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=**Leaping with Physics:** = =**Aspects of Physics in Pole Vaulting** = Created by Julianna Fritzinger & Melanie Otte

A Brief Description of Pole Vaulting Pole vaulting is one of many track and field events appearing at high school, college, and Olympic levels. An athlete takes a running start and then using a pole usually made from either fiberglass or carbon fiber, they propel themselves both up and over a target onto a mat on the other side. It is said that pole vaulting originates from The Netherlands and the Fens. Poles were used to pass over natural obstacles in marshy places. In order to cross the network of open drains and canals that helped to drain these marshes without getting wet and yet still traveling the shortest distance, poles were kept at every house in order for the family members to vault over the canals. The gondolas in Venice also use a similar fashion in order to move the boat to shore using a punting pole. In 1843, one of the earliest pole vaulting competitions took place at the Ulverston Football and Cricket Club, Cumbria where height was measured. Modern poles used for pole vaulting are no longer made from stiff materials such as bamboo or aluminum but from fiberglass and carbon fiber to allow vaulters to reach greater heights. In order to pole vault effectively, one must have both speed and agility as well as technical skills to clear the horizontal bar also known as the crossbar without knocking it down. How can the height of a pole vaulter be maximized?

To find the maximum potential height, simple physics equations can be used to get a rough estimate. Basically, a pole vaulter takes the horizontal acceleration and converts it into vertical acceleration (counteracting the acceleration of gravity) through a compressible spring in this case the pole. Newton's second law of motion states that force equals mass times acceleration (f=ma). In this case, the amount of force applied to the pole at the time of the planting (right before the vaulter lifts off) equals the mass of vaulter times the vaulter's acceleration at the plant. In order to maximize the vaulting height it is assumed that the energy at the plant is converted into vertical lift without losing any energy. This however is not completely realistic however, we will ignore that detail and say that all of the kinetic energy is converted into potential energy.

PE = mgx KE = 1/2 mv2 mgx = 1/2 mv2 x = (1/2 v2)/g

Based on the last equation, height is ultimately determined on the velocity. It is important to note that the equation does not take into consideration the shape of the vaulter's body. The height is calculated based on the center of mass. This graph shows that the velocity before the takeoff is 4.294 m/s. The direction is negative only because during the video analysis the pole vaulter is running towards the left. Taking this velocity the maximum height that should be achieved is: x = (1/2 v2)/g x = (1/2 (4.294^2))/ 9.8 x = .94 m

The highest position of the pole vaulter is .761 meters higher than the position running. The origin was set at the hips of the pole vaulter. The percent difference between the actual height and the maximum achievable height with the given velocity is 21%. Energy is lost through wrong technique and is also lost in the pole during take off and the motion towards the crossbar. The average velocity of the pole vaulter after planting until falling back towards the ground is 1.73 m/s. Ultimately, it can be seen how much energy is lost/transferred during the entire motion through the analysis of the position time graph of both the vertical and horizontal and then using velocity at given points to calculate the actual height achieved and the maximum height that could be achieved if all energy was conserved.