Linear momentum- is my answer correct?

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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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Answers and Replies

  • #2
gneill
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The final velocity of what is supposedly 53.6 m/s? Surely not the 4kg block?
 
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a.
For an instant, the collision is inelastic
mv1i + Mv2i = (m+M) vf
Solve for vf--> vf= 5.6 m/s

This part seems correct to me, although I wouldn't call it 'for and instant'. It's the total time for the spring to compress. But maybe we're talking semantics here.

All kinetic energy goes into compressing the spring:
.5mv^2=.5kx^2

I think you should reconsider this part. If all the kinetic energy goes into the spring as potential energy then both blocks would be at rest. However, both blocks were moving in the same direction and had a collision. By what mechanism would would both blocks come to rest? Even if the 1kg block was brought to a stop by the spring force, the 4 kg block would be pushed from the rear increasing its velocity. I think it would be correct to say that 'some of the kinetic energy goes into compressing the spring.'

My review book uses the same method as me but says that final velocity should be 53.6 m/s.

gneill is skeptical of this answer and so am I. I think it's way too high. I got an answer that was less than 10m/s.
 

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