Half pipe with friction in the middle

1. The problem statement, all variables and given/known data
Consider a half pipe of height L. The middle section, non sloping part, has a friction coefficient of ##\mu_k = 0.1## and frictionless every where else. The length of this section is L. How many times can the skateboarder go back and forth before he stops?

2. Relevant equations
##\sum\mathbf{F} = m\mathbf{a}##

3. The attempt at a solutionIn the friction section,
$$
\sum F_x = v_x – F_f = v_x – .1N
$$
since ##F_f = \mu_k N##.
For the frictionless section, we would have (not sure about this part)
\begin{align}
F_y &= mg\cos(\theta)\\
F_x &= mg\sin(\theta)
\end{align}
Not sure how to determine how many times the skateboarder can go back and forth.

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