1. The problem statement, all variables and given/known data A particle is placed on top of a smooth (frictionless) sphere of radius R. If the particle is slightly disturbed, at what point will it leave the sphere? 2. Relevant equations Same as first question, just F = ma = ΣF_i 3. The attempt at a solution Similarly, we want to know when the normal force of the sphere on the particle is overcome: F_norm = F_cent mg CosΘ = (mv2/r) CosΘ = y/R (where y is the height above the center of the sphere) So: y = v2/g Finding v2: Using conservation of energy, PE_initial = PE_final + KE_final mgR = mgy + mv2/2 Solving for v2 v2 = 2g(R-y) Placing into equation for y: y = 2g(R-y)/g = 2(R-y) Solving for y: y = (2/3) R Correct? Or am I making a horrible mistake?