Ship Bobbing in the Ocean (Frequency Problem)

[Seth Newman]

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!

 

[TJGilb]

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?

 

[Seth Newman]

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?

 

[TJGilb]

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.

 

[haruspex]

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?

 

[haruspex]

@Seth Newman , do you need more help?