Ship Bobbing in the Ocean (Frequency Problem)

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Homework Help Overview

The problem involves a spherical ship, "SpaceForce One," and seeks to determine the frequency at which it bobs in the ocean. The ship's mass and radius are provided, but no specific equations are given. Participants are exploring the implications of the ship's shape on the problem and the assumptions that can be made to facilitate a solution.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss various approaches to the problem, including the challenges of accounting for the volume of the sphere and the implications of using different coordinate systems. Questions arise about the assumptions that can be made to simplify the problem.

Discussion Status

The discussion is active, with participants offering insights and asking clarifying questions. Some guidance has been provided regarding the volume of displaced water and the potential effects of amplitude on simple harmonic motion (SHM). There is no explicit consensus, but multiple lines of reasoning are being explored.

Contextual Notes

Participants note the liberty to make approximations, which raises questions about the assumptions necessary for solving the problem. The lack of specified amplitude for the bobbing motion is also highlighted as a potential factor in determining the nature of the motion.

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Homework Statement


"SpaceForce One" is a perfectly spherical ship of mass 2.5·10^6 kg and Radius 42 meters bobbing up and down in calm seas on Earth At what frequency does SpaceForce ship bob?

Homework Equations


None explicitly given.

The Attempt at a Solution


We approached this problem in a number of ways. We really struggling with making assumptions (we are given quite a bit of liberty to make approximations) that make the problem solvable. We can pretty easily solve the problem if it's a cylinder, but we are having a lot of issues accounting for the change in volume of the sphere.

What would be some helpful assumptions to make? Any hint in the right direction is appreciated. Thanks!
 
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You say you're having trouble accounting for the change in volume of the sphere. What coordinate system are you working in? Have you tried spherical?
 
TJGilb said:
You say you're having trouble accounting for the change in volume of the sphere. What coordinate system are you working in? Have you tried spherical?

We have, but the equation for the volume of a sphere ends up the same no matter what coordinate system we work in. Is there something we are not thinking about?
 
The nice thing is that you can get the volume of displaced water into a convenient equation of depth of the sphere and it's far easier to work in is all. Since it sounded like accounting for the volume was your biggest issue. I can't say what you might have missed without first seeing what you have.
 
Seth Newman said:
At what frequency does SpaceForce ship bob?
No amplitude is specified. Consider whether it would truly be SHM if bobbing at large amplitudes. What does that suggest regarding an approach?
 

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