Calculating Acceleration on Planet X Using Pendulum Period Measurements

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SUMMARY

The discussion focuses on calculating the acceleration due to gravity on Planet X using pendulum period measurements. The periods measured are 1.4 seconds on Earth and 2.25 seconds on Planet X. The lengths of the pendulum for both planets are derived as 0.487 meters and 1.257 meters, respectively. The challenge lies in solving for the acceleration due to gravity (g2) on Planet X without the mass of the pendulum, using the relationship between period and gravitational acceleration.

PREREQUISITES
  • Understanding of pendulum motion and its period formula
  • Familiarity with gravitational acceleration concepts
  • Basic algebra for solving equations with two unknowns
  • Knowledge of the relationship between length, period, and gravity
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  • Study the derivation of the pendulum period formula: t = 2π * sqrt(L/g)
  • Research methods for solving systems of equations with two variables
  • Explore the effects of gravity on pendulum motion in different environments
  • Learn about experimental techniques for measuring gravitational acceleration
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Students in physics, educators teaching mechanics, and anyone interested in gravitational studies and pendulum dynamics.

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Homework Statement


A pendulum (on earth) has a length of l and a mass of M and a period 1.4s. The pendulum is taken to planet X where the period is measured to be 2.25s. What is the acceleration due to gravity on planet X?


Homework Equations


So, t1 = 1.4s and t2 = 2.25s

I solved each of them for length t = 2pi * sqrt(L/g)
L1: .487m
L2: 1.257m

The Attempt at a Solution



The problem is that the velocity, the mass isn't given in the problem, so I am stuck on how to solve for acceleration. I don't think using kinematics would work, but any help would be appreciated.
 
Physics news on Phys.org
What is known? t1 and t2, and actually, g1 (being 'g' on earth).

Two equations, two unknowns (g2 and L), and you don't even strictly care what L is...
 

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