# Max Velocity While Compressing a Spring?

#### peterbishop

1. The problem statement, all variables and given/known data

A 17 kg box slides 4.0 m down the frictionless ramp shown in the figure, then collides with a spring whose spring constant is 210 N/m. (picture attached)

a) What is the maximum compression of the spring? (solved this part)
b) At what compression of the spring does the box have its maximum speed?

2. Relevant equations

F = -kx
Kspring = 1/2 * k* x^2

3. The attempt at a solution

I solved part a already and the answer was 2.2 m, so that's all good. Part b I'm having some trouble with. I've seen this problem attempt to be answered on other threads but no one ever discusses part b thoroughly, it's usually about part a, which I didn't have a problem with. I've seen quite a few people on the internet say that the answer is zero compression, because the spring will slow the box down when it hits it, but this is not the case, as the spring only lessens the acceleration: it is still accelerating, I believe until a point when mgsin(theta) = kx, x being the compression of the spring. Using this I get an answer of .023 m though, which isn't correct either. Any help would be appreciated. (Also I tried putting zero for the answer just for the heck of it but masteringphysics says it's wrong as well.)

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#### Doc Al

Mentor
I've seen quite a few people on the internet say that the answer is zero compression, because the spring will slow the box down when it hits it, but this is not the case, as the spring only lessens the acceleration: it is still accelerating, I believe until a point when mgsin(theta) = kx, x being the compression of the spring.
Sounds good to me.
Using this I get an answer of .023 m though, which isn't correct either.

#### peterbishop

Yep you're right, thanks, for some reason whenever I wrote it down in my notes before I did the calculation I left out mass.

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