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# PART IV: Application of Science to Martial Arts - page 3 / 6

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In a collision, we have that the Force equals the change in Momentum divided by the change in time, or F=∂M/∂t. This leads us to the second important concept, called Impulse. The Impulse is simply the Momentum delivered in a specific time.

Impulse [kg m/s2] = Momentum delivered in a specific time. M*∂V/∂t

As you can see from above, ∂V/∂t is really Acceleration, so this can also be stated as F=MA. In fact, this is known as Newton’s Second Law. All Momentum is delivered only if the two bodies are allowed to remain in contact for an infinite amount of time. For our purposes, when hitting another person, we have only a short amount of time in which to transfer our momentum.

The next critical point is that of the transfer and dissipation of energy. There are many different kinds of energy. You have potential energy due to gravity and the chemical bonds in your body. You have energy stored in your muscles like a spring. But the most important for Taekwondo is your Kinetic Energy. This is just a fancy way of saying that you foot has energy because it is in motion.

Kinetic Energy [j] = Energy of a moving object 1/2mv2

Just like momentum, Energy is conserved. It may change forms, sometimes to unusable forms like heat and sound, but it will not be totally lost.

What happens when one person strikes another?

There are two main kinds of kicks, pushing kicks and snapping kicks. Pushing kicks include linear kicks like cut kick, and front kick and back kick can also be done in a pushing way. Even roundhouse kick can be done to push, although this is rare. In pushing kicks, the main purpose is to move the other person’s body. Thus, the main equation is F=MA. You are trying to apply a Force in order to cause the other person’s body to undergo an Acceleration. What happens if the other person is big? M will be large and then that will make A small. This just proves what you already know, that if you kick a bigger person they will not go as far. However, because of the concept of impulse, if you are in contact with the person for a shorter time (lower t) there will be a larger change in (MV). Thus, hitting for a shorter time will let you move someone farther.

Pushing kicks are not done to score, and the main scoring kicks are snapping kicks. In these kicks you are transferring momentum to the opponent and also transferring energy. Here the physics term Power comes in as the amount of Energy we can transfer in a specific time. Energy transfer is what is really important in snapping kicks, especially roundhouse kick. When your foot is in contact with a person, the Kinetic Energy from your foot is transferred to their chest protector. Some of this energy is transferred to heat energy, some is transferred to sound energy, and some penetrates into their body. Energy is the physical force that is responsible for causing damage, not Force or Momentum. Energy is also the physical quantity responsible for breaking boards.

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