# Zero Force Still Hurts

1. Jul 18, 2007

### Deep Thought

I think I understand this concept but wanted to get other opinions. My son and I are Taekwondo Black Belts and have to break boards occasionally. My son frequently has trouble breaking his and this got me thinking about the physics aspect of board breaking.
I know that the force applied to the board in a strike is F=ma where the body is the mass and the acceleration is the velocity change of the punch. (This example assumes the punches are parallel to the ground). If he tries to strike the board and reaches constant velocity before impact then the force should be zero since acceleration is zero. Additionally, the force could be negative if he pulls the punch so that it is slowing (decelerating) before impact. This just seemed counter-intuitive that the force is 0 since it certainly doesn't feel like a zero force impact.
After thinking about this, my conclusion is that when the force = 0, then the board exerts the same force as the punch resulting in a net of 0. If the force is negative then the energy of the punch (which is not the same as force) is transmitted back to hand by the board (which is why it hurts). Only by creating a positive force that exceeds the breaking strength of the board through punch acceleration can the board be broken.
Do I have this analysis correct?

Thanks!
Deep Thought

2. Jul 18, 2007

### Staff: Mentor

The fact that the striking hand may have a constant velocity before contact is made does not imply that the force of impact is zero! The acceleration that matters is the one caused by the collision of hand with board, not the acceleration of the hand caused by your muscles prior to the strike making contact.

You will always be exerting a "positive" force on the board. And, from Newton's 3rd law, the board will always hit back with the same force that you hit it--but since the forces act on different objects (your hand versus the board), they do not result in a net force of zero on either object.
It's certainly true that if your strike is off (too slow, wrong hand formation, poor body mechanics, wrong focus) you will not transmit enough energy to break the board or, alternatively, not create enough force upon impact to break the board. When it doesn't break, some of that energy gets absorbed by you. Not fun.
Your analysis is off, but nonetheless you generally want the strike to be as fast as possible and to be timed so that contact is made when the striking hand still has some "juice" left in the strike. (How's that for physics terminology? I'm a TKD blackbelt also, so I've been there; however, I no longer practice that art.)

3. Jul 19, 2007

### mgb_phys

The acceleration in "F=ma" is one thing that confuses people the first time.
The slowing down to a stop in an impact is also 'acceleration', so in a car crash if you go from 55mph to zero in 0.1s that provides a lot of 'F'.

Breaking boards require that you hit the board with as much speed as possible, the deceleration time will depend on only on the size and material of the board. So the faster you are going to start with the more 'acceleration' there is when you hit the wood.
The skill is in both being able to hit the board as fast as possible and in pulling the blow immediately AFTER the impact so that any residual forward movement is stopped before your hand either hits the floor or you pull a muscle.

(I'm only a karate white belt so can probably break matchsticks)

4. Jul 19, 2007

### Deep Thought

Well, I may not know the Physics as well, but I do know board breaking.

The most critical parts of the breaking art is the speed and size of the impact area. The goal is to concentrate the force in as small an impact area as possible. I've never really had an issue with pulling the punch back as I find that my hand rarely travels farther than the length of my arm and forward motion is usually stopped by the hapless fellow student holding my boards.

5. Jul 19, 2007

### GoldPheonix

The area and force thing deal with pressure, with deals with (correct me if I'm wrong here, I haven't studied Rhealogy very well, I'm only about to enter Freshmen year of college) Tensile points and pressure.

$$P = \frac{F}{A}$$

And since the force is constant (when it hits the board), it's a question of how much area. When dividing by smaller numbers, pressure goes up. When you reach the right pressure, the Tensile point is reached and the board breaks.

The force, however, is not determined by:

$$\Sigma F = m a$$

It is determined by how much force your muscles can give due to the electric interactions within them.

6. Jul 19, 2007

### mgb_phys

That's true in a static force but not in a kinetic Karate punch.
The reason you can easily break boards and rocks with a hand is that you hit them with high speed. The punch is slowed to an almost stop in a very short time giving high accelaration and so a high force.