SHM: Planet Problem Homework Statement

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SUMMARY

The discussion revolves around calculating the mass of a newly discovered planet based on the speed of a transverse wave traveling through a string suspended from a lead weight. The planet's radius is 7.20 × 107 m, and the time for the wave to travel the string is 0.0685 s on the new planet compared to 0.0390 s on Earth. The tension in the string, influenced by the gravitational force of the planet, is key to determining the planet's mass using the relationship between wave speed, tension, and linear mass density.

PREREQUISITES
  • Understanding of wave mechanics, specifically transverse waves.
  • Familiarity with the formula for wave speed on a string: v = √(T/μ).
  • Knowledge of gravitational force and its relation to mass and radius.
  • Basic algebra and physics problem-solving skills.
NEXT STEPS
  • Research the relationship between wave speed and tension in strings.
  • Learn about gravitational acceleration on different celestial bodies.
  • Study the concept of spherical symmetry in mass distribution.
  • Explore the derivation of formulas used in wave mechanics and gravitational physics.
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone interested in celestial mechanics and wave dynamics, particularly in the context of planetary exploration and analysis.

komarxian
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Homework Statement



You are exploring a newly discovered planet. The radius of the planet is 7.20 * 107 m. You suspend a lead weight from the lower end of a light string that is 4.00 m long and has mass 0.0280 kg. You measure that it takes 0.0685 s for a transverse pulse to travel from the lower end to the upper end of the string. On the earth, for the same string and lead weight, it takes 0.0390 s for a transverse pulse to travel the length of the string. The weight of the string is small enough that you ignore its effect on the tension in the string. Assuming that the mass of the planet is distributed with spherical symmetry, what is its mass?

Homework Equations

The Attempt at a Solution


I don't really know where to go with this? I was thinking something about comparing the radi of the planets, but I'm not sure??
 
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What result/formula do you know for the speed of a transverse wave on a string? The speed of the wave is different in the new planet than at earth, because in the new planet the weight of the lead and hence the tension of the string (those two forces will be approximately equal during the experiment) is different.
 
komarxian said:
I don't really know where to go with this?
When you don't know where to start with a problem, try listing all the physics principles that you can recognize being involved in the problem statement. Then list any formulas involved with that physics. That should give you some clues as to how to move forward.
 

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