Displacement of spring of a block going down an incline

AI Thread Summary
The discussion revolves around a physics problem involving a block sliding down an incline and compressing a spring. The inclined plane has an angle of 20 degrees, and the spring has a force constant of 455 N/m. The block, with a mass of 2.71 kg, is projected downward towards the spring with an initial speed of 0.750 m/s from a distance of 0.330 m. The user attempts to apply energy conservation principles but arrives at an incorrect compression value of 0.226 m. The thread seeks clarification on the error in the calculations leading to this incorrect result.
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Homework Statement


An inclined plane of angle θ = 20.0° has a spring of force constant k = 455 N/m fastened securely at the bottom so that the spring is parallel to the surface as shown in the figure below. A block of mass m = 2.71 kg is placed on the plane at a distance d = 0.330 m from the spring. From this position, the block is projected downward toward the spring with speed v = 0.750 m/s. By what distance is the spring compressed when the block momentarily comes to rest?

Homework Equations


dE=dk+du=0

Kf-Ki+Dfsp-Disp+Dfg-Dig=0
Ki=1/2mv^2
Dfsp=1/2kx^2
Dig= mg[h + x(sin20.0)]

The Attempt at a Solution


Kf,Disp, and Dfg all Equal zero
so by substitution:

-1/2mv^2+1/2kx^2-mg[h + x(sin20.0)]=0
-(2.71)(.75^2)/2+455/2x^2-(2.71*9.8)[0.33+xsin(20)]=0

which simplifies to
227.5x^2-9.084x-9.52=0

My answer is .226, which is the incorrect answer. What am I doing wrong?

Thanks!
 
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