The Role of Kinetic Energy and theMechanics of Kicking a Soccer Ball Jordan ScottIB MathMs. Egloff12/19/2017 The Role of Kinetic Energy and theMechanics of Kicking a Soccer Ball My interest in doing a math IA that centerson soccer, came from my actual love of the game of soccer. I developed my love for soccer early in mylife while a student in preschool. Itseemed that it started out as just a form of exercise that my parents thoughtwould be good for me.
They thought thatgetting involved in a team sport, would also provide a good foundation for meto engage in a social setting that was organized, disciplined, andmotivational. I soon found that all ofthis was true, but the real excitement for me was the fact that as I continuedto develop my soccer skills, my mind was free of the stressors of the day as Ifocused my attention on getting better and better with each practice andgame. As one can guess, soccer is a verycompetitive and dangerous sport. However, these are two characteristics that adds an element of fun tothe sport. Therefore, it is imperativefor a soccer player, regardless of his or her position, to engage in creativethoughts and reflections, during both practice and competitive games, in orderto gain skills that are superior to his or her opponent.
I always wanted to try new ways to improve mygame. So, I thought of a problem thatwill test the kinetic energy relative to the velocity of a kicked soccer ballwhen struck with different parts of one’s foot. Kinetic energy is defined as the energy of abody or a system with respect to the motion of the body or of the particles inthe system (Teixeira). It is often saidthat…A body at rest, tends to stay at rest (Newton). Hence, a soccer ball just sitting in mygarage or left out in my yard, had to purpose if not kicked.
When I was old enough to understand the gameof soccer better, I decided to keep playing because I was fascinated with themany “tricks” I had observed from many of the older players. They also shared the secret as to how theyhad developed and this was a very simple formula. I was told that “perfect practice led toperfect performance.” Sometimes, I would practice with myfamily members as well as alone.
Thiswould even happen before some of my games because I wanted to improve my skillsand emulate the older individuals. Asone should know, the only players allowed to use their hands during a soccergame would be the two goalies. AlthoughI have played this position before, I much rather would like to play as aplayer on the field.
This is where allof the action is as one must use his or her feet to engage the soccer ball aseither an offensive or defensive player. Kicking a soccer ball is the mostcomplicated soccer skill for an individual to learn (Asai, Akatsuka,Haake). My coaches realized that it wasvery important to teach us the proper technique regarding this action as theconcept of learning through trial and error could prove to be frustrating andvery difficult, which could also mean that we would have to “unlearn” any badhabits. This paper will focus on severalof the proper techniques that have supported my development as a soccer playerwhile also studying the effects of kinetic energy and its relationship to thevelocity 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, andToe Shot I think thatcalculating the speed of the ball is rather easy, but it cannot be done withoutnumbers.
In fact, one can do this byusing two numbers to measure the time and distance relative to kicking a soccerball. Recently I was here at HickoryHigh School and while on the soccer field, I passed the ball a total distanceof 24 m (meters). It took the ball atotal of 8 s (seconds) before it reached my teammate.
By doing this, I was provided with twonumbers to use in my equation. In orderto calculate the speed of the ball that I kicked, I would have to combine bothof these numbers. Speed (or Velocity) iscalculated in the equation V= ?d/?t where ?drepresents distance, ?t represents time, and V represents velocity(Teixeira). Therefore the velocity ofthe ball I kicked was 3 m/s. At this point, I would like togo a little further with the simple concept of velocity. Take a moment and picture someone kicking asoccer ball into the net.
In fact, I didthis in order to get my measurements and calculations. The ball I kicked initially started out at 6m/s before it sped up and started traveling at 14 m/s. We can see that the ball accelerated bylooking at these two numbers because it went from a lower speed to a higherspeed. Hence, we can now calculate justhow much it accelerated before crossing the goal line. However we need another variable; distance ortime. I also wanted to prove that youcan calculate acceleration with both distance and time. So, I measured both.
It took 4 s before the ball changed speed andit was in at a distance of 40 m. Icalculated 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 theother markers until the ball reached the goal line. These times were recorded and later used inmy equation. Tosolve for the acceleration of the ball using the distance looks like this: The steps I took tosolve for the acceleration are as follows:1. Rearrange theequation to solve for a (acceleration)2.
Substitute thevariables with the actual numbers3. Follow the order ofoperations (Brackets, exponents, divide, multiply, add, subtract)To solve for theacceleration of the ball using the time looks like this: Inany 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, theopportunity for it to accelerate increases due to the impact that gravity hason it. This means that the maximum speedthe ball reaches while in flight is relative to the amount of velocity it hitsthe ground (Lees & Nolan).
Also, Inoted that gravity is a factor until it reaches a height of 0 m or back on theground. Additionally, we can also solvefor the maximum height of any ball as long as we have a couple variables. Thediagram above shows a situation from a recent practice session. I was in my backyard when I kicked the ballinto the air. I measured the distance itcovered, and calculated the initial speed (V= d/t).
So I drew up this diagram to show you how tocalculate the maximum speed generated when I kicked the ball. With this diagram, one can see the variable Iwant to solve for, which in this case is the final velocity (maximumspeed). 9.8 m/s^2 is a constantrepresenting the acceleration due to gravity, and it is negative because it isacting 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 importantfor the player (Ishii & Maruyama). If a player could predict the initial and final velocity they kick theball 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 theamount of distance the ball will be able to travel.
With that information at hand, the playerknows how far away they can be from the goal in order for the ball to go intothe net rather than go over or land before the net. This could also work for passing betweenteammates (Apriantono, Nunome, Ikegami, & Sano). Atthis point, I wanted to further explore other aspect relative to kicking asoccer ball. Projectile motion andkinetic energy come to mind. First of all, what isprojectile motion? Projectile motion isa type of motion that is under the influence of gravity and is not self-powered(Kellis). Projectile motion is seen veryoften in sports. With projectile motion the vertical and horizontal componentsact independently of each other. Furthermore, an object will travel at a constant vertical accelerationof 9.
8m/s^2 down (acceleration due to gravity) hence, there will always be aconstant horizontal velocity. The onlyfactor that the horizontal and vertical components share is the time it takesfor the ball/object to travel through the air. Considering the projectile motion questions are separated betweenhorizontal and vertical components.
Thevalues are vector (Kellis). Vector is aquantity that has both size and direction. Therefore, one of the first steps tosolving a projectile motion question is to differentiate which two directionsare positive, one in the vertical and one in the horizontal (Kellis). Onanother day, I kicked my soccer ball from 40m away from the goal. The ball traveledat an initial velocity of 20m/s 50 degrees above the horizontal and then itreached the goal line and the goalie caught it.
I wanted to calculate for the final velocity the ball had before the1.7m tall goalie caught it. To startsolving this question, I had to draw a right-angled triangle of the horizontalvelocity, the vertical velocity, and the velocity travelling diagonally ofboth. Asyou can hopefully see by the triangle, we can now solve for the initialvelocity in the vertical, and the velocity in the horizontal using SOH CAH TOA(Mathworld).(I am not going tosolve for them just yet because I do not want to deal with decimals until Isolve for something.) The next step isto define or determine the differences between the horizontal and verticalcomponents and define which directions are positive (Kellis). The chart above showswhat we know based on what is given, and what we NEED to solve for in order tosolve for the final velocity. To get thefinal velocity we need the final velocity in the vertical.
Therefore we must solve for this velocitylike this: Nowthat we have the final vertical velocity, we can solve for the final velocityof the ball diagonally. To do this weneed the final horizontal velocity, but also must remember the velocity in thehorizontal for projectile motion question is constant. In other words, it will always remain thesame. Therefore, we already haveit. Furthermore, to solve for the finalvelocity we must use the Pythagorean Theorem (Mathworld).
Perfect! However, we are not finished yet. Remember, that with any projectile motionquestion the values must be vector (Lees & Nolan). I know the value of the final velocity, but Ido not know the direction it is going. Hence, one need only to refer back to the triangle provided earlier inthis paper. In that triangle it showsall the initial velocities of the ball. Now, having the final velocities and each side length of the newtriangle, one can solve for the angle the final velocity is above thehorizontal.
Now, the whole vector value isavailable along with the magnitude and the direction of the speed, the finalvelocity of the soccer ball is 19 m/s 48° above the horizontal. But, what about the kinetic energy and itsrelationship to the various kicking techniques used by soccer players? Let us look at a few shots and note that theydepend on the use of a different part of the foot. Also, rather than using the previousequations, the app “KickPower” was used to obtain the speed of the ball when itwas kicked using these (4) four methods. The methods or techniques are: 1.
Chip/Inside Shot: The inside shot can be used when you need excellentaccuracy. Using it may depend on thepower or kinetic energy one can generate when he/she kicks the ball. One may want to use this shot when he/she isnear the box or a short distance from the goal. To do a chip or inside shot, one would need to move his/her hip outsideand 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 theball across the goal at a right angle. To do an outside shot, slice the ball with the outside of yourfoot. Have you heard the statement… “Bend it like Beckham?” Use a bending shot to kick the ball arounddefenders, score from tough angles, or surprise a goalie.
Use any part of the foot to do a bendingshot. However, using the inside oroutside 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 yourleg around the ball and follow through to the outside of your body. If you are using the area around the knuckleof your big toe or the outside of the foot, one will need to follow through across his/her body. 3. Laces Shot: Strikingthe ball with the laces is used more often than any of the other shots. This shot is the most effective shot in mostsituations. In order to perform thisshot, one will need to approach the ball at a slight angle and kick the ballwith the area around the knuckle of his/her big toe, yet allowing the laces ofthe shoe to strike the ball. 4.
Toe Shot: Thetoe shot can be very effective. It may not provide as much power or accuracy asother shots, but one can shoot the ball quickly. To do a toe shot, stick your leg out in frontof you and kick the ball with your toe. Do not move your leg back to build momentum like you would whenperforming every other type of soccer shot. Chart 1,Results of Kicking a Soccer Ball. Chart 1 depicts theaverage speed of each type of shot when made at a distance of 20 meters fromthe goal. The app “KickPower” was usedto gather the average of (5) five shots.
Type of Shot Average Speed Chip/Inside 41.0mph Outside 30.8mph Laces 47.2mph Toe 36.
0mph Chart 1: Results of Kicking a Soccer Ball For a soccer player, knowing the physics of soccer can helptheir play. Considering we know theacceleration due to gravity that acts on the ball, a smart soccer player cantake that into consideration when they kick the ball, along with the distancethey are trying to reach. For example,when a soccer player takes a penalty kick, they are 12 yards away from thekeeper and the net. When they are thisclose to their target, it is not smart to hit the ball up because the distanceis so small. In other words, this meansthat the ball will be decelerating in the air until it reaches its peak heightin which the goalie can catch it.
It isvery hard for a soccer player to kick the ball into the air and then it beaccelerating downwards toward the net in a penalty kick. This is why most players shoot with the ballremaining on the ground. The benefit ofthis is that the ball is not travelling a great distance which means it willnot be decelerating.
The relationship between themechanics of kicking a soccer ball and kinetic energy may seem to be complexwhen viewed by the novice or entry level player. However, as one can see from this paper, itis possible for any player to improve his/her “game” by knowing the mathematicaland 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 canassist any soccer player, novice to professional, in accompanying his/her”goal” of being the best that he/she can be when attempting any of thesix/seven shots previously mentioned. Success should be the ultimate goal. This is because, when one can successfully compute the mechanics ofkicking a soccer ball, the only thing that may stop the ball is the goalieor….the back of the net! Finally, asthis 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 oninstep kicking kinetics and kinematics in association football. Journalof Sports Sciences, 24: 951-960.Asai, T., Akatsuka, T.
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Ishii, H. and Maruyama, T. 2007. Influence of foot angle and impact point on ball behavior in side-footsoccer kicking. The Impact of Technology on Sport, II: 403-408.Kellis E, Katis A. Biomechanical characteristics and determinants of instepsoccer 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 sourcesof constraint on accuracy. Perceptual and Motor Skills, 88:785-789. Newton, I.
, “Mathematical Principles of Natural Philosophy, 1729. Englishtranslation based on 3rd Latin edition (1726), volume 2, containing Books 2& 3. mathworld.wolfram.com/SOHCAHTOA.htm