# Freshman mechanics: 2 balls and spring [closed]

I got a trouble with solving this problem.

"Two balls with masses $m$ each are connected by spring of length $l$ and stiffness $k$ and initially at rest on the table without friction. One ball acquires initial speed $v$ perpendicular to the line connecting two balls. Determine this speed if the maximum length of spring during motion is $L$."

I thought that it is just about conservation of energy

$$\frac{m v^2}{2} = \frac{k (L-l)^2}{2}$$ where I assumed that when the stretching is maximum the velocities are zero. But it seems that it is completely wrong and one needs more accurate solution.

I also found some hint that one of the ways to solve this problem is to solve it in the center of mass reference frame. But I don't understand two things:

1. How to find the speed of center of mass right after the initial moment? It looks like one of the balls has speed $v$ and another is at rest (in the laboratory reference frame), so the speed of center of mass is

$$v_{com} = \frac{m v}{m + m} = \frac{v}{2}$$

It in its turn means that on the center of mass ref. frame one ball (with speed $v$) moves with speed $v/2$ while another moves with $-v/2$ in the opposite direction.

Am I right?..

1. Why do the balls continue their motion while the stretching is maximal? In other words, why does not all kinetic energy transform to the potential one?

P.S. And also why is it simpler to introduce COM reference frame? I think we can use both conservation laws (energy and angular momentum) in the laboratory frame, can't we?

## closed as off-topic by Kyle Kanos, John Rennie, Jon Custer, Yashas, sammy gerbilSep 7 '17 at 20:03

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "Homework-like questions should ask about a specific physics concept and show some effort to work through the problem. We want our questions to be useful to the broader community, and to future users. See our meta site for more guidance on how to edit your question to make it better" – Kyle Kanos, John Rennie, Jon Custer, Yashas, sammy gerbil
If this question can be reworded to fit the rules in the help center, please edit the question.