Am I doing this problem correctly?

[bcjochim07]

Homework Statement

a) A 50 g ice cube can slide without friction up and down a 30 degree slope. The ice cube is pressed against a spring at the bottom of the slope, compressing the spring 10 cm. The spring constant is 25 N/m. When the ice cube is released, what total distance will it travel up the slope before reversing direction?

b) The ice cube is replaced by a 50 g plastic cube whose coefficient of kinetic friction is 0.20. How far will the plastic cube travel up the slope?

Homework Equations

Us=.5kx^2
U=mgy
change in thermal energy= (force of kinetic friction)*(displacement)

The Attempt at a Solution

I got part a, and I want to make sure I am doing part b correctly.

Here's what I did.

Fk= mgcostheta * coefficient of friction
Fk= (.05kg)(9.80)(cos30)(.20)=.085 N

change in thermal energy= Fk* distance covered up slope (d)
change in thermal energy = .085 * d

I called y the final height so y=dsin30

Kf + Uf + change in thermal energy = Ki + Ui

(.05kg)(9.80)(dsin30) + (.085d) = (.5)(25 N/m)(.1m)^2
d= .379 m = 37.9 cm

 

[jamesrc]

Looks good.