Finding the Next Collision Point in an Elastic Collision Problem

[OVB]

Homework Statement

A mass of .59 kg and a velocity of - 0.75 m/s approaches a stationary mass of 0.35 kg that is 53 cm away from the edge of a wall. The stationary (m2) pushes against a spring (elastic collision) that is within the 53cm of separation and reverses direction. How far from the end of the track does the next collision occur?

Homework Equations

vcm = (m1v1)/M = -0.47m/s

The Attempt at a Solution

I think i need to find the time between the first and second collisions, and then use this to find the second xcm (using the vcm I already know), relative to the first collision, and this should get me the answer, but I am not sure how to find the time it takes for the second collision.

 

[Astronuc]

Here is some useful background on elastic collisions.

http://hyperphysics.phy-astr.gsu.edu/hbase/colsta.html

http://hyperphysics.phy-astr.gsu.edu/hbase/elacol2.html

An elastic collision is defined as one in which both conservation of momentum and conservation of kinetic energy are observed. This implies that there is no dissipative force acting during the collision and that all of the kinetic energy of the objects before the collision is still in the form of kinetic energy afterward.

One needs to determine the velocities of each mass after the collision, then determined the equations of motion for each, and then solve for the position where the two particles meet (at the same time).

When a larger mass collides with a (smaller) mass, the large mass will continue in the same direction, assuming the collision is 'head on'. The smaller mass will rebound in the direction of the velocity large mass. In the case of the spring, the spring starts to compress which slows the second mass, until either the larger mass catches up to the smaller mass, or the smaller mass changes direction and collides with the larger mass.

To obtain a numerical solution, one needs the spring constant and rest length of the spring. Or, is the rest length of the spring 53 cm?

 

[OVB]

Oh, I understood the background info, it's the spring that's confusing me. The diagram shows it is small compared to the 53cm so I can't say what its length is. Since I don't know the k (or how to solve for it since there is no length of spring or force given) I can't determine the time between the initial collision between the smaller mass and the spring and the final release point of the mass on its way back.