1. The problem statement, all variables and given/known data I have gotten the following task: "A smal object is placed in a right circular cone turned "upside-down" with an apex angle equal to 90-2α degrees. The coefficient of friction is big enough to keep the object at rest when it's placed on the inne-side of the cone. After that, the cone is set in rotation with the period time T. If the object starts to slide or not, depends on its distance r to the vertikal axis the coen is spinning around. Show that the maximum value of r is given by: [itex] r = ( g T^2 / 4 π^2 ) (cot(α-β)) [/itex] where tanβ = μ " 2. Relevant equations Relevant equtions are: The equation for centripetal force: Fc = (mr4π^2/T^2) The equation for friktion force : Ff = FN μ 3. The attempt at a solution My thoughts are the following: The object will feel that there's a force pushing it outwards, the centrifugal force (this is a ficitive force, but I have tried and the real centripetal force leeds to the same eqation after a short while). The maximum value of r is when the valueforces pulling the object downward the slope equals those pulling it upwards. As r grows, so does the centrifugal (centripetal) force, causing the friction to change direction after a while. The force pulling the object downwards is one composant of the object's weight and the force pulling it upwards is one composant of the centrifugal force minus the friction. When the force pulling it upwards grows stronger than the force downwards, the object starts to slide upwards. r is therefore given by: sinx Fc - Ff = F1 where x = 45 - α The rest of my soloution can be seen in the attached picture (in the beginning of it I have renamed β to y). The problem is that I end up with an euqation saying r = (g T^2 / 4 π^2) cos (x-y) So all I have left to prove is that cos(x-y) = cot(α-β), but this is not really working out, partly becaus α-β = -45 degrees. So it must be a mistake somewhere, eighter in my calculations or (and this is probably more possible) in my reasoning about the problem. I would be very happy if you could help me find it and show me how the problem should be solved. I do also appriciate pictures/figures very highly, I helps me understand things a lot better. :) Thank you!