In fact, the bed-of-nails trick has a lot more to do with the simple concept of pressure than it does with the complex training required to achieve a black belt in karate. Now, we all know that if we step on a nail, it might go right through our shoe and into our foot (as has happened to me on more than one occasion). But it is not the force that the nail exerts on your foot that drives it through layers of skin and muscle. Whether you stand on a sharp object or a flat floor, the force exerted on your foot from below is the same. Assuming you are not accelerating, the upward force of the surface under your feet must exactly cancel the downward force of gravity. In terms of Newton's second law:
Fnet = Fsurface \-- mg = ma = 0
Fsurface = mg (your weight force).
However, we all know that standing on a sharp object hurts a lot more than standing on the floor. That's because although the force is the same, the pressure exerted by the sharp object is greater. Pressure is defined as force per area:
P = F/A
So the same force applied over a smaller area applies a greater pressure, and in the case of a nail, possibly enough to exceed the tensile strength of skin!
However, in the first video we are told that there are one thousand and seventy five nails protruding from the wood. The large quantity is even emphasized, giving the impression that the more nails, the more the potential danger. Of course it's just the opposite. Instead of having the weight of the sensei supported over the miniscule area of a single nail tip, it is supported by the total area of 1,075 nails. Meaning the pressure exerted by each nail is 1,075 times less than it would be for a single nail -- not even close to enough pressure to puncture the skin.
But what about that sledge hammer and the cinder block? That looks painful. Well, it's a good thing the cinder block is there to absorb a large percentage of the kinetic energy of the sledge. Because not that much kinetic energy is transferred into the body, it's really not so bad. And of course the large surface area of the cinder block reduces the pressure upon impact. (The demo wouldn't work so well if you replaced the large cinder block with a narrow cylinder!)
Now all of this being said: do not try this at home. It's dangerous! Wait a minute. Why? Not because of the nails or the cinder block, but because the hammer might just miss its intended target. This actually happened to Paul Hewitt, the physics professor in the video, and the result was a seriously fractured arm. Notice he's not the one lying down on the bed of nails!
Adam Weiner is the author of Don't Try This at Home! The Physics of Hollywood Movies.