whilst we appreciated the help physixguru, how does posting answers help the OP to understand the concept? Would it not be better to guide the student rather than just providing answers? Furthermore, your answers are incorrect.

jdeakons
I agree with your answer for the first question. As for the second question, how much longer is the period of the pendulum when g=9.797 m/s/s rather than the original value? Therefore, in the time taken for the first pendulum to measure 24 hours, how much time will have passed according to the second?
 
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  • #5
Hootenanny said:
Whilst we appreciated the help physixguru, how does posting answers help the OP to understand the concept? Would it not be better to guide the student rather than just providing answers? Furthermore, your answers are incorrect.

jdeakons
I agree with your answer for the first question. As for the second question, how much longer is the period of the pendulum when g=9.797 m/s/s rather than the original value? Therefore, in the time taken for the first pendulum to measure 24 hours, how much time will have passed according to the second?

I duly apologize, but for the clarification it was a typing error. i had copied the wrong data from the question.i respect the rules of the forum and promise to abide by it.This has happened with me the first time .
 

1. What is a pendulum and how does it work?

A pendulum is a simple device that consists of a weight (called a bob) suspended from a fixed point by a string or rod. When the bob is pulled to one side and released, it swings back and forth in a regular motion. This is due to the force of gravity pulling the bob downward and the tension in the string or rod keeping it from falling.

2. What is the period of a pendulum?

The period of a pendulum is the time it takes for one complete swing, from one side to the other and back again. It is affected by the length of the pendulum, the force of gravity, and the starting angle of the pendulum's swing.

3. How do you calculate the period of a pendulum?

The formula for calculating the period of a pendulum is T = 2π√(L/g), where T is the period in seconds, π is a mathematical constant (approximately equal to 3.14), L is the length of the pendulum in meters, and g is the acceleration due to gravity (9.8 m/s2 on Earth).

4. What is "24h loss" in relation to the period of a pendulum?

"24h loss" refers to the small change in the period of a pendulum over a 24-hour period. This is due to the Earth's rotation and the fact that the gravitational force varies slightly depending on the location of the pendulum on Earth's surface.

5. How do you calculate the new period and 24h loss of a pendulum?

To calculate the new period and 24h loss of a pendulum, you must first measure the length of the pendulum and the local value of gravity. Then, using the formula T = 2π√(L/g), you can calculate the new period. To calculate the 24h loss, you can use the formula Tnew = Told + (24h loss), where Tnew is the new period and Told is the original period. The 24h loss can be calculated by taking the difference between the new and old periods and dividing by 24.

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