## More discussion on Shock

Impulse is a change in momentum, measured in units of momentum (Mv), and integrating all of these tiny changes over the time of impact (dwell time) gives ½ Mv², which happens to be the formula for kinetic energy, and the dimensional recipe for the metric energy unit of the joule (kg.m²/s²). So Shock is the integral of impulse.

Following the First Law of Thermodynamics, we note that an impact of a ball with a racquet is an adiabatic process (negligible heat transfer), so the change in the internal or potential energy of the particles of the racquet is equal to the sum of the work done on the racquet by the player and by the ball. More background on the change in kinetic energy: If you drop something, its mass (M), accelerated by gravity (g = 9.81 m/s²), goes a certain distance (h) before hitting the ground. Mass times acceleration is force (Newton’s Second Law), and force times distance equals energy (in joules), so the kinetic energy of the object right before it hits the ground is Mgh. Just before impact, the object had a certain velocity v due to its acceleration by gravity, and it therefore had a kinetic energy of ½ Mv². At the bottom of its path its kinetic energy is zero because its velocity is zero, and all of the kinetic energy it used to have has been turned into potential or internal energy. If it rebounds, some of this potential energy becomes kinetic energy again, the amount recycled into kinetic energy being determined by the elasticity of the collision (coefficient of restitution). What is not recycled but remains in the racquet as an increase in its internal energy is Shock.