tak wrote:I've thought about this before... consider this excerpt on how the pole vault works from
www.howstuffworks.com :
Let's say our pole vaulter can run as fast as anyone in the world. Right now, the world record for running 100 m is just under 10 seconds. That gives a velocity of 10 m/s. We also know that the acceleration due to gravity is 9.8 m/s2. So now we can solve for the height:
1/2 x (102 / 9.8) = 5.1 m
So 5.1 meters is the height that a pole vaulter could raise his center of mass if he converted all of his KE into PE. But his center of mass is not on the ground; it is in the middle of his body, about 3 ft (1 m) off the ground. So the best height a pole vaulter could achieve is in fact about 20 ft (6.1 m). He may be able to gain a little more height by using special techniques, like pushing off from the top of the pole, or getting a really good jump before takeoff.
What this tells us is that Bubka's world record is already in the ballpark of what is humanly possible. The analysis here is even optimistic because it ignores the fact that a perfect conversion from kinetic energy from your run to height is impossible (think of the impact of the pole in the back of the box, for example), and I doubt there are many people out there who are able to be master technicians and run 10 seconds in the 100m, even if everyone was trying it.
So... I'm gonna have to say that the world record isn't going to get all that much higher any time soon-- certainly not 22'.
...OK, so what you're using is Conservation of energy. A good idea, however, there are some gray areas associated with that.
First off, all that is saying is that if we were to take off the ground, it would raise our center of mass 5.1m. With doing nothing after leaving the ground, if all the energy was to be returned (which it's not, energy is lost in sound and strain energy is lost in the pole bending) a jumper with that speed could potentially jump that. My main question with that (and being a physics major, I have deliberated over this one a lot...) is those relationships do not have anything to do with the pole. It is simply comparing the potential energy with the kinetic energy. Technically, this means that if you were to fall from the 5.1m, just before landing you would be traveling just over 10 m/s.
So then we would need to look into how we convert the horizontal velocity into vertical velocity. The fast one moves, by laws of inertia, it gets harder to change ones path (this is why even though a long jumper tries to jump up, it doesn't happen very well).
Bottom line, in my opinion, is that it's a good starting point, but there are too many other things that happen in the vault to simply compare potentail and kinetic energy values. Much higher than 20' right now, I don't see it, but if it were all we every worked on as a human race, it would be a totally different event.
...I'll get off my soap box now, and I'll stay off... I swear...