# Maximum compression distance of a spring

## Homework Statement

Block #1 (m=2.00 kg) traveling to the right at 5.00 m/s along a level frictionless surface collides elastically with block #2 (m=3.00 kg) attached to a massless spring of spring constant 275 N/m. Assume that block #2 was at rest before the collision.
(a) calculate the celocity of each of the two blocks immediately after the collision
(b) calculate the maximum compression distance of the spring

## The Attempt at a Solution

I found the answer to part a by using the equation m#1*V#1+m#2V#2=(m#1+m#2)V
(2)(5)+(3)(0)=(2+3)V
v=2m/s
but i'm not sure how to go about part b

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Doc Al
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I found the answer to part a by using the equation m#1*V#1+m#2V#2=(m#1+m#2)V
(2)(5)+(3)(0)=(2+3)V
v=2m/s
but i'm not sure how to go about part b
The collision is elastic, not inelastic. Use a different equation for momentum.

What else is conserved besides momentum?

Doc Al
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## The Attempt at a Solution

I found the answer to part a by using the equation m#1*V#1+m#2V#2=(m#1+m#2)V
(2)(5)+(3)(0)=(2+3)V
v=2m/s
On second thought, the question is a bit ambiguous when is says "immediately after the collision". If they mean at the point of maximum compression, then your method is correct. But if after the collision means after they separate, then you'd need a different equation. Given that they probably want you to use (a) to solve (b), I'd say you probably interpreted it as they wanted you to and have the correct answer. To solve (b), answer my question: What else is conserved?

ok so i tried V#1-V#2=V#2-V1
and i got V#2=V#1+5
then i plugged that into m#1*V#1+m#2v#2=m#1V#1+m#2V#2 and that came out to be 4
is that correct? and i'm still not sure how to find the maximum compression distance of the spring

i believe kinetic energy is conserved

Doc Al
Mentor
ok so i tried V#1-V#2=V#2-V1
and i got V#2=V#1+5
then i plugged that into m#1*V#1+m#2v#2=m#1V#1+m#2V`#2 and that came out to be 4
is that correct?
If you interpret question (a) as I first did (find the speeds after they separate), then that's correct. But you'll need to find the speed of the other mass as well.

As I said above, it's not clear to me which interpretation of "immediately after the collision" was intended.

and i'm still not sure how to find the maximum compression distance of the spring
Find the speed of the system when the spring is maximally compressed. Hint: You already did!

i believe kinetic energy is conserved
Not kinetic energy, but total mechanical energy is conserved. Don't forget about the spring.