What Happens to Block Velocities and Spring Compression in a Collision?

[abbie]

Homework Statement
A block of mass M1 = 13.6 kg and initial velocity v0 = 4.7 m/s collides with a block of mass M2 = 4.4 kg and initial velocity of -4.7 m/s. Attached to M2 is a spring with a force constant k = 10000 N/m. At one point the velocities of block M1 and block M2 are equal. What is the speed of block M1 at that point?
What is the compression of the spring when the velocities of the blocks are equal?

Relevant equations
conservation of momentum
conservation of energy

The attempt at a solution
I figure the moment when both masses have equal velocity is when they are presses together with M1 pressing against the string. At that point both masses will act as one and have the same mechanical energy, so using conservation of energy, I get:
0.5*(M1+M2)*V^2 + 0.5*K*X^2 = 0.5*M1*V1(ini)^2 + 0.5*M2*V2(ini)^2
I get the 2 variables that I'm trying to find but I'm missing another equation.
I tried using conservation of momentum, but I'm not sure if I can, since I'm looking for the moment right after the collision and I'm not sure final velocities to put there..

Any help would be good. I would prefer to figure it out by myself, but a little push in the right direction would be great :)

 

[abbie]

Just figured it out and feeling a little idiotic for not doing it sooner, so thanks anyway :)

 

[thomate1]

Your approach using conservation of energy is a good start. However, you are correct in needing another equation to solve for the two unknowns, the speed of block M1 and the compression of the spring.

To find this additional equation, you can use conservation of momentum. Before the collision, we know that the total momentum of the system is zero, since the two blocks are moving in opposite directions with equal but opposite velocities. After the collision, the blocks will stick together and move with a common velocity. This means that the total momentum after the collision is the sum of the two masses multiplied by their common velocity.

So, using conservation of momentum, we can set up the equation:
M1*V1(ini) + M2*V2(ini) = (M1+M2)*V
Solving for V, we get:
V = (M1*V1(ini) + M2*V2(ini))/(M1+M2)

Now, we can substitute this value of V into your equation for conservation of energy to solve for the compression of the spring.

Hope this helps! Keep up the good work in solving this problem.