Physics of Soccer

Matthew Hemerlein

Physics’ of Soccer

Eleven men take the field on a warm sunny day in South Korea. Thousands of anxious soccer fans await the blow of the referee’s whistle to commence the culmination of the world’s greatest sporting event, The World Cup. Thirty-two once stood now only two remain .The pitch is fair and the competition is fierce, four time defending champ Brazil looks confident as it glares across at its nemesis for the duration of ninety minutes, Germany. The entire world is spell bound by the natural creativity that ensues from a high level soccer match, but do they know the necessary physical laws that make the game possible? The answer is no, the average soccer fan has no idea the physical restrictions and factors involved in moving a ball one hundred meters, the standard length of an international playing field.

Once in Yokohama stadium the able athletes stretch their finely tuned musculature in order to get ready for today’s athletic competition. Roberto Carlos the star left back, for the acclaimed Brazilian national team has the important job of defending the goal and preventing the ball from crossing the threshold of the goal line at any cost. A good defender can boot the ball weighing approximately one pound the length of the field at any given time. Carlos is not good, he is great, solid legs and a supple foot he is quite capable of accomplishing this feat. His leg is so strong he his able to strike the ball at 613.57 Newton’s making possible at a 45 degree angle to land exactly 100 meters away.

As you know the length of the field is 100 meters so what forces involved exactly are necessary in order to project a soccer ball through the air that entire distance?

To start we must assume that are athlete is in peak condition, with the capable leg muscle to kick the ball this length. Secondly the athlete is kicking the ball at 45 degrees; an angle that when met with enough Newton’s is capable of kicking the ball the required length. There are two vectors acting on the ball at all times: gravity and velocity, in order to overcome these two obstacles the initial velocity must be very high. With an angle of 45 degrees the initial velocity must be 62.609mps(meters per second), the hours of weight training and running needed to get ones leg able to exert this force is unfathomable. Once this force is exerted the ball will soar through the air exactly fifty feet up, in a perfect semicircle. The amount of actual flight time is 2.25 seconds, almost the exact amount of time it takes to say “oh my god”. When the initial velocity is multiplied by one kilo (9.8newtons) you get the answer of 613.57 Newton’s. These are the forces necessary to send a 1 kilo ball the length of a standard international field exactly 100meters away. All of these calculations are assuming that no wind or weather will come into play; however if there was a slight wind, once the ball touched the ground it would skip for a good distance and still make it possible to run the length of the field.

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