RBH Pole Vault
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Pole Vault Mechanics
Physics of the Pole Vault

Vaulting Pole:
The vaulting pole is a very advanced piece of equipment. It is constructed from carbon fibre and fibreglass composite materials in several layers.
How Force, Power, Torque and Energy Work
The pole must be able to absorb all of the vaulter's energy while bending, and then return all of that energy as it straightens out. These advanced composite materials waste very little energy when they bend, and have a good strength-to-weight ratio.
What is Energy?
If power is like the strength of a weightlifter, energy is like his endurance. Energy is a measure of how long we can sustain the output of power, or how much work we can do. Power is the rate at which we do the work.
There are two kinds of energy: potential and kinetic:
Potential Energy Kinetic Energy
Potential energy is waiting to be converted into power. 
When you lift an object higher, it gains potential energy. The formula to calculate the potential energy (PE) you gain when you increase your height is:
PE = Force x Distance
the force is equal to your weight, which is your mass (m) * the acceleration of gravity (g), and the distance is equal to your height (h) change. So the formula can be written:
PE = mgh
Kinetic energy is similar to potential energy. The more the object weighs, and the faster it is moving, the more kinetic energy it has. The formula for KE is:
KE = 1/2 x m x v2,
where m is the mass and v is the velocity.
One of the interesting things about kinetic energy is that it increases with the velocity squared.
Bringing it Together
Now that we know about potential energy and kinetic energy, we can do some interesting calculations. Let's figure out how high a pole-vaulter could jump if he had perfect technique. First we'll figure out his KE, and then we'll calculate how high he could vault if he used all of that KE to increase his height (and therefore his PE), without wasting any of it. If he converted all of his KE to PE, then we can solve the equation by setting them equal to each other:

1/2 x m x v2 = m x g x h

Since mass is on both sides of the equation, we can eliminate this term. This makes sense because both KE and PE increase with increasing mass, so if the runner is heavier, his PE and KE both increase. So we'll eliminate the mass term and rearrange things a little to solve for h:

1/2 x v2 / g = h

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 meters

So 5.1 meters is the height that a pole-vaulter could raise his centre of mass if he converted all of his KE into PE. But his centre of mass is not on the ground; it is in the middle of his body, about 1 meter off the ground. So the best height a pole-vaulter could achieve is in fact about 6.1 meters, or 20 feet. 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.

Figure 4. Animation of pole-vault

In Figure 4 you can see how the pole-vaulter's energy changes as he makes the vault. When he starts out, both his potential and kinetic energy are zero. As he starts to run, he increases his kinetic energy. Then, as he plants the pole and starts his vault, he trades his kinetic energy for potential energy. As the pole bends, it absorbs a lot of his kinetic energy, just like compressing a spring. He then uses the potential energy stored in the pole to raise his body over the bar. At the top of his vault, he has converted most of his kinetic energy into potential energy.

Our calculation compares pretty well with the current world record of 6.15 meters, set by Sergey Bubka in 1993.

(Extracted From "How Stuff Works")