I am constructing a piece of sports equipment that requires me to know the amount of pounds of force the ball impacts on the equipment with the ball weighing 55 grams traveling a maximum of 75 mph a minimum distance of 10 feet or a maximum of 50 feet. the ball is 5.5 inches around when measuring around the entire exterior. The materials to be used vary greatly in weight and their pounds of force capabilities. I appreciate any and all help in advance. Thank you
The force depends greatly on the types of materials involved. You can read more here: http://en.wikipedia.org/wiki/Impulse_(physics) Softer materials that can change shape experience less force than rigid materials. This is because soft materials are in contact for a relatively long time during a collision. Since the the change in momentum is the average force times the time, when the time goes up, the force goes down. It also matters how much the material bounces, since a ball that bounces back changes its momentum more than one that is just stopped. But by far the biggest factor is the rigidity of the material, since the length of the collision can be an extremely tiny fraction of a second for a rigid material, while a much more considerable fraction of a second for a soft one.
thanks for replying, the ball is more rigid than a baseball, harder than compressed cork. It is very lively, but due to the core which is a very compressed hard springy rubber with solid exterior. It is running into a still, solid object
If the still object is much harder than the ball, then you can assume that all of the compression takes place in the ball to a good approximation. The force calculation then hinges on how much the ball deforms. You need some quantitative information on how compressible the ball is to calculate a force. If you have some information about how far the center of mass of the ball continues to move forward during the collision, then you can calculate the average force during the collision like this: kinetic energy of incoming ball = mass*velocity^2 change in kinetic energy = mass*velocity^2 - 0 = mass*velocity^2 change in kinetic energy = F*distance (work-energy theorem) so F=mass*velocity^2/distance this should be a good approximation. I'm only looking at the part of the collision where the ball slows down completely, ignoring the bounce back. This should not be a problem.
the safe assumption is that the object is not as hard as the ball, thereby being able to be torn apart by the collisions if not made with the correct materials