1. The problem statement, all variables and given/known data A ball is released from height h. The friction coefficient between the straight part and the ball is 'u'. I need to find the smallest h so that the ball doesn't fall off the track. The angle alpha=45 degrees. 2. Relevant equations Work of non-conservative forces = Change in mechanical energy 3. The attempt at a solution I calculated the work done by the friction force while the ball is going down the straight part. Wf=-u*mg*cos(alpha)*X X=the length of the straight part. We get that: Wf=-u*mg*h since cos(alpha)/sin(alpha)=1 Now I want to say that Wf=change in mechanical energy, so: -u*mg*h=mg(0-h)+0.5*m(v^2-0) when v=the velocity of the ball when it reaches the end of the straight part. We get: v^2=g*h(1-u) Now to the second part, the frictionless rail. Since all the forces are conservative now: 0.5*m*V1^2=0.5*m*V2^2+mg2R When V1^2=g*h(1-u) -----> (the velocity we found before) V2=the velocity at the top of the loop So I want that V2>0, so after some work we get: h>(2R)/(1-u) but when I put in a numerical answer I'm told that I'm wrong. Is there a mistake in my solution?