Two blocks with masses 1 kg and 4 kg, respectively, are moving on a horizontal frictional surface. The 1-kg block has a velocity of 12 m/s, and the 4-kg block is ahead of it, moving at 4m/s. The 4 kg block has a massless spring attached to the end facing the 1-kg block. The spring has a force constant k equal to 1000 N/m.
a. What is the maximum compression of the spring after the collision?
b. What are the final velocities of the blocks after the collision has taken place?
conservation of momentum (inelastic and elastic)
The Attempt at a Solution
For an instant, the collision is inelastic
mv1i + Mv2i = (m+M) vf
Solve for vf--> vf= 5.6 m/s
All kinetic energy goes into compressing the spring:
Solving for x gets .396 m.
My review book uses the same method as me but says that final velocity should be 53.6 m/s. And thus, x= .05 m. Am I correct or is the book correct? Also, it doesn't matter what units mass is in, right?