1. The problem statement, all variables and given/known data A particle slides on a curved surface. It is restricted to move on a vertcial plane. The intersection of the plane with the surface is described in cartesian coordinates as y + a[cosh(x/a)+1] = 1. At which point will the particle stop having contact with the surface? https://photos-3.dropbox.com/t/0/AADzWSgbMZLGXIdOCX6lb0oMu6bl-mH71cbJsCVrx4Xzbw/12/28182931/jpeg/2048x1536/3/1390528800/0/2/2014-01-24%2001.11.44.jpg/oZ2_oe1_iEhNFra4ShU6Cyr6DYP7-a7nG4XenoDOSSs [Broken] 2. Relevant equations The section of the surface is described by y + a[cosh(x/a)+1] = 0, with a > 0. 3. The attempt at a solution I know the particle will leave the surface when the centripetal force is greater to the reaction force. By deriving the equation of the surface I can find the slope of the tangent at every point. That allows me to find a relation between the projection of the gravity force along that tangent and the projection towards the inside of the surface. I think that the centripetal acceleration if equal to the acceleration "along the surface", but I'm not sure of it. https://photos-3.dropbox.com/t/0/AAAHKCS9qlt1bta9g89jwVHfuAtG0dhl8wW_gPdvo9rAqA/12/28182931/jpeg/1024x768/3/1390528800/0/2/2014-01-24%2001.13.06.jpg/_b0bZJNQ9rimmLezj0yM8ld1bk56jww3cGt1w-yhZDo [Broken] Another solution I found is to find an expression v(x) from the conservation of energy and then derive it to find the aceleration, but this is the rate of change of the velocity modulus, so I'm not sure that it is related to the centripetal acceleration. Help please.