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

BryceHarper

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

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?


2. Relevant equations

Ei=mgh
Ef=1/2kx^2

3. 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?

Villyer

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?

BryceHarper

The spring is laying on the ramp and the 4m refers to the distance it slid along the ramp.

Villyer

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?

BryceHarper

Ohhhhhhhhh!!!

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

?

Villyer

The left side should read 11(9.8) instead of (1/2), but besides that yes.

BryceHarper

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?

Villyer

That looks right to me.

I wonder what the nature of the roots will be of that equation?

BryceHarper

Got it! Xmax is equal to 1.8m

Thanks for the help Villyer!

Villyer

Of course