Collision of a ball with the ground.
1) Suppose you have a ball and you let it fall from a height h1. It will acquire a final velocity, say v1, before touching the ground. Suppose the ball then bounces and reaches a new height h2

Question

Collision of a ball with the ground.
1) Suppose you have a ball and you let it fall from a height h1. It will acquire a final velocity, say v1, before touching the ground. Suppose the ball then bounces and reaches a new height h2<h1. Does anybody know which mechanism makes the height to be lower apart from friction? I mean, is friction with the air the most important contribution or is there anything else? (Take h1 and h2 of the order of some meters).
2) Same situation of point 1). Suppose that we know than in the collision some potential energy is stored in the ball. What do you think should happen now? Should such energy be released again in form of kinetic energy of the ball or should it be dissipated in some way? I think the first possibility should be excluded or h2 would be equal to h1. Could h2 be <h1 and still the energy be conserved? What do you think?

anonymous · Answer

Concerning point 2) I'd say that the elastic energy stored during the collision is given by
$${1 \over 2} m v_1^2=E_{el}+{1 \over 2}mv_2^2=E_{el}+mgh_2$$
where I imagine that v2 is the upward velocity of the ball after bouncing.