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?
[Physics] Karate and Newton’s 3rd law
collisionforcesnewtonian-mechanics
Related Solutions
Despite 11 answers to this question already, I don't feel that any have answered the question well.
(Note: This answer is simplified and assumes the punch is slow enough to ignore inertia and relativity)
Firstly, let's look at force at the atomic level. This is where the force is really happening. The forces that we feel in everyday life are generally the forces between atoms and molecules (intermolecular forces). I'll use Helium atoms as an example, because they're easy to draw. When two He atoms get close together, their electron shells overlap and cause them to repel each other. Note that you never get a situation where one atom repels, and the other does nothing, or one repels and one attracts. Always they both repel each other, or both attract each other, and both atoms feel the same magnitude force, in exactly opposite directions.
The force they feel is a function of the distance between them. The force between them behaves basically like a spring. In the illustration above, the two atoms are repelling each other, and will accelerate away from each other. As they move apart, the force decreases, until at a certain point, it reaches zero, and we consider them not to be 'touching' any more.
Now imagine we start with one atom stationary, and throw another atom at it. When the moving atom gets close enough to the stationary one, they will feel the force of repulsion. Both will accelerate based on the force between them. They accelerate in opposite directions, so the stationary atom accelerates and flies off, while the moving one decelerates to a stop.
Molecules behave in a similar way towards each other.
Since a wall is made up of molecules, it behaves pretty much like the force between molecules, except in a solid object, neighboring molecules are bonded together, meaning that when you push them closer together, they repel, and when you pull them further apart, they attract. The wall is basically a very stiff spring. When you push on a wall, it bends.
Bending is the only way it can push back on you. Bending means that some of the molecules in the wall are pushed closer together, and some are pulled further apart. The harder you push, the more it bends. It bends just so that it's pushing back on you as hard as you're pushing. If you're pushing with a constant force, everything is in equilibrium, and all the force vectors acting on each molecule add up to zero, so nothing is accelerating.
If you push hard enough, you'll manage to stretch some molecules far enough apart that their bond breaks. At that point the force between them drops to zero. Now those molecules are not in equilibrium, and they will accelerate away from each other.
If you push hard enough, and the wall breaks, it's no longer bending, it's accelerating away from your hand, just like the atoms in the example above. As it accelerates away, the force between your hand and the wall decreases and reaches zero when your hand and the wall are no longer 'touching'.
When you punch a wall, the forces you and the wall are feeling are entirely made up of the forces between atoms and molecules. So whether the wall stands or falls, Newton's 3rd law holds the whole time. The wall can only push back on your hand to the extent that it can bend without breaking.
But what if I push really hard on the wall?
The answer is you can't. You can put a lot of effort into the punch, but if you were to measure the actual force applied to the wall, it would increase up to the point, then the wall would break, then the force would drop back down to zero.
Newton's 3rd law doesn't mean that everything is indestructible.
Added:
If you haven't already discovered Veritasium's excellent YouTube channel, you should. He has a good video helping us to understand Newton's Third Law:
To the first question: Newton's third law states that every force has an equal and opposite force. Thus, the force that Earth exerts on you with gravity (a big mass causing a huge acceleration on a small mass) is countered exactly by the normal force of the ground (again, a big mass causeing a huge acceleration on a small mass, but this time in the opposite direction). You can see this when you jump, and the normal force is no longer applied to your body, you quickly fall to Earth. In a sense, the force the ground pushes back on you is really equal and opposite to the gravity of the Earth pulling on you.
I'm not sure I understand your second question. It doesn't really specific the situation well, and it's poorly worded; if you rephrase it I can hopefully give you answer.
Best Answer
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.