## dx13 3 years ago Two blocks are on a frictionless, horizontal surface. Block II is stationary and has a spring attached facing block I, which approaches with a speed v. The spring compression is a maximum when the blocks have the same velocity. Briefly explain why this is so.

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1. AERONIK

use momentum conservation equations or solve the problem using the concept of reduced mass from the cm frame...

2. dx13

no I figured out the different velocities and the compression I need to know why the max compression is when they are at the same velocity, I need a conceptual explanation rather than the computational one.

3. AERONIK

actually this result comes only when you solve it that way, there is no perfect conceptual reason for it, it is just the way nature works and you get to know that by solving some trivial equations

4. dx13

would it have anything to do with it being an elastic collision and that this may be the point in which the most kinetic energy has been converted in potential energy in the spring?

5. AERONIK

the 2 blocks will never collide with each other.

6. dx13

yes but I mean as a system it would be an elastic collision, such as if block II is thought of as a whole object not as a block and spring, it would be an elastic collision between the two systems

7. AERONIK

yes it will be elastic just to say that energy is not lost when the block collides with the spring...

8. dx13

and the energy would briefly be transferred into potential energy of the spring due to compression so when the velocities are the same that would mean the spring has its max potential energy is there a reason for that?

9. AERONIK

yes correct..

10. dx13

but is there a reason it happens at that moment?

11. AERONIK

no it just comes that way naturally and that is what the equations tell, due to the spring the first block slows and the second block fastens and it so becomes tht the compression is max, when both have the same velocity.

12. dx13

I see I understand what you mean I'm just trying to put that in terms of an explanation of the equations since I can see the graph of it but I'm having trouble putting it into a conceptual explanation past thats just the way it works.

13. AERONIK

strange but true,

14. dx13

ok thank you I'll try and go from there and I'll come back if anything else comes up thanks for your help.

15. AERONIK

welcome. where are you from ?

16. AERONIK

i mean which school ?

17. dx13

im still in high school this is for a physics ap course

18. AERONIK

in the united states ?

19. dx13

yes

20. dx13

which school are you from?

It is because when both blocks are of the same velocity, their relative speed to each other is zero. I.e. The block does not see the other block moving. It is impossible to have the blocks phase through each other so their relative velocity at that time must be same, i.e. zero. When such an event happens, it also happens that the spring cannot be compressed further. Do you follow?

22. AERONIK

his question is why cant the spring compress further when such an event takes place?

As said, during that even, due to the blocks unable to phase into each other, the spring will not compress further. The blocks cannot go into one another.

Naturally, from logic, since the blocks cannot go into each other, they have to bounce away. So, during that time, the spring is max. compressed.

25. AERONIK

during such a collision the maximum compression doesnt mean that the spring is totallly compressed, it is the highest limit that the spring is compressed with the particular given speed of the blocks...

Yes, that's why the choice of words is max. compression. :)

27. AERONIK

yes that word is quite misleading...