Connected bodies - Spring and 2 blocks

AI Thread Summary
A block of mass m is connected to another block of mass M by a massless spring on a smooth horizontal plane, with a constant force F acting on block M. The discussion focuses on finding the maximum extension of the spring from the ground frame rather than the center of mass frame. The net forces on both blocks are expressed, but there is confusion regarding the inclusion of internal forces in the calculations. Participants express uncertainty about whether to consider only external forces and how to account for the spring's behavior as the system moves. The conversation highlights the complexity of the problem and the need for further exploration of the equations involved.
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Homework Statement


A block of mass m is connected to another block of mass M by a massless spring of spring constant k. The blocks are kept on a smooth horizontal plane. Initially, the blocks are at rest and the spring is unstretched when a constant force F starts acting on the block of mass M to pull it. Find the max. extension of the spring.


The Attempt at a Solution



I can find the answer working from the reference frame of COM of the system of 2 blocks and spring.

I am interested in finding it from ground frame.

Net force on M, F1 = F-kx, where x is the extension in the spring
Net force on m, F2 = kx

Let the displacements of the two blocks be x1 and x2.

F1x1 + F2x2 =0.5k(x2-x1)2 (x2-x1 is the extension produced)

I am unable to find another equation.
 
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Abdul Quadeer said:
F1x1 + F2x2 =0.5k(x2-x1)2 (x2-x1 is the extension produced)

You should not include F2x2. Only include external forces!
But anyway this even won't give you result :frown:

I don't know if you can just subtract the forces or not.
I mean as soon as force F will act, body will start to move ... with even little expansion in spring, m2 will move with force kx'
this force will inc. with time till kxmax
I am not sure if you can just use the initial and final conditions and ignore the intermediate stages!
well I'm still trying and tell you my progress!
 
Did you come up with something?
 

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