Elongation of a spring in a two mass system

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Discussion Overview

The discussion revolves around the elongation of a spring in a two-mass system, specifically addressing the dynamics when one mass is twice the other. Participants explore how to approach the problem, focusing on force balance and the implications of unequal masses on the system's behavior.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant notes that the problem involves a mass of '2m' instead of 'm', leading to questions about the system's behavior.
  • Another participant asks for the force balance on each mass at an arbitrary time, indicating a focus on the mechanics involved.
  • There is a suggestion that the maximum elongation will not occur at the force balance point, which some participants seem to agree with.
  • A participant expresses confusion about how to find the answer when the masses are unequal, emphasizing that they won't stop consecutively.
  • Another participant reiterates the need for force balance equations to solve the problem, indicating a desire for clarity in the mathematical approach.
  • One participant proposes considering a frame of reference where the center of mass is at rest as a potential method to analyze the problem.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the approach to the problem, with multiple competing views on how to analyze the system's dynamics, particularly regarding the implications of unequal masses.

Contextual Notes

There are unresolved aspects regarding the assumptions made about the system, particularly in relation to the behavior of the masses and the spring under varying conditions.

jha192001
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The Question is posted as a photograph with a. little change. One of the mass in the photo is equal to '2m' rather than 'm'. Now the block won't stop consecutively.
How would we approach the question?

1538057568873~2.jpeg
 

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What is your force balance on each of the masses at some arbitrary time?
 
Chestermiller said:
What is your force balance on each of the masses at some arbitrary time?
Yes Ofcourse as per the question it clearly seems it will.
But please don't say it will be the maximum elongation when force balances cause it will not.
 
jha192001 said:
Yes Ofcourse as per the question it clearly seems it will.
But please don't say it will be the maximum elongation when force balances cause it will not.
This answer doesn't seem to relate to my question at all. Please write down for us the force balance equations you derived to solve this problem.
 
sir,
if both the blocks are of equal masses then the maximum compression would. be seen. at the time they both stop momentarily and consecutively the first time..Hence their kinetic enengirs would turn into potential for spring.

But my ques. of what if masses are unequal.
one is m and. other. is 2m.
Idont know how to find the answer then as both masses won't stop consecutively
 
You still haven't answered my question. What are the force balance equations on the masses?
 
jha192001 said:
Idont know how to find the answer then as both masses won't stop consecutively
Have you considered changing to a frame of reference where the center of mass is at rest?

Or you could consider writing down some equations as @Chestermiller has asked. Both roads lead to a solution.
 
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