The guess, soccer is a very competitive and

The Role of Kinetic Energy and the Mechanics of Kicking a Soccer BallJordan ScottIB MathMs. Egloff12/19/2017The Role of Kinetic Energy and the Mechanics of Kicking a Soccer Ball         My interest in doing a math IA that centers on soccer, came from my actual love of the game of soccer.  I developed my love for soccer early in my life while a student in preschool.  It seemed that it started out as just a form of exercise that my parents thought would be good for me.  They thought that getting involved in a team sport, would also provide a good foundation for me to engage in a social setting that was organized, disciplined, and motivational.  I soon found that all of this was true, but the real excitement for me was the fact that as I continued to develop my soccer skills, my mind was free of the stressors of the day as I focused my attention on getting better and better with each practice and game.  As one can guess, soccer is a very competitive and dangerous sport.  However, these are two characteristics that adds an element of fun to the sport.  Therefore, it is imperative for a soccer player, regardless of his or her position, to engage in creative thoughts and reflections, during both practice and competitive games, in order to gain skills that are superior to his or her opponent.  I always wanted to try new ways to improve my game.  So, I thought of a problem that will test the kinetic energy relative to the velocity of a kicked soccer ball when struck with different parts of one’s foot.         Kinetic energy is defined as the energy of a body or a system with respect to the motion of the body or of the particles in the system (Teixeira).  It is often said that…A body at rest, tends to stay at rest (Newton).  Hence, a soccer ball just sitting in my garage or left out in my yard, had to purpose if not kicked.  When I was old enough to understand the game of soccer better, I decided to keep playing because I was fascinated with the many “tricks” I had observed from many of the older players.  They also shared the secret as to how they had developed and this was a very simple formula.  I was told that “perfect practice led to perfect performance.”              Sometimes, I would practice with my family members as well as alone.  This would even happen before some of my games because I wanted to improve my skills and emulate the older individuals.  As one should know, the only players allowed to use their hands during a soccer game would be the two goalies.  Although I have played this position before, I much rather would like to play as a player on the field.  This is where all of the action is as one must use his or her feet to engage the soccer ball as either an offensive or defensive player.         Kicking a soccer ball is the most complicated soccer skill for an individual to learn (Asai, Akatsuka, Haake).  My coaches realized that it was very important to teach us the proper technique regarding this action as the concept of learning through trial and error could prove to be frustrating and very difficult, which could also mean that we would have to “unlearn” any bad habits.  This paper will focus on several of the proper techniques that have supported my development as a soccer player while also studying the effects of kinetic energy and its relationship to the velocity of the ball.Techniques include:1. Take a good touch.2. Look at the ball.3. Place your foot.4. Swing your arms.5. Bring back your kicking leg.6. Lock the ankle.7. Keep your body straight.8. *Kick the ball with the correct part of your foot.9. Follow through.10. Follow up.*Chip/Inside Shot, Outside Shot, Laces, and Toe Shot         I think that calculating the speed of the ball is rather easy, but it cannot be done without numbers.  In fact, one can do this by using two numbers to measure the time and distance relative to kicking a soccer ball.  Recently I was here at Hickory High School and while on the soccer field, I passed the ball a total distance of 24 m (meters).  It took the ball a total of 8 s (seconds) before it reached my teammate.  By doing this, I was provided with two numbers to use in my equation.  In order to calculate the speed of the ball that I kicked, I would have to combine both of these numbers.  Speed (or Velocity) is calculated in the equation V= ?d/?t where ?d represents distance, ?t represents time, and V represents velocity (Teixeira).  Therefore the velocity of the ball I kicked was 3 m/s. At this point, I would like to go a little further with the simple concept of velocity.  Take a moment and picture someone kicking a soccer ball into the net.  In fact, I did this in order to get my measurements and calculations.  The ball I kicked initially started out at 6 m/s before it sped up and started traveling at 14 m/s.  We can see that the ball accelerated by looking at these two numbers because it went from a lower speed to a higher speed.  Hence, we can now calculate just how much it accelerated before crossing the goal line.  However we need another variable; distance or time.  I also wanted to prove that you can calculate acceleration with both distance and time.  So, I measured both.  It took 4 s before the ball changed speed and it was in at a distance of 40 m.  I calculated this by setting markers out on the field.  After kicking the ball, my dad (my helper) would start a new timer when the ball reached the first marker and each of the other markers until the ball reached the goal line.  These times were recorded and later used in my equation. To solve for the acceleration of the ball using the distance looks like this:The steps I took to solve for the acceleration are as follows:1. Rearrange the equation to solve for a (acceleration)2. Substitute the variables with the actual numbers3. Follow the order of operations (Brackets, exponents, divide, multiply, add, subtract)To solve for the acceleration of the ball using the time looks like this:                                           In any activity, when a ball or object is hit, thrown, or kicked through the air, gravity adds an acceleration to the ball (Lees & Nolan).  As the ball travels through the air, the opportunity for it to accelerate increases due to the impact that gravity has on it.  This means that the maximum speed the ball reaches while in flight is relative to the amount of velocity it hits the ground (Lees & Nolan).  Also, I noted that gravity is a factor until it reaches a height of 0 m or back on the ground.  Additionally, we can also solve for the maximum height of any ball as long as we have a couple variables.         The diagram above shows a situation from a recent practice session.  I was in my backyard when I kicked the ball into the air.  I measured the distance it covered, and calculated the initial speed (V= d/t).  So I drew up this diagram to show you how to calculate the maximum speed generated when I kicked the ball.  With this diagram, one can see the variable I want to solve for, which in this case is the final velocity (maximum speed).  9.8 m/s^2 is a constant representing the acceleration due to gravity, and it is negative because it is acting down on the ball when the ball is moving upward (Lees & Nolan).         Obviously, I did not hit the ball very hard because its maximum speed was only 5.1 m/s. However, knowing the maximum speed of the ball one might kick is very important for the player (Ishii & Maruyama).  If a player could predict the initial and final velocity they kick the ball with (i.e. calculating the average initial and final velocity of 5 kicks) he/she could use it to his/her advantage.  Knowing these two velocities will allow the player to calculate the amount of distance the ball will be able to travel.  With that information at hand, the player knows how far away they can be from the goal in order for the ball to go into the net rather than go over or land before the net.  This could also work for passing between teammates (Apriantono, Nunome, Ikegami, & Sano).         At this point, I wanted to further explore other aspect relative to kicking a soccer ball.  Projectile motion and kinetic energy come to mind.  First of all, what is projectile motion?  Projectile motion is a type of motion that is under the influence of gravity and is not self-powered (Kellis).  Projectile motion is seen very often in sports. With projectile motion the vertical and horizontal components act independently of each other.  Furthermore, an object will travel at a constant vertical acceleration of 9.8m/s^2 down (acceleration due to gravity) hence, there will always be a constant horizontal velocity.  The only factor that the horizontal and vertical components share is the time it takes for the ball/object to travel through the air.  Considering the projectile motion questions are separated between horizontal and vertical components.  The values are vector (Kellis).  Vector is a quantity that has both size and direction. Therefore, one of the first steps to solving a projectile motion question is to differentiate which two directions are positive, one in the vertical and one in the horizontal (Kellis).         On another day, I kicked my soccer ball from 40m away from the goal. The ball traveled at an initial velocity of 20m/s 50 degrees above the horizontal and then it reached the goal line and the goalie caught it.  I wanted to calculate for the final velocity the ball had before the 1.7m tall goalie caught it.  To start solving this question, I had to draw a right-angled triangle of the horizontal velocity, the vertical velocity, and the velocity travelling diagonally of both.         As you can hopefully see by the triangle, we can now solve for the initial velocity in the vertical, and the velocity in the horizontal using SOH CAH TOA (Mathworld).(I am not going to solve for them just yet because I do not want to deal with decimals until I solve for something.)  The next step is to define or determine the differences between the horizontal and vertical components and define which directions are positive (Kellis). The chart above shows what we know based on what is given, and what we NEED to solve for in order to solve for the final velocity.  To get the final velocity we need the final velocity in the vertical.  Therefore we must solve for this velocity like this:         Now that we have the final vertical velocity, we can solve for the final velocity of the ball diagonally.  To do this we need the final horizontal velocity, but also must remember the velocity in the horizontal for projectile motion question is constant.  In other words, it will always remain the same.  Therefore, we already have it.  Furthermore, to solve for the final velocity we must use the Pythagorean Theorem (Mathworld).         Perfect!  However, we are not finished yet.  Remember, that with any projectile motion question the values must be vector (Lees & Nolan).  I know the value of the final velocity, but I do not know the direction it is going.  Hence, one need only to refer back to the triangle provided earlier in this paper.  In that triangle it shows all the initial velocities of the ball.  Now, having the final velocities and each side length of the new triangle, one can solve for the angle the final velocity is above the horizontal.            Now, the whole vector value is available along with the magnitude and the direction of the speed, the final velocity of the soccer ball is 19 m/s 48° above the horizontal.  But, what about the kinetic energy and its relationship to the various kicking techniques used by soccer players?  Let us look at a few shots and note that they depend on the use of a different part of the foot.  Also, rather than using the previous equations, the app “KickPower” was used to obtain the speed of the ball when it was kicked using these (4) four methods.  The methods or techniques are:    1.  Chip/Inside Shot:  The inside shot can be used when you need excellent accuracy.  Using it may depend on the power or kinetic energy one can generate when he/she kicks the ball.  One may want to use this shot when he/she is near the box or a short distance from the goal.  To do a chip or inside shot, one would need to move his/her hip outside and back then kick the ball with the middle of the inside of your foot.2.  Outside Shot:  The outside shot is effective when you have to shoot the ball across the goal at a right angle.  To do an outside shot, slice the ball with the outside of your foot.  Have you heard the statement…  “Bend it like Beckham?”  Use a bending shot to kick the ball around defenders, score from tough angles, or surprise a goalie.  Use any part of the foot to do a bending shot.  However, using the inside or outside of one’s foot produces the most bend.  To do a bending shot, kick the sides of the ball at an angle.  If you use the inside of your foot, wrap your leg around the ball and follow through to the outside of your body.  If you are using the area around the knuckle of your big toe or the outside of the foot, one will need to  follow through across his/her body.  3.  Laces Shot:  Striking the ball with the laces is used more often than any of the other shots.  This shot is the most effective shot in most situations.  In order to perform this shot, one will need to approach the ball at a slight angle and kick the ball with the area around the knuckle of his/her big toe, yet allowing the laces of the shoe to strike the ball. 4.  Toe Shot:  The toe shot can be very effective. It may not provide as much power or accuracy as other shots, but one can shoot the ball quickly.  To do a toe shot, stick your leg out in front of you and kick the ball with your toe.  Do not move your leg back to build momentum like you would when performing every other type of soccer shot.Chart 1, Results of Kicking a Soccer Ball.  Chart 1 depicts the average speed of each type of shot when made at a distance of 20 meters from the goal.  The app “KickPower” was used to gather the average of (5) five shots.           Type of ShotAverage SpeedChip/Inside41.0mphOutside30.8mphLaces47.2mphToe36.0mphChart 1:  Results of Kicking a Soccer Ball         For a soccer player, knowing the physics of soccer can help their play.  Considering we know the acceleration due to gravity that acts on the ball, a smart soccer player can take that into consideration when they kick the ball, along with the distance they are trying to reach.  For example, when a soccer player takes a penalty kick, they are 12 yards away from the keeper and the net.  When they are this close to their target, it is not smart to hit the ball up because the distance is so small.  In other words, this means that the ball will be decelerating in the air until it reaches its peak height in which the goalie can catch it.  It is very hard for a soccer player to kick the ball into the air and then it be accelerating downwards toward the net in a penalty kick.  This is why most players shoot with the ball remaining on the ground.  The benefit of this is that the ball is not travelling a great distance which means it will not be decelerating.   The relationship between the mechanics of kicking a soccer ball and kinetic energy may seem to be complex when viewed by the novice or entry level player.  However, as one can see from this paper, it is possible for any player to improve his/her “game” by knowing the mathematical and scientific methods associated with the relationship of kinetic energy, projectile motion, and the part of the foot used to kick the ball.  The ten techniques offered in this paper can assist any soccer player, novice to professional, in accompanying his/her “goal” of being the best that he/she can be when attempting any of the six/seven shots previously mentioned.  Success should be the ultimate goal.  This is because, when one can successfully compute the mechanics of kicking a soccer ball, the only thing that may stop the ball is the goalie or….the back of the net!  Finally, as this is the Twentieth Century, and you get tired of doing the math, remember, there probably an app for that.                       REFERENCESApriantono, T., Nunome, H., Ikegami, Y. and Sano, S. 2006.  The effect of muscle fatigue on instep kicking kinetics and kinematics in association football.  Journal of Sports Sciences, 24: 951-960.Asai, T., Akatsuka, T. and Haake, S. J. 1998.  The physics of football.  Physics World, 11: 25-27.Ishii, H. and Maruyama, T. 2007.  Influence of foot angle and impact point on ball behavior in side-foot soccer kicking.  The Impact of Technology on Sport, II: 403-408.Kellis E, Katis A. Biomechanical characteristics and determinants of instep soccer kick. J Sports Sci Med 2007; 6(2): 154-165.Lees, A. and Nolan, L. 1998. Biomechanics of soccer: A review. Journal of Sports Sciences, 16: 211-234.Teixeira, L. A. 1999. Kinematics of kicking as a function of different sources of constraint on accuracy.  Perceptual and Motor Skills, 88: 785-789.  Newton, I., “Mathematical Principles of Natural Philosophy, 1729. English translation based on 3rd Latin edition (1726), volume 2, containing Books 2 & 3.  mathworld.wolfram.com/SOHCAHTOA.htm