Elongation of a spring in a two mass system

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SUMMARY

The discussion focuses on the elongation of a spring in a two-mass system where one mass is 'm' and the other is '2m'. Participants emphasize the importance of deriving force balance equations to analyze the system's behavior, particularly when the masses are unequal. It is established that the maximum elongation does not occur at the force balance point, as the blocks will not stop consecutively. A suggestion is made to change to a center of mass frame of reference to simplify the analysis.

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  • Understanding of Newton's laws of motion
  • Knowledge of spring force equations
  • Familiarity with center of mass concepts
  • Ability to derive and solve force balance equations
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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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