RahatMadarasmi October 3, 2011 Period 1 Eales Independent Research Project: Pressure and Kinetic Energy of a Soccer BallIntroduction: A soccer ball can contain different pressures within it. When kicking asoccer ball, it is important that the ball is filled up to a certain point at which,when kicked, will travel at a great velocity with high kinetic energy so that thegoalie has difficulty stopping it, thus resulting in a goal. What is to beinvestigated here is the relationship between the pressure and the velocity andkinetic energy of the ball. When the pressure within a soccer ball is altered, the velocity at which ittravels when struck also changes. Due to this change in velocity, there is also achange in the kinetic energy that the ball possesses when struck at differentpressures. When pressure is withdrawn from a soccer ball, the skin tends to foldand cause friction, thus when the ball is kicked in this state, the ball deforms andthere is a loss in energy due to the friction. The greater the deformation of theball, the greater the energy loss in the skin. In order to find out the relationship between the change in pressure andthe kinetic energy, the velocity of the ball must be measured for it is acomponent that is required in the formula to find kinetic energy. The formula forkinetic energy is: Ek= ½ mv2 (1) Where Ekis the kinetic enery, m is the mass and v is the velocity. The predicted outcome that can be gathered from the informationpresented above is that due to the fact that the less the pressure the greater thefriction, as the pressure increases, the kinetic energy of the ball will increase aswell.
Design: Research Question: How does the pressure within a soccer ball effect the kinetic energy of the ball when struck by a pendulum at a constant velocity? Independent & Dependent Variables: The independent variable is the pressure because the pressure is what we are changing. The pressures that are measured are 19,600 Pascals, 39,300 Pascals, 58,800 Pascals, 73,500 Pascals, 98,000 Pascals, and 117,600 Pascals. The dependent variable is the kinetic energy of the ball because it is what is affected by the change in pressure (independent variable). Controlled Variables: There were a number of variables that had to be controlled. One control was the soccer ball that was used had to be the same for the entire experiment. The pendulum that was used was another control, as it had to remain the same for the entire experiment. The height from which the hammer was released had to remain constant in order to ensure that it was traveling at the same velocity for every trial when it struck the ball. In order to control this, a bar was clamped onto the pendulum, protruding out at the point where the pendulum (hammer) would be released. The spot in which the ball was placed had to be controlled so that the pendulum would strike the ball at the same point for each trial. To do this, a piece of masking tape was taped on the spot at which the ball was placed for each trial.Figure 1: Experimental set-up Figure 2: Experimental set-up. Motion Detector is visible. Materials and Procedure: Begin by creating the pendulum. Model the pendulum after Figures 1 and 2 above. First, take two clamp stands and connect them by clamping a bar loosely across them (loosely so that it the bar can swing). Then use duct tape to tape the hammer to the bar and test to see if the bar will swing with the hammer on it.
Take this entire set up and mount it on two text books, one for each clampstand, and use clamps to clamp the set up to the table. Then use another clampto clamp a platform (on which the ball will rest) to the table in the middle of thetwo clamp stands and in front of the hammer. Then take a small piece of ducttape and tape it onto the front of the platform so that the position of the soccerball remains constant. Once this is done, in order to control the height fromwhich the pendulum is dropped, take a bar and clamp it perpendicular to the barthat is resting across the two clamp stands (does not necessarily have to beperpendicular. It can be greater than 90 degrees according to how high you wantto raise the hammer). Once this is done, set up the motion detector on anothertable approximately 1 meter in front of the set up so that it can measure themotion of the ball. Once all of the set-up is done, the data collection process canbegin. For each measure of pressure, the ball must be massed on a scale becausethe mass is essential to calculating the kinetic energy. Place the ball on theplatform where the duct tape marking is. Then raise the hammer to theprotruding bar and release the hammer so it swings and makes contact with thesoccer ball. Record your results that were picked up by the motion detector andproceed with the rest of the trials. There will be three trials for each of the sixdifferent pressure measures.Data Collection & Processing:Figure 3: Sample graph of the Position vs Time graphs of the ball being hit by thehammer. This is the graph from the second trial of 1 kg/cm2.
Gauge Pressure Mass (kg) Velocity (±0.2m/s) Average(±0.001kg/cm2) Velocity Trial 1 Trial 2 Trial 3 (±0.2m/s)0.200 0.430 2.157 2.463 2.399 2.340.400 0.431 2.391 2.443 2.508 2.450.600 0.432 2.548 2.494 2.524 2.530.750 0.433 2.524 2.563 2.566 2.551.000 0.434 2.576 2.598 2.587 2.591.200 0.435 2.489 2.402 2.424 2.44Table 1: Raw data collected from all the trials in the experiment. Data shows eachpressure value and for each pressure value the mass of the ball and the velocitiesof the three trials. Also shows the average velocities. In order to find theuncertainty of the velocity, the ranges of the trials for each pressure value had tobe divided by 2. Then the greatest value would be the uncertainty.Pressure Average(±100 KineticPascals) Energy (±0.2 J)19,600 1.239,300 1.358,800 1.473,500 1.498,000 1.5117,600 1.3Table 2: Table that shows the Average Kinetic Energy for each pressure valuewithin the ball. In order to find the Kinetic Energy, the values from Table 1 wereplugged into the formula: ½ mv2. In order to obtain the pressure value in its
correct units (pascals), the Gauge Pressure value in (kg/cm2) had to bemultiplied by 9.8*104.Sample Calculations:Calculating uncertainty for velocities:Trials 1 and 2 for the pressure value 0.2kg/cm2 had the largest range.2.463 - 2.157 = 0.153 = ± 0.2m/s uncertainty for velocities 2Actual Value for Kinetic Energy= ½ (0.43kg)(2.3m/s)2 = 1.177 JHighest Value for Kinetic Energy= ½ (0.43+0.001kg)(2.3+0.2m/s)2= 1.347JLowest Value for Kinetic Energy= ½ (0.43-0.001kg)(2.3-0.2)2= 0.946JUncertainty = (1.347J – 0.946J)/2 = ± 0.2JFigure 4: Graph of the Pressure compared to Average Kinetic Energy. Linear fitfunction is utilized to show the slope of the graph.
Figure 5: High-Low fit graph of Pressure compared to Kinetic Energy of the ball.Conclusion: According to Figure 4, it can be seen that the relationship between thepressure within the ball and the kinetic energy is linear. Due to this, it can beconcluded that, although there is an outlying point at the end, as the pressurewithin the ball increases, the kinetic energy of the ball increases as well. Fromthe graph in Figure 4, an equation for the relationship between pressure with asoccer ball and kinetic energy was found: y= (0.0669 0.099)x + (1.140 0.2965) (2) Apart from the final outlying point, the equation of the graph supports theinitial theory that the kinetic energy of the ball would increase as its pressureincreases. In order to attain this equation, the linear fit on the graph onlyincluded the first five points and not the sixth point because it was an outlier.Although it was not included in the calculations of the equation, the outlier is infact quite significant as it explains the flaws of having too much pressure withinthe ball. The outlier (sixth point) is not inaccurate data as it is explained to be thepoint at which there is too much pressure within the ball. When the pressurewithin the ball is increased too much (in this case to 117,600 Pascals) the kineticenergy within the ball actually decreases because although a certain amount ofelasticity is good, too much elasticity does not allow for as much contact timewhen struck. This means that the pendulum was not able to strike the ball fullybefore the ball’s great amount of elasticity resulted in the ball rapidly bouncingoff the hammer before it could follow through.
Due to the considerably low uncertainty in the graph, the confidence levelof the results is fairly high as the experiment was carried out quite accurately.Also, the data collected correlates very well with the linear fit, thus suggestingthat this data is fairly reliable. These results only apply as long as the same soccer ball is used and thesame pendulum (same hammer) is used. It is also important that the height fromwhich the hammer is released remains the same. The same pressure values mustalso be used.Evaluation: There were a number of things that could have been improved over theduration of the experiment. Firstly, when collecting data, the ball placement onthe platform could have been better if it was more accurately placed each time.The problem was that the ball was often not perfectly centered with the hammerbecause the main challenge was stabilizing the ball. Due to this challenge ofstabilizing the ball, whenever the ball was stable, whether central or not, weproceeded with the collection of the data. In order to improve on this, a dentcould have been made in the platform in order for the ball to sit nicely for eachand every trial. In order to have minimal interference from the dent, it isimportant that the dent is not very deep. Another thing that could have been improved in this experiment was themovement of the hammer. Because the hammer was attached to a bar that wasloose (so that it could swing), it also was loose enough to slide from side to side.Due to these minor horizontal movements, the point at which the hammer struckthe ball was not always the same as it was often shifting from left to right. Inorder to improve this, barriers could have been installed on either side of the barin the attempt to halt or minimize horizontal movement. One final flaw that could have been improved upon was the security of thehammer onto the metal bar. Because duct tape was used to fasten the hammeronto the bar, as the experiment progressed, due to the mass of the hammer, thetape loosened allowing the hammer to wiggle as it swung. In order to avoid this,a more secure way of attaching the hammer to the bar must be developed. Inorder to maximize security of the hammer, the hammer could be bolted to apiece of metal and the piece of metal could be welded to the bar. This wouldmake sure that the hammer stays completely still throughout the experiment.Analysis:In my Independent Research Project for Physics, I used Reason and Perceptionwhen analyzing my data to make sure that my results were accurate, or werewhat I perceived as accurate. Primarily when looking at the data that I got, I usedperception to know what was supposed to be the correct data and then I usedreason to see whether the data that I got out of the experiment matched theseperceived values. In order to attain the information that was supposed to be
correct, research had to be done and based on this research, my perception wasaltered to fit what I had learned. Thus it is the research that shaped myperception and this perception was what I relied on to compare my results to. Iused deductive reasoning when analyzing my data in order for it to seem correctand accurate. Deductive reasoning allowed me look at what the data was ideallysupposed to be like, and thus I shaped my data accordingly. My reasoningactually a product of my perception because, depending on my perception Iwould use reason accordingly in order to match up the data. Had I perceived thecorrect data differently, I would have used reason accordingly and concludedwith different results.