Understanding Simple Harmonic Motion in a Loaded Floating Log

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Homework Help Overview

The discussion centers around understanding the dynamics of a cylindrical wooden log loaded with lead, which floats vertically in water. The problem involves demonstrating that the oscillation of the log can be classified as simple harmonic motion, with specific attention to the roles of gravity and buoyancy.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • Participants explore the forces acting on the log, particularly the balance between gravitational force and buoyant force. Questions arise regarding the modeling of the motion and the identification of angular frequency (omega).

Discussion Status

Some participants have suggested that the equation of motion could resemble that of a simple harmonic oscillator if the forces are correctly analyzed. There is ongoing exploration of how to model the motion and derive the necessary equations.

Contextual Notes

Participants are navigating the complexities of the problem, including the need to establish relationships between the submerged distance and the forces involved. There is an acknowledgment of the algebraic manipulation required to reach a recognizable form of the motion equation.

falcon0311
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A cylindrical wooden log is loaded with lead at one end so it floats vertically in water. The submerged part is 2.56 m (called L). I'm supposed to show the oscillation is simple harmonic.

Can someone point me in the right direction? For some reason I'm thinking gravity and density play a big part of find the this equation. After that, I can find the period.
 
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Gravity pulls the log down and buoyancy pushes it up. The buoyant force is equal to the difference between the weight of the submerged portion of the log and water that would occupy the same volume. If you work these out correctly your equation of motion should look like a simple harmonic oscillator.
 
how would you model this motion? How do you find w(omega). D

Do you model this as a spring force on the object? I have a similar problem and am stuck. Thanks!
 
The buoyant force goes like distance submerged. That will push it up, gravity will push it down. Work out the algrebra and get it into a form where you recognize.
 

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