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## Homework Statement

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?

## Homework Equations

conservation of momentum (inelastic and elastic)

## The Attempt at a Solution

a.

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:

.5mv^2=.5kx^2

--> mv^2=kx^2

(m+M)vf^2=1000N/mx^2

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?

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