Exam - Math Behind Pole Vaulting
Pole vault is a sport in which the athlete jumps over objects with the aid of a pole. Although the origin is unknown of, pole vaulting likely started as a practical means of clearing things such as fences and ditches. Trackandfield.about.com says, "Egyptian relief sculptures from approximately 2500 B.C. depict warriors using poles to help climb enemy walls." However, it became a competitive sport in the mid-19th century, as people competed to vault for the highest height. In 1904, the poles were being made out of bamboo, replacing the heavier wooden poles. In the 1960's, glass fiber started to be used to make the poles out of, as is still used today. In the sport, a bar is set up (depending on height) across two stands so that the bar will easily fall off if touched.
To vault, the vaulter runs fast at the pit, plants the end of their pole into a "box" (which is basically a metal hole with its back placed below the crossbar), uses that momentum and the pole's bend (which is energy absorbed from the runner) to catapult their body up and over the bar. Coordination, timing, and speed is all key when trying to vault.
To understand the math that goes with pole vaulting, we must figure out the kinetic energy of the vaulter to the gravitational potential energy, corresponding to the point of maximum height the vaulter reaches while vaulting. Here's the equation that would be used to determine the maximum height (1/2)(M)(V^2) = (M)(G)(Δh). M is the would stand for the mass of the pole vaulter, V stands for the velocity (speed) of the pole vaulter just before the vault, g is the gravitational constant (9.8 m/s2), and Δh is the change in height of the vaulter's center of mass. Both kinetic energy and potential energy increase, the heavier the mass is.
To solve for h, you could rearrange the equation into (1/2)(V^2)/G=h. If I'm using my average time, I typically run a 100 meter race in 15 seconds. So, 100 meters divided by 15 seconds would be about 6.7 meters per second. Now to plug everything in, it would be 1/2x(6.7^2/9.8)=2.29m. The 2.29 meters is the height the vaulter could raise their center of mass to, if they were to convert all of their kinetic energy into potential energy. However after that, you have to take into consideration that the vaulters center of mass isn't at the ground, but is in the middle of their body. For me, as I'm 5 foot and 2 inches, my body's center of mass would be at 2.6 feet (0.79248 meters), so you'd add 2.29 meters and 0.79248 meters, getting about 3.08248 meters, which converts to about 10.1 feet. However, that doesn't mean that that's the highest height I can achieve. Using special techniques, or gaining more speed, a greater height is achievable.
Example Vault | |
File Size: | 8467 kb |
File Type: | mov |
As a demonstration, above is a video of Lara attempting to pole vault. As you can see, she's running slower, not achieving her fastest speed, so that contributes to the reason behind why she doesn't get up too high. On top of that, she doesn't convert all of her kinetic energy she makes while running into potential energy.
Works Cited:
http://www.real-world-physics-problems.com/physics-of-pole-vaulting.html
http://trackandfield.about.com/od/polevault/ss/illuspolevault.htm