Question: Three identical billard balls form an equilateral triangle on horizontal surface. They only lightly touch each other therefore no force between them. The fourth billard ball is carefully lowered to the center and four balls form a regular tetrahedron. There is no friction between the balls and between the ball and the surface, no rotational motions for any of the billard balls. Assume perfect three-fold symmetry.
a) Because of symmetry both the top ball and three base balls are in one dimensional motion. Form a dimensionless lagrangian with two degrees of freedom, one for the top ball and one for three baseball. These two are related to each other through constraint.
b) Determine the equation of motion and solve equation of motion.
c) Solve the force between the top ball and one of the base balls. And use this force to determine the point where the solution of the equation of motion from a) stops to be validd)If R is 4 cm, Find the time it takes for the top ball to hit the surfacee) and the speed with which it hits the surface.