Collisions with Springs

1st2fall

When a mass collides with a spring attached to a different mass; why is the maximum compression of the spring when the velocity of both masses is the same? (Spring is massless and surface is frictionless to make things simpler)

My mechanics teacher told me this when I was solving (or rather, failing to solve) something I saw in a book (for fun).

Also, how would an equation of motion for the "chunk" that is the masses+plus spring come out? I felt like I was over complicating things when I did it.

So basically, I'd like help understanding collisions that are inelastic...then elastic.

(Can anyone help me find some similar situations I could look at?)

*This wasn't for homework and I am not looking for a solution~ I'm just looking for understanding of motion.

**Thanks in advanced!!!

tiny-tim

Hi 1st2fall!
That's just geometry …

maximum compression is when the d/dt (x₁ - x₂) = 0,

which is the same as dx₁/dt = dx₂/dt,

ie both velocities are the same.
There are no external forces on it, so its centre of mass … ?

1st2fall

But there is a potential being stored in the spring shouldn't this be "sucking up" kinetic energy for a brief period of time and slowing the bulk motion?

tiny-tim

Hi 1st2fall!

(just got up …)
This has nothing to do with physics.

It's just geometry … "maximum compression" means minimum distance between the masses (it doesn't matter why), and that means the masses have the same velocity.

1st2fall

Wait...is this because if both sides attached are moving at the same velocity....there'd be nothing "pushing" it in? oh...fail...I think I understand...

No, I mean while the velocities *are* different, while it's in the process of compression. If the spring is moving relative to it's initial position... the kinetic energy is being converted into potential, wouldn't the moving spring slow down? Or am I badly missing something here too... ??

Energy conservation and me don't get along very well. I got 33.75 on my practice exam multiple choice (35 questions, .25 deducted per incorrect) for mechanics because I missed a simple spring problem.... I really need to understand this and conservation much better so that I don't have such trivial problems when I'm in mechanics II next year @.@

tiny-tim

You're making this too complicated.

Just because it's a spring, that doesn't mean any of the laws of springs are needed.

"Maximum compression" means the spring is shortest.

Never mind why it's shortest … you're told that it is shortest, and if it's shortest (or longest), the two ends must have the same velocity.