1. The problem statement, all variables and given/known data A small block of mass m starts from rest and slides along a frictionless loop-the-loop as shown in the image. What should be the initial height h, so that m pushes against the top of the track (at a) with a force equal to its weight? Ans. h=3R 2. Relevant equations KE=(1/2)mv2 PE=mgh Fc=mv2/r 3. The attempt at a solution PEi=mgh KEa=PEi-PEa=mgh-2mgR (1/2)m(va)2=mgh-2mgR va=√(2gh-4gR) Fc=mg mg=(2mgh-4mgR)/R 2h-4R=R h=(5/2)R I think I attempted the problem in the correct manner, but perhaps made a subtle algebraic mistake since the coefficient is only off by 1/2.