Compressed Spring Between Two Boxes

[Soniteflash]

Homework Statement

Two blocks of masses M and 2M are on a frictionless horizontal surface and are held in place with a compressed spring of negligible mass between them. If the blocks are then released and the block of mass 2M leaves the spring with a velocity v, the velocity of the center of mass of the blocks is

A zero
B -(v/2)
C -(2v/3)
D -(3v/2)
E -2v

Homework Equations

n/a ?

The Attempt at a Solution

I do not understand how the center of mass relates to the movement of the blocks. I remember from class that if an object exploded into thousands of pieces the center of mass would still be at the original position.
So I assume it is A. Zero.

 

[AlephNumbers]

I do not understand how the center of mass relates to the movement of the blocks. I remember from class that if an object exploded into thousands of pieces the center of mass would still be at the original position.
So I assume it is A. Zero.

Can you explain why it would be zero? I mean, you are right. But it might be beneficial to examine the problem a little more deeply.

 

[Soniteflash]

Can you explain why it would be zero? I mean, you are right. But it might be beneficial to examine the problem a little more deeply.

I am not quite sure but I thought it is similar or identical sort of to an explosion.

 

[AlephNumbers]

It is very similar to an explosion. Try using conservation of linear momentum and the equation for the velocity of the center of mass of a system of particles (or blocks, in this case) to show why your answer is correct.

 

[Soniteflash]

For linear momentum :
P_i=P_f
0 = m(-2v) + (2mv)
0 = -2mv + 2mv
0 = 0
Linear momentum is conserved.

Hmm, I don't really know an equation for the velocity of the center of mass of a system of particles. I know that the velocities of the boxes are both in opposite directions.

 

[AlephNumbers]

It isn't too difficult to prove.

Start with the equation for the center of mass of a system of particles. If you don't know that either, you can find it here http://hyperphysics.phy-astr.gsu.edu/hbase/cm.html.

Any ideas on what you can do to this equation to create an equation for the velocity of the center of mass?
It involves calculus.