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so there is an exercise where you need to find out what the maximum compression is of two blocks hitting eachother, what the velocities are after the collision and if the collision is elastique. I've tried and tried but didn't seem to get anywhere. Maybe I'm just making a stupid reasoning error. Hopefully one of you could help me, it would be very much appreciated :). The question goes as follows:

A mass of 3kg and a mass of 4kg lay on a frictionless surface. The mass of 3kg moves with a velocity of 8m/s towards the second mass, to which a spring is attached with a spring constant of 850N/m.

Question 1: What is the max. compression of the spring? Question 2: What velocities do the 2 objects have after the collision? Question 3: Is the collision elastique?

If someone knows the answer it would be very much appreciated if you would share your wisdom.

Thanks in advance

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  • $\begingroup$ Have you tried to solve the problem yourself? $\endgroup$
    – Gert
    Commented Jan 7, 2021 at 22:17
  • $\begingroup$ Possible duplicate: physics.stackexchange.com/questions/59952/… $\endgroup$
    – fgoudra
    Commented Jan 7, 2021 at 22:21
  • $\begingroup$ It would be good if you included your work as at least we will know what you tried. $\endgroup$
    – Notwen
    Commented Jan 8, 2021 at 1:54

2 Answers 2

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I am just going to explain the process going on.

As they collide the spring will compress first till both the blocks reach same velocity; as now they move with same velocity the spring does not compress further and max compression is reached. Now due to $F_{spring}$ the blocks will seperate and the spring will extend back to orginal position.

Momentum and Energy remains conserved throughout as no external force is acting, you have to find max compression which occurs when they move with same velocities.

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In addition to the prior answer: an ideal spring is always elastic, as it has zero mass and zero damping. The spring can only store energy, temporarily. It cannot dissipate it, or keep it stored (as potential/kinetic energy oscillations after the collision, as $m=0$).

A spring with damping, of course, cannot be elastic: it losses energy if it moves.

A linear spring with finite mass can never have an elastic collision, even with zero damping. It returns to $x=0$ with velocity, which means momentum, which means energy, and if it lets go of the mass after passing $x=0$, then it has stored energy.

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