Sunday, November 29, 2015

Football Injury

This Thanksgiving my family had to watch a heartbreaking defeat of the Dallas Cowboys by the Carolina Panthers. The most devastating part of the slaughter was the unfortunate fracture of Tony Romo’s collarbone. This is the second time that he has injured his collarbone this season and means the end of the season for the Cowboys (according to my dad and my uncle). My dad’s theory is that Romo did not have enough time for his collarbone to heal to be able to play in the game. I decided to use the physics of collisions and tensile stress in order to determine if he should have played in this game.
To determine the force exerted by Panther’s Linebacker Thomas Davis on Tony Romo during their collision, I used the work energy principle WNet=1/2mv2f - 1/2mv2i
as well as the equation for work W=Fd. I observed the video footage of the collision to determine that the collision was inelastic since Davis rolls with Romo approximately 5 yds or 4.572m. I used Davis’ 40 yd stats to determine that his starting velocity was probably 8.074 m/s and after the collision I approximated that his velocity was reduced to 4.037 m/s. The errors in accuracy of this calculation would come from this approximation of velocities. According to Davis’ stats, his mass is about 102 kg. The amount of work done by Davis ends up being 2506 J and thus the force he exerts is about 548 J. The collarbone is about .00647 m in diameter, and after calculating the cross sectional area of the bone and dividing the force exerted by Davis by this number, I determined that 16x106 N/m2 was exerted on Tony Romo’s collarbone. The maximum strength of bone ranges from 104x106 - 121x106 N/m2, which indicates that this impact should not have broken a fully healed collarbone. Therefore, it stands to reason that Romo had not fully recovered from the first fracture of his collarbone, and probably should have sat out on this game.



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