Energy/ work problem set(last question )

[Moe*]

Energy/ work problem set(last question!)

Homework Statement

A 53.5 g ice cube can slide without friction up and down a 33.0° slope. The ice cube is pressed against a spring at the bottom of the slope, compressing the spring 12.0 cm. The spring constant is 22.0 N/m. When the ice cube is released, what total distance will it travel up the slope, from the time the spring is fully compressed until reversing direction?

Homework Equations

1/2kx^2, mgh, maybe 1/2mv^2

The Attempt at a Solution

here's my best shot:
PE(spring) at bottom=PE(grav) at top
1/2kx^2 = mgh
since gravity has a component in x direction:
1/2kx^2 = mhgsin33
since sin33=h/d, h=dsin33:
1/2kx^2=m(dsin33)(gsin33)

using this, i got 1.02m+.12m (compression of spring).
i tried with and without compression of the spring, stillc ouldn't get the right ans. I'm sure 1 m is too long for a titchy little icecube to travel. any help would be appreciated.

 

[rl.bhat]

1/2kx^2=m(dsin33)(gsin33)

While calculating the PE due to gravity you should not take the component of g.
So 1/2*k*x^2= mgdsin 33

 

[Moe*]

thank you... and sorry about the long response