How Far Will a Mass Travel on a Frictionless Incline After Going Through a Loop?

[eestep]

Homework Statement

A mass starts at top of incline with a length of 10 meters with an angle of 36 degrees. Incline has friction with a coefficient of kinetic friction of .26. At bottom of incline is a horizontal, frictionless surface which has a loop of radius 2 meters. After loop is a frictionless incline which is inclined at an angle of 33 degrees. If mass is given enough velocity at top of first incline with friction such that it just makes it around loop, how far up second incline will mass travel in meters? Answer is 9.18.

Homework Equations

$$\Delta$$E=W_nc

The Attempt at a Solution

h=Lsin$$\theta$$
Wnc=Wfk+WFn=-fkL
Ef-Eo=-fkL
Eo=uo+KE
Ef=uf+KEf

 

[rock.freak667]

So using conservation of energy, what is the initial energy? At the bottom of the incline (just before the loop) what is the speed?

 

[eestep]

vo=4.9m/s
vf=9.9m/s