Wednesday, May 12, 2010

Turns out that walking on water is not that special

There is a well known phenomena to all children who grow up next to a lake or a river. If you throw a flat rock fast enough with a little bit of spin, you can make it skip off the surface of the water several times before it eventually sinks.



This takes advantage of several laws of physics. Newton's third law of motion states that "For every action, there is an equal and opposite reaction." So if you were to punch a wall, your hand would hurt because not only are you delivering a force to the wall, but the wall also applies a force to your hand. This force is called the "Normal Force" in physics jargon because it is directed perpendicular to the surface of contact.

Usually water does not provide a very large 'normal force' because its particles can easily move around. If you were to lay the rock gently on the water surface, the particles have plenty of time to move out of the way and the rock sinks.

But if the rock hits the water with more speed, the normal force will increase. When an object hits a solid surface, like a wall, the normal force is quite large due to the law of conservation of momentum which states that the change of momentum is equal to the impulse.



But because water can move out of the way, it is more important to consider Archimedes' Principle.  Without going into too much detail, the amount of water displaced by the object is proportional to how much of a buoyant force is created.  When high divers hit the water, they try to reduce their cross sectional area to reduce the splash.  This also reduces the amount of force they feel on impact.  But if you've ever done a 'belly flop' into the pool you know that you receive a much bigger force from the water, i.e. IT HURTS!



Essentially, the bigger the area of the object, the more water that is displaced, and the object will get a larger upward force from the collision.  So, with a big enough area, moving at a fast enough speed, the force from the displaced water can overcome the weight of the object, making it bounce back up.


The basilisk lizard has evolved a neat use of this.  It has relatively large flat feet and can run very fast.



These are the perfect attributes needed to be able to run on water. And because of that, it is sometimes called the "Jesus Lizard".




And really, it was only a matter of time until humans were able to do this too!



So a new type of water-repellent shoe allows these guys to create enough displacement of water without impeding their ability to run. But there was another subtle bit of physics hidden in that video.

The runners do not go directly at the water. Instead, they take a curved path. This takes advantage of yet another well known physics phenomena, surface tension.


The water molecules are attracted to each other because they have a polar geometry.  That just means that one side of the water molecule is a little bit positive, and the other side is more negative, even though the molecule itself is neutral.


So they are attracted to each other like the way a statically charged balloon will stick to your head, or the wall. Or a cat!




But while the molecules in the middle of the water are pulled in all directions, the molecules at the surface only have a net force towards the center.



This compresses the molecules at the surface, giving the water a slightly more dense 'skin'.  It also provides some nice art inspiration.



By running in a curve, these guys are vectoring their force so that it is directed more against the surface. This is why when you try to skip a stone, you throw it parallel to the surface of the water, not straight at it.


So if you want to get the maximum reaction force from the water, you would need to direct your vector even more horizontally than pictured above.  Running in a curve allows you to do that without changing the angle of your foot, sacrificing surface are.

In conclusion, maybe Jesus walking on water wasn't really a miracle.  Maybe Jesus was just really good at physics!



And wearing wooden shoes...

UPDATE: Nevermind, the video of the guys running on water was just a viral marketing scheme. You can see the platform move at 0:48. But at least we still have the lizard!
Oh well, maybe Jesus was just a viral marketing scheme too...

Thanks to the diggers for getting the evidence.


In penance, here's some real (kite assisted) walking on water.



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