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In the case of board breaking by a karate practicioner there are two possible scenarios. First is that the board isn't broken so the karateka's hand really hurts. In the second possibility the board is broken and the hand hurts a lot less. So, by the pain on the hand, we can assume that in the first case the force exerted by the board towards the hand is greater than the second case. Accordingly to Newton's third law, this force is the same with that of the hand's exerted to the board in each case. So, a relatively low force can break the board and a higher one can't?

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Try it yourself - you don't need a board, you can just use a wall and a piece of paper. Let's assume that your punch is of standard strength. If you punch the wall, chances are you'll hurt a lot. If you punch the piece of paper, chances are you won't hurt at all. Since your punch is of standard and unchanging strength, why is there a difference?

The reason is the acceleration your hand feels at the moment of impact. When you punch the paper, the paper deforms around your arm before breaking. That means your arm takes (comparatively) more time to decelerate - say, 0.1s. When you punch the wall, the wall doesn't budge and your arm takes much less time to decelerate - say, 0.001s. That translates to an acceleration that's 100 times larger. By $F = ma$, the force you feel in the second case is also a hundred times larger than in the first case.

For the same reason, if you jump off a table, it's preferable to bend your knees upon landing. The more you bend, the more comfortable the jump is going to be.

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  • $\begingroup$ Thanks for the answer. I believe that the two speculations you make can't be both true. It is not possible that the force I apply to the wall and the piece of paper is the same and that each of these exert to me a different force. This would violate Newton'w third law. I agree that the wall applies more force to me, but that should mean that I also apply a greater force to the wall than the paper. $\endgroup$ – john k Dec 8 '17 at 11:07
  • $\begingroup$ Sorry my answer wasn't complete enough. When your fist goes through the paper, it both takes more time to decelerate and doesn't decelerate as much. To put some numbers, say your fist moves at 10 m/s. After going through the paper, it's slowed to 9 m/s. With the times given above, the acceleration is 1 m/s divided by 0.1s = 10 N, and that's the force you feel. On the other hand when your fist rebounds from the wall, it would have something like -10 m/s velocity after rebounding. That's a force of 20000 N. Newton's 3rd law is not violated. $\endgroup$ – Allure Dec 8 '17 at 20:57
  • $\begingroup$ I totally agree with what you said now. But if paper and wall are replaced by a board which breaks in the first case and doesn't in the second. Does this mean that a 10N force was able to break the board but a 20000N one wasn't? $\endgroup$ – john k Dec 8 '17 at 21:46
  • $\begingroup$ If it's the same board that won't happen. If they're different boards then it just means that the first board is made of a material that's a lot weaker than the second board's. $\endgroup$ – Allure Dec 9 '17 at 10:22
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    $\begingroup$ I am sure it will happen. If you punch a board with medium power and speed it won't break and you will hurt your hand. If you punch it with much more speed it will break and the pain on your hand will be much less. $\endgroup$ – john k Dec 10 '17 at 19:40
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A karate punch is much more than exerting as much force as possible. It's important to hit the target in a precise way that

  1. minimizes the impact area in order to maximize pressure, and
  2. makes use of the body hardened spots and damping structures in order to minimize damage to self.

So, the more intense pain of a failed attempt doesn't necessarily correspond to a larger force, but it may instead simply result from the force being applied to the hand in a more damaging way. And, even if a stronger force is involved, it might fail to break the board because it's spread over a larger area or not applied abruptly enough, allowing the board to deform instead of break.

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    $\begingroup$ Also, physical damage often depends on the third derivative $x'''$ (jerk), not just on the acceleration $x''$. For example, a constant acceleration can never cause vibration, and vibration often damages things. $\endgroup$ – Ben Crowell Dec 19 '17 at 20:36
  • $\begingroup$ @BenCrowell, good point, I hadn't thought of it. $\endgroup$ – stafusa Dec 19 '17 at 20:51
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Accordingly to Newton's third law, this force is the same with that of the hand's exerted to the board in each case.

This is an incorrect assumption, and perhaps part of the problem you are facing.

As mentioned in other answers; an important factor is the time required to slow down your hand. Something softer will compress more. The more it compresses, the longer it should take to slow down the hand (assuming the same impact speed for comparison). Since it takes longer to slow down, it has less acceleration on your hand. Net force is proportional to acceleration; so the less the object deforms; the more force it applies to your hand.

Another important factor that seems to have gotten overlooked in these answers is the difference in motion between going through a block, and hitting into it.

Another way to think of applied force is to think of the acceleration required to reach your new speed.

In the case of going through the block; your final speed is not $0$. You still have some velocity after breaking it, which is used to keep your hand going.

When you hit into the block, your hand stops completely. This means the force applied by the block to your hand is based on the acceleration required to stop your hand.

When you go through, since you still have some velocity, you must have experienced less acceleration due to the block than in the scenario where you are stopped by the block.

This means that not only does the hardness of the surface effect the impact force; but the impact force is actually less when you go right through, as compared to when you hit the block and are stopped by it.

That's not really to say that it should be easier to go through a block than to hit into it; but really it means that blocks that you are able to break through will apply less force to your hand than ones that you cannot break through; even if impact times are the same.

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  • $\begingroup$ I agree, this is exactly what I claimed in my original post. So, as said yourself, when you go right through the impact force is less. By Newton's third law the impact force your hand feels is the same as the force applied by your hand onto the board. So, a smaller force is able to break the board but a greater force isn't? $\endgroup$ – john k Dec 21 '17 at 16:35
  • $\begingroup$ @johnk No. That's a separate problem entirely. If the board is too strong; you wont have enough force to make it through anyways; and you get the full reaction on your hands. If the board is weak enough to chop through, you should experience less of a reaction force than a stronger board that you don't break through; even if you supply the same force to your arm in both scenarios. $\endgroup$ – JMac Dec 21 '17 at 16:39

protected by Qmechanic Dec 19 '17 at 15:01

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