# Physics of power

## Examples of inelastic collisions

• Example 1: When billiard balls collide at normal speeds, they suffer no measurable damage because their collisions are almost perfectly elastic. All collisions conserve momentum, but only elastic ones conserve kinetic energy. So, if one ball with a certain velocity strikes a stationary ball on-center, it will transfer all of its momentum and kinetic energy to the stationary ball, stop, and cause the other ball to move away at the same velocity as the striking ball. If a perfectly elastic taekwondo student struck a perfectly elastic target, the target would fly off undamaged, but with lots of kinetic energy, perhaps sustaining damage when it hits the floor.
• Example 2: If, instead of hard balls, we use balls made of soft clay, then, when one ball strikes a stationary ball, both balls will mush together and move away with half the velocity of the striking ball. The kinetic energy before the collision is MV2/2. The kinetic energy after the collision is MV2/4. Half of the kinetic energy has gone into damaging the balls. Since both balls are equally damaged, each ball got damaged in the amount MV2/8.
• Example 3: If a hard ball strikes a stationary clay ball, only the clay ball will be damaged. Therefore, all of the lost kinetic energy MV2/4 went into damaging the clay ball.
• Example 4: If a clay ball strikes an anchored hard ball, all the momentum of the clay ball will be transferred to the earth, and all of its kinetic energy MV2/2 will be expended in damaging the clay ball. This is twice the damage of example 3, and four times the per-ball damage of example 2.

Therefore, as a taekwondo student, you should be as elastic as possible as protection against damage. Proper focus unites the bones, muscles, tendons, and ligaments into a structure that is better able to distribute forces elastically (non-destructively), such as pre-stressed concrete does in buildings. It also means that an onrushing opponent who is impaled on a well-rooted reverse punch will sustain more damage than a stationary opponent. The effect of having a firm stance is most important when the opponent is stepping toward you, therefore, your best strategy for causing damage is to wait for the opponent to step toward you with an attack, deflect the attack, and then use a well-rooted reverse counter punch. Colliding elastically does not transfer any kinetic energy, so it should be avoided. An inelastic collision with the target transfers kinetic energy that damages the target rather than your striking limb. You want your victim to be damaged, not pushed backward. To cause maximum damage to an opponent, targets should be chosen for their inability to respond elastically. The ability of a target to respond elastically depends on its structure, the speed of the impact, and the area of impact pressure.

All tissues have a range of pressures over which they are capable of responding elastically. The transition from elastic response to inelastic response is called "yielding." As pressure builds in a collision between two objects, both objects are initially elastic. A striker strives to have a larger elastic domain than the target. Once the target yields, the pressure between the two objects stops increasing and starts decreasing. When we consider momentum rather than pressure, the speed at which your technique travels has a greater effect upon the collision than the mass of the technique. Therefore, maximize speed to maximize damage. If purpose of a technique is to break bone, then use a high velocity impact with a small target area. If purpose of a technique is to cause internal damage, then use a technique that will transfer momentum.