Displacement of spring of a block going down an incline

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SUMMARY

The discussion centers on calculating the compression of a spring when a block slides down an inclined plane. The inclined plane has an angle of θ = 20.0°, and the spring has a force constant of k = 455 N/m. A block with a mass of m = 2.71 kg is projected towards the spring with an initial speed of v = 0.750 m/s from a distance of d = 0.330 m. The user attempted to solve the problem using energy conservation principles but arrived at an incorrect compression value of 0.226 m, indicating a miscalculation in their energy balance equation.

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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!
 
Last edited:
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I forgot to post the picture. Here it is:
7-p-063.gif
 
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