1. The problem statement, all variables and given/known data A small mass m slides without friction along the looped apparatus shown in the attached file. (a) If the object is to remain on the track, even at the top of the circle(whose radius is r), from what minimum height hm must it be released(from rest)? (b) If it is released at a height h = 0.80hm, at what height will it lose contact with the track? 2. Relevant equations ac = v2/r KE = .5mv2 PEgrav = mgh 3. The attempt at a solution For a: I knew that for the object to complete the loop, it must be able to complete the extreme case: the top. I knew that the centripetal acceleration must be g. Therefore, from the centripetal acceleration formula, the speed had to be at least v = √(rg). From the law of the conservation of energy, I equated the initial and final(at the top of the loop) energies: mghm = 2rmg + .5mv2 I cancelled out the m and substituted v from the centripetal acceleration equation and got ghm = 2rg + .5rg = 2.5rg Cancel out g hm = 2.5r For b: The initial height .80hm = 2r. Using the law of the conservation of energy 2rmg = mgh + .5m(0)2. I substituted 0 for v in the equation above because I thought that the velocity had to be 0 when the object left the track. Solving for h, I got h = 2r. I have no idea if this is right. Could someone please tell me if this is right, and if not, give me a nudge in the right direction. Thanks.