Need Help on an Elastic Potential Energy Problem on an incline

[portuwhat]

Homework Statement

A spring (k=75 N/m) has an equilibrium length of 1 m. The spring is compressed to a length of .5 m and a mass of 2 kg is placed at its free end on a frictionless slope which makes an angle of 41 degrees with respect to the horizontal. The spring is then released. a) If the mass is not attached to the spring, how far up the slope will the mass move before coming to rest? b) If the mass is attached to the spring, how far up the slope will the mass move before coming to rest? c) Now the incline has a coefficient of kinetic friction. If the block, attached to the spring, is observed to stop just as it reaches the spring's equilibrium position, what is the coefficient of friction?

Homework Equations

Conservation of mechanical energy
.5mvi^2 + mgyi + .5 kxi^2 = .5 mvf^2 + mgyf + .5 kxf^2

The Attempt at a Solution

So I began using the conservation of mechanical energy but I'm not even sure where to begin with that. What do I say the y is or x is in the equation? I have no clue, is there anyway someone can explain this to me without giving me the answer? Thanks.

 

[tiny-tim]

Welcome to PF!

Conservation of mechanical energy
.5mvi^2 + mgyi + .5 kxi^2 = .5 mvf^2 + mgyf + .5 kxf^2
…
What do I say the y is or x is in the equation?

Hi portuwhat! Welcome to PF!

This is just geometry …

y is the height (measured vertically, of course).

x is the extended length of the spring (measured along the 41º slope).

Have a go!