Why Do Different Methods Yield Different Spring Constants in Physics Problems?

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Homework Help Overview

The discussion revolves around determining the spring constant \( k \) for a mass \( M \) suspended from a vertical spring, with a focus on different methods yielding varying results. The problem involves concepts from mechanics, particularly energy conservation and Hooke's Law.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants explore the relationship between energy conservation and Hooke's Law, questioning why different methods yield different values for \( k \). Some suggest using Hooke's Law directly, while others express confusion about the assumptions made regarding the system's stability and the application of forces.

Discussion Status

There is ongoing exploration of the problem, with participants offering guidance on using Hooke's Law and questioning the reasoning behind energy conservation methods. Multiple interpretations of the situation are being considered, particularly regarding the effects of additional velocity on the spring's behavior.

Contextual Notes

Participants are discussing the assumptions related to the stability of the system and the conditions under which the spring is analyzed, including scenarios involving horizontal motion and energy transformations.

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Homework Statement


A block of mass M is hung on a vertical spring.
We have to find spring constant k, x (displacement from mean position) given.

Homework Equations


1/2kx^2 = mgx
mg=kx

The Attempt at a Solution


When i conserve energy,
1/2kx^2=mgx
⇒ k= 2mg/x

But when i use mg=kx,
I get k=mg/x

But mg/x≠2mg/x,
Help please :)
 
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You don't need to compute energy here.
Just use Hooke Law directly.

What force is M applying to the spring?
How far is this causing the spring to stretch?

The assumption here is that the system is stable at x.
 
Last edited:
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.Scott said:
You don't need to compute energy here.
Just use Hooke Law directly.

What for is M applying to the spring?
How far is this causing the spring to stretch?

The assumption here is that the system is stable at x.
after that it is given some velocity v from down, i need to calculate how high will it go.
i used 1/2kx2=1/2mv2 is it correct?
 
I love physics said:
i used 1/2kx2=1/2mv2 is it correct?
Is that based on some reasoning or just a wild guess?

If it rises above the equilibrium point by a maximum of h, what are the changes in
  1. KE
  2. GPE
  3. Elastic PE
?
 
Consider the situation of the mass moving horizontally along a frictionless surface.
What is the difference in the two situations?
 

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