Multiple choice question involving conservation of energy on inclined planes

[mkwiatko]

Homework Statement

You have a pair of inclined planes such that a block that slides down one can slide up
the other without losing any energy in the transition. The inclined planes are both at an
angle θ from the horizontal, as shown in the diagram. The inclined plane on the left is
frictionless. You start the block sliding down either side from a height h. Which side do
you start the block sliding down to have it slide the greatest distance up the other side?

a) right side
b) left side
c) it doesn’t matter — it’s the same result starting from either side
d) one needs more information to answer the question

Homework Equations

Total work = change in kinetic energy (1/2mvf^2-1/2mvi^2)
change in mechanical energy = change in ke + change in pe

The Attempt at a Solution

I know that the answer is most likely starting from the left side, but I can't quite apply the conservation principles to show that this is the case. It slides down the entire length of the frictionless plane, whereas if you start in the plane with friction, it probably will slow down before it reaches the frictionless plane. Any help showing this would be much appreciated.

 

[PhanthomJay]

Can the block slide down one plane and up the other without losing energy, if either plane is not frictionless?