How Is Momentum Conserved in a One-Dimensional Collision?

[Soph]

Homework Statement

A block, which has a mass of m1 = 9.50 kg is moving towards the left with a velocity of v1 = 7.20 m/s. When it collides with a second block, which has a mass of m2 = 5.50 kg, it is also moving towards the left, but with a velocity of v2 = 4.60 m/s.

What will be the total momentum of this system after the blocks collide?

Homework Equations

p = mv
Ek = 1/2 mv^2

The Attempt at a Solution

What I did was write out the equation of the initial momentum that equals to the final:

(9.5)(-7.2) + (5.5)(-4.6) = (9.5)v1prime + (5.5)v2prime

giving me: -93.7 = (9.5)v1prime + (5.5)v2prime

I also wrote out the initial and final kinetic energy equation:

(0.5)(9.5)(-7.2)^2 + (0.5)(5.5)(-4.6)^2 = (0.5)(9.5)v1prime^2 + (0.5)(5.5)v2prime^2

giving me: 304.43 = 4.75v1prime^2 + 2.76prime^2

I'm stuck on the process of substituting the two equations to find the final velocities of the two objects. Could someone lead me through the process of substituting the numbers or is there another way of looking at this?

 

[lewando]

What is the momentum of the system before the collision? Assuming no heat loss during the collision, what can we conclude about the momentum of the system after the collision?