Spring Compression on an incline

AI Thread Summary
The discussion focuses on a physics problem involving a box sliding down a frictionless ramp and colliding with a spring. The box has a mass of 11 kg and slides 4.0 m down a 30-degree incline before compressing the spring with a spring constant of 190 N/m. The maximum compression of the spring was calculated to be approximately 0.568 m, but confusion arose regarding the energy equations used. It was clarified that the initial gravitational potential energy should equal the elastic potential energy at maximum compression, without the additional gravitational term on the right side of the equation. The user has not yet addressed the second part of the problem regarding the compression at maximum speed.
luvey
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Homework Statement


A 11kg box slides 4.0m down the frictionless ramp which has an incline of 30o to the horizontal, then collides with a spring whose spring constant is 190 N/m.

a.What is the maximum compression of the spring?
b.At what compression of the spring does the box have its maximum speed?


Homework Equations


Spring: PE=1/2*k(\Deltas)2
Gravity: PE=mgsin(\theta)d
PEspring initial+PEgravity initial=PEspring final+PEgravity final


The Attempt at a Solution


I tried plugging in the numbers which gave me:
0+11*9.81*sin(30)*4=1/2*190(\Deltas)2+11*9.81*sin(30)*(4+\Deltas)
Which gave me the max compression of 0.56795 m

I haven't made it to part b yet because I can't seem to obtain the max compression.
 
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luvey said:

The Attempt at a Solution


I tried plugging in the numbers which gave me:
0+11*9.81*sin(30)*4=1/2*190(\Deltas)2+11*9.81*sin(30)*(4+\Deltas)
Which gave me the max compression of 0.56795 m

I haven't made it to part b yet because I can't seem to obtain the max compression.

You do not need the extra 11*9.81*sin(30) on the right side.

The left side is the initial energy which when it reaches the spring is being entirely stored as elastic potential energy.
 
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