IMPULSIVE FORCES, COLLISIONS (IMPACT)

The effect of the applied force and the time over which the force is applied is called impulsive force or just impulse. These impulsive forces occur when two or more objects collide. In sport, there are many examples. A tennis

player or golf player hits the ball, a karateka hits an opponent or hits the punching bag, and a fencer executes a straight cut on the mask of the opponent and so on. The equation of the impulse is J = FΔt or N ⋅ s.

In physics, we talk about the impulsive force for a given time interval, which is equal to the change in momentum produced over that time inter-val, that is, J = m(vf – vi), where m is the mass, vf represents the final veloc-ity, and vi represents the initial velocity. This conception of the change in momentum is derived from Newton’s second law and is known in sports as the impulse–momentum relationship.

There are many different kinds of impulses in science. In sports, there are three different kinds of impulses:

1. Controlled impulse refers to the muscle effort and bone leverage, for example, striking or kicking.

2. Transmitted impulse occurs when, for example, a karateka is about to take off for a flying side kick. The take-off leg acts against the floor, but the magnitude and direction of impulse is determined by the free arms and leg, and not through the take-off leg.

3. Physiological impulse includes the nervous impulse initiated by dif-ferent agents and conditions: sound, light, taste, smell, mechani-cal, electrimechani-cal, and so on. In our case, we will refer to the first two impulses. It is important to explain the difference between impulse and impact.

The impulse (F × time) is not a force (N), it is an integral of force over time. The impact is a force (N). Impact deals with force and of course force deals with acceleration. The impact force is usually extremely short. The impact force has the same unit as the force (F = m ⋅ a). Impulse deals with momentum, which in turn deals with velocity. The impulse unit is kg ⋅ m/s.

Impulse can be increased by adding more force to the impact or by increasing the delivery time before the impact. There is a complete inverse proportionality about the force and time used before the col-lision. When a large force is used, usually the time must be extremely short or when the force is reduced, then the time delivery for the force must be much longer.

A body that is about to collide with another body does not change its physical shape. At the time of collision, one of the bodies or both can change their physical shape; however, they can regain their initial shape or form after the collision. In this case, we speak about elasticity of the object(s).

A collision in which the total kinetic energy after the collision is less than that before the collision is called an inelastic collision. To be more explicit, the body or bodies will change their physical shape. Example includes a car crash or when two bodies stick together after the collision, for example, a sticky material thrown against the wall.

A collision in which the total kinetic energy of a system will remain the same after the collision is called elastic collision. To be more explicit, the bodies will deflect each other with no physical change of shape. An example is when two billiard balls collide.

The body has the tendency to return to its normal shape once it has been deformed, that is, its elasticity differs from one body to another.

Some return very quickly to their original shape, while others do so less quickly. Because there is no way of directly calculating the elasticity of a body, it is necessary to rely on the different experiment results to predict the outcome of any given impact.

Newton formulated an empirical law, Newton’s law of impact, which states that if two bodies move toward one another along the same straight line, the difference between their velocities before the impact is propor-tional to the difference between their velocities after the impact. In order to correctly calculate the velocities before and after the impact, there is a term coefficient of restitution, which must be used in our calculation.

The coefficient of restitution (e) or COR is an indicator of elasticity of an object reflecting the ability of the object to return to its original shape once deformed, measured by the ratio of the impulse of rebound to the impulse of impact. This coefficient has a value between “1” and “0.” The value of “1”

indicates an elastic collision. The value toward “0” indicates an inelastic collision. To be more precise, the COR is an indicator of impact resistance.

The equation could be v₁ − v₂ = −e(u₁ − u₂) or v₁ − v₂/u₁ − u₂ = −e, where v₁ and v₂ represent the velocities immediately after impact of bod-ies 1 and 2; u₁ and u₂ are their respective velocities immediately before impact; and e is a constant known as the coefficient of restitution.

In martial arts, the impacts are almost 100% elastic collisions, when a strike hit a hard target (like the head). The only inelastic collision that could happen is when one or both of the combatants will have some broken bones. All collisions involve momentum p = (m ⋅ v) and impulse J = (F ⋅ t). In order to understand the importance of these terms, here are some examples with explanations.

In throwing objects such as tennis ball, football, javelin, discus, baseball, golf ball, and so on, the speed/velocity is important for gaining distance.

Using the impulsive force, the athlete should use a prolonged time in order to gain distance, but in karate particularly, speed is not important for gaining distance but it is extremely important to reach the target in the shortest time as possible.

In track and field and also in baseball, to successfully gain the distance, the athlete uses his hip power first, and then continuously uses the torso, the shoulder, and the arm finally to liberate the object. However, the hip is a pretty rigid entity and cannot turn more than 45° angle or a little bit more (see Chapter 4, Figure 4.3). That is why in order to gain speed, the athlete prolongs the time for force liberation, for example, for discus throwing, the athlete spinning his body and the baseball hitter executing the hit by a follow-through.

The importance of creating as large an impulse as possible is evident in the case of a baseball pitcher. The pitcher uses the longest time over which to apply the force to the ball before releasing it. Another example in base-ball is the hitter who is often encouraged to follow-through when striking the ball. We can find the same examples in tennis or golf as well.

High-speed films of the collision between bats/rackets and ball have shown that the act of following through serves to increase the time over which collision occurs. Surprisingly, this prolonged time for hitting favors not the force of the impact between the ball and the bat rather the change velocity of the ball to gain distance.

Karate, however, is a different story. The karateka must favor force over time. Where the force is larger and the time is shorter, the impact will be devastating, especially when the punching arm may bounce off the target like a whip on a heavier object. The withdrawn arm or in karate term, Snap-punch is which creates a more devastating effect on the opponent.

See the time and force relations that are inversely proportional. Table 8.2 will demonstrate this.

Let us say we need to have 100 N for the maximal effect of a blow/

throw/push.

TABLE 8.2 Force, Time, and Impulse Relationship F × t = J Force (N) Time Required (s) Acquired Impulse

100 1 100 units (max. impulse)

50 2 100 units (max. impulse)

25 4 100 units (max. impulse)

1 100 100 units (max. impulse)

8.6 ENERGY, WORK, AND POWER