The discussion centers on the impulse experienced by a tennis ball during three distinct phases: throwing, bouncing, and catching. It is established that the bounce results in the greatest change in momentum, calculated as -2m\vec{v}, compared to the throw and catch phases, which yield changes of m\vec{v} and -m\vec{v}, respectively. The reasoning is based on the principle that the momentum before and after the bounce involves a reversal of velocity, leading to a significant change. The analysis assumes no loss of kinetic energy, affirming that the conclusion remains valid even if energy is lost.
PREREQUISITESStudents studying physics, particularly those focusing on mechanics, as well as educators and anyone interested in understanding the dynamics of motion and momentum in sports scenarios.
IssacNewton said:yes you are right. bounce has the greatest change in momentum. let's say that velocity before the impact is \vec{v} , then velocity after the bounce would be
-\vec{v}. so initial momentum is m\vec{v} and final momentum is
-m\vec{v}. so the change in momentum would be -m\vec{v}-m\vec{v} which is -2m\vec{v}. but when the ball is caught, final momentum is zero, so the change in momentum is 0-m\vec{v} which is -m\vec{v}
same argument can be made for the case when the the ball is thrown.
Edit: I am assuming above that the kinetic energy is not lost. Even if the kinetic energy is lost, the reasoning is not affected.