Mass on incline plane sliding into spring, need to find max compression

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Homework Help Overview

The problem involves a mass sliding down a frictionless incline and colliding with a spring. The objective is to determine the maximum compression of the spring after the collision.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the energy conservation approach, questioning the energy transformations involved during the mass's descent and its interaction with the spring. There are clarifications regarding the setup of the spring and the distance measurement along the ramp.

Discussion Status

Participants are actively engaging with the problem, exploring different interpretations of the energy equations and the physical setup. Some have proposed adjustments to the energy equations based on the height change during compression, while others are verifying the correctness of their approaches.

Contextual Notes

There is a need for clarity on the ramp's geometry and the definitions of the distances involved, particularly whether the 4m refers to the distance along the ramp or the vertical displacement. The discussion also reflects uncertainty about the energy conservation principles applied in this context.

BryceHarper
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Homework Statement



A 11 kg box slides 4.0 m down the frictionless ramp shown in the figure , then collides with a spring whose spring constant is 190 N/m. The angle of the ramp is 30°. What is the maximum compression of the spring?


Homework Equations



Ei=mgh
Ef=1/2kx^2

The Attempt at a Solution



Ei=Ef
mgh=1/2kx^2
mgLsinθ=1/2kx^2
11(9.8)(4sin30)=1/2(190)x^2
1.5m = Max compression

I swear this is right but it's not, can anyone help me out?
 
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Is the spring laying on the ramp, or is there a flat part before the mass hits the spring, making the spring horizontal?

Also, does the 4m refer to the distance it slid along the ramp, or the vertical displacement?
 
The spring is laying on the ramp and the 4m refers to the distance it slid along the ramp.
 
You made the statement that the energy of the block 4 meters above the uncompressed spring is equal to the energy of the compressed spring, but that is leaving out a portion of energy.

From the point when the block is released to the time is stopped (at the maximum compression point of the spring) what is its change in height?
 
Ohhhhhhhhh!

So i should do:
1/2(4+Xmax)sinθ=1/2k(Xmax)^2

?
 
The left side should read 11(9.8) instead of (1/2), but besides that yes.
 
Whoops! I guess I was so excited to have finally figured it out that I wrote the equation wrong lol.

To verify

mg(4+Xmax)sinθ=1/2k(Xmax)^2

So...

1/2k(Xmax)^2 - mgsinθ(Xmax) - mg4sinθ = 0

And then use quadratic equation to solve for Xmax?
 
That looks right to me.

I wonder what the nature of the roots will be of that equation?
 
Got it! Xmax is equal to 1.8m

Thanks for the help Villyer!
 
  • #10
Of course :smile:
 

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