Solve Mass Spring System: Find Velocity & Compression

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In a mass-spring system with two masses (M and 4M) and a third mass (M) colliding inelastically, the proper approach involves using conservation of momentum rather than energy due to the nature of the collision. After the collision, both masses move together, and the velocity of the center of mass can be calculated as v/6. At maximal compression of the spring, both masses momentarily have zero velocity, allowing for the calculation of maximum compression by equating kinetic energy to elastic potential energy. The discussion emphasizes the importance of understanding the forces exerted by the spring on both masses during this process. The key takeaway is that the velocity of the smaller mass after the collision is v/6.
breez
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A mass M is attached to the left end of a spring with a spring constant K and a mass 4M is attached to the right end. A third mass of mass M slides with velocity v and hits mass M in a completely inelastic collision.

What is the velocity of the smaller mass and of the larger mass when the spring is maximally compressed?

What is the maximum compression of the spring?

Solve in terms of the variables; the surface is frictionless.


What I did was assume both springs have 0 velocity at maximal compression, and just solved for the compression by equating the elastic potential energy with the kinetic energy of the masses the instant after impact. I know my assumption is very unsound.

What's the proper way to solve this?
 
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For an inelastic collision, conservation of energy does not apply, one must use conservation of momentum. It will be useful to note that in a completely inelastic collision, both masses will 'stick together' forming a single body.

Next, you should realize that whatever force is exerted on the smaller mass (2M) by the spring is also exerted on the larger mass.
 
I understand that, but I stated I used Conservation of Energy AFTER the collision. Energy is conserved after the inelastic collision.
 
Last edited:
breez said:
What I did was assume both springs have 0 velocity at maximal compression

Hi breez! :smile:

Hint: what is the velocity of the centre of mass at maximal compression? :smile:
 
It would just be v/6. I really have no idea where to go on this one...
 
What's the speed of the left mass immediately after the collision?
 
breez said:
It would just be v/6. I really have no idea where to go on this one...
Yes, v/6.

Now what is the relative velocity of the two ends of the spring at maximal compression? :smile:
 

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