Spring-block question from mechanics

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In the discussion, two blocks connected by a spring are analyzed to determine the velocity of the center of mass (COM) when the left block detaches from the wall. The conservation of energy principle is applied to the system, considering the spring's potential energy and the kinetic energy of the blocks. The left block's initial velocity is confirmed to be zero as it is stationary against the wall until released. The net force on the left block is zero at that moment, leading to this conclusion. The conversation emphasizes the importance of understanding the forces acting on the blocks during the spring's compression and release.
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Two blocks, masses m1 and m2 are connected by an ideal spring of spring constant 'k' (Please see the figure in the attachment). The right block is shifted towards the left, pressing the spring by a distance 'x', and then released. We have to find the velocity of the COM of the spring-blocks system as the left block leaves the wall. (All surfaces are smooth)
The leftmost block breaks of the wall when the spring will regain it's natural length. Hence, I applied the law of conservation of energy with respect to the ground, taking the spring and blocks as a system, between the times when the right block is released and the time when the left block leaves the wall. I'm not sure how to go about after this, as I have two variables, the velocity of the two blocks, and The law of conservation of momentum of the system from the ground frame won't be applicable as the wall exerts a normal reaction of the left block. Please help!
 

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Why can't you just use conservation of energy? What will be the initial velocity of the left block as it leaves the wall?
 
It's unknown!
 
Ashu2912 said:
It's unknown!
Take a guess! :smile:
 
Well, if you are saying that it's not a variable then it must be zero, but I don't understand how... Is it because the net force on the left block is zero at that instant, and thus, it's velocity remains zero?
 
Ashu2912 said:
Well, if you are saying that it's not a variable then it must be zero, but I don't understand how... Is it because the net force on the left block is zero at that instant, and thus, it's velocity remains zero?
Yes, it's zero. The left block is jammed against the wall--it's not moving. When it starts moving, its initial speed is zero.
 
OK. Thanks, Doc! :smile:
 

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