Question for Wiccans. Help please!?

It's gravitational potential energy has diminished by an amount equal to mgR(1-cos(?)). The normal force from the sphere does no work, and therefore we can equate the work done by gravity to the increase in kinetic energy of the particle: 1/2 mv^2 = mgR(1-cos(?)) This means that the speed at angle? Is given by v^2 = 2gR (1-cos(?)).

For this circular motion, the combination of normal force and gravitational force component perpendicular to the surface gives the needed centripetal force: mv^2 / R = mg cos(?) - Fn So at any point along its path the particle experiences a normal force of Fn = mg cos(?) - mv^2/R The particle losing contact implies that there Fn=0, so that occurs when v^2 = gR cos(?). Using the equation we found from energy conservation thus gives 2gR (1-cos(?) ) = gR cos(?).

I cant really gove you an answer,but what I can give you is a way to a solution, that is you have to find the anglde that you relate to or peaks your interest. A good paper is one that people get drawn into because it reaches them ln some way.As for me WW11 to me, I think of the holocaust and the effect it had on the survivors, their families and those who stood by and did nothing until it was too late.