Originally Posted by bhupaes
Suresh, the force we need to worry about is the external one being applied by the player wielding the racquet. That is a component that could skew the otherwise perfect equations of momentum and energy conservation, should it be significant enough.
Of course, the racquet and ball exert huge forces on each other. The equation for conservation of momentum will apply if that is the only force we need to worry about. The equation for energy conservation will also apply if the collision is perfectly elastic. However, an external force like the player can skew things, but in this case, as pointed out earlier, its contribution in terms of energy during the collision period can be ignored for the purposes of getting an approximate result.
The impulsive force is the force of collision and the equation for it is just the 2nd law. It applies whether or not momentum is conserved. The calculation uses the observed speed of the ball before and after to determine the change of momentum, and some other technique to determine the contact time.
From the racket point of view, the same force would be calculated it its initial and final speeds were recorded. We are interested in the initial speed because that is the independent variable.
This speed (at contact) is due to the acceleration of the racket till impact. For this acceleration, the force applied is difficult to calculate - it is the integral of m*a as a itself changes. The player then must exert this force plus the component of gravity force which is pulling down on the upward swing.
As I said before, toly can suspend a ball and a racket and swing the racket back and see if the ball shoots off at 80 mph. That will settle once for all whether gravity is the main force. I suspect strongly it is not. It is better to do this than claim stuff based on some math.