A 20 Kg. mass slides up on an infinitely long inclined plane (that forms an angle of 30º with the horizontal) with a velocity of 12 m/s. It's known that the mass returns to the starting point with a velocity of 6 m/s. Find,μ, the coefficient of friction between the plane and the body. This is the problem I'm struggling with. By the mechanical energy conservation principle I know that the work done by the friction force is the increment in kinetic energy. But, how can I relate that to Newton's equation to find μ. I thought, since the frinction force is μ*mgcos30, we can say μ*s*mgcos30 = ΔKinetic energy where s is the distance, but we don't even know the distance!! Thanks in advance, I'm new here!