Time Period of pendulum on another planet? Given gravity

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The discussion revolves around calculating the period of a pendulum on Jupiter, given its period on Earth and the difference in gravitational acceleration. The formula T=2π√(L/g) is used, where L is the length of the pendulum and g is the acceleration due to gravity. The user attempts to derive the length of the pendulum based on its Earth period of 6 seconds and then apply that to find the period on Jupiter, where gravity is 26 m/s². Despite several calculations, the user struggles to arrive at a correct answer from the provided options. Ultimately, the conversation emphasizes understanding how gravity affects the pendulum's period and the importance of algebraic manipulation in solving the problem.
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Homework Statement



9. A simple pendulum on Earth has a period of 6.0 seconds. What would the period of this pendulum be on Jupiter, if the acceleration of gravity on the surface of Jupiter is 26 m/s2

A. 2.3 sec
B. 3.7 sec
C. 6.0 sec
D. 15.6 sec

Homework Equations


T=2pi * sqrt (L/g) Where L= Length of the pendulum

g=grav


The Attempt at a Solution



i know that 6.0s=2pi * (L/9.8) <-since that is the gravity on earth.
and T= 2pi* (L/9.8)

maybe, 6= 2pi * (L/9.8) ? But then ill be solving for L...
i have no idea what to do if anyone could please help me/explain the concepts.
 
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They're asking you what T would be, so that is what you need to solve for under Jupiter conditions.

What changes on the right hand side when you move to Jupiter?
 
maybe sub "6on Earth" somewhere, but i don't know how to word that into a mathmatical form. like present the ratio between Earth and Jupiter somewhere
 
im doing 6= 2pi sqrt(L/26)

6^2=4pi^2 L/26

i keep getting 23. which is not an option.
 
The period is 6 sec. on earth. It will not be 6 sec on Jupiter. Don't you have enough information to calculate the period on Jupiter? (Hint: use algebra)
 
OKAY, cross multiply, try number 3:

6sec = Xsec x=15.91, which again, is not an option.
/9.8 / 26
 
so now i have solved for the LENGTH of the pendulum on earth: L= 6^2/4pi^2 * 9.8

(i think that's right) and used 870, the Length and solved for T on Jupiter.

I get 36.34. Hmm, the squroot of 36.34 is 6. ahhh!
 
In the formula for the period of the pendulum, you have enough data to determine the length of the pendulum based on its behaviour on earth. Taking the same pendulum to Jupiter, where the gravity is higher, what would the period of the pendulum be?
 
is the length, 870, correct, you think? at least tell me tHat much. <?>
 
  • #10
thanks everyone for the help! Gotta 100 on the quiz!
 

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