How Far Will the Ice Cube Travel Up the Slope?

[Ritzycat]

Question statement
A 55g ice cube can slide without friction up and down a 25∘slope. The ice cube is pressed against a spring at the bottom of the slope, compressing the spring 10cm . The spring constant is 25N/m. When the ice cube is released, what distance will it travel up the slope before reversing direction?

Relevant equations
PE_s = PE_g
PE_s = 1/2kx^2
PE_g = mgh

Attempt at a solution
Maximum height is when all energy is converted to gravitational potential energy (frictionless environment)

Thus,

PE_s = PE_g

1/2kx^2 = mgh

1/2(25N/m)(0.1m)^2 = (0.055kg)(9.8m/s^2)(h)

h = 0.23m or 23 cm
(Answer is asked for in cm)

Not sure what I am doing wrong here...

 

[Orodruin]

You computing the height, not the distance along the slope.

 

[Ritzycat]

I'm so silly. I need to learn to read questions further before answering something different.

Distance up slope would be
0.23(sin 35°) = 0.40m = 40cm

but that's not right!

How do I compute the distance up the slope?

 

[NTW]

Wasn't it a 25º slope?

 

[Ritzycat]

Yes, it was... Thanks...