Aim:To investigate the relationship between the change in pressure of the basketball and the rebound height of the basketball after one bounce by dropping the basketball from a controlled height of 92 cm above the surface, and measuring the height of the rebound height (first bounce) by using a meter ruler and a slow-mo video camera to determine the height. Introduction:I decided to choose this topic for my IA because I follow the NFL and have been a big fan of the New England Patriots for quite some time now. However, in recent time, the New England Patriots and their quarterback Tom Brady have been accused of deflating the ball used in the game which could’ve game them an advantage as it could have been easier for Tom Brady to throw the ball to one of his wide receivers. Furthermore, I have also been a fan of the NBA and I have been supporting my hometown team, the Toronto Raptors, and I recently found out that there is a certain pressure that the basketball needs to be maintained at and when I read the article that said that, I wondered why that was. Then I found out because it can affect how you shoot the ball when it is in the air and as well as how it bounces which are two essential areas of the game. Thus, these two implications, the New England Patriots deflating the ball, and how the ball needs to be at a certain pressure in the NBA allowed me to choose this topic because I am able to test what effect pressure has on a basketball, allowing me to further understand why the NBA sets a certain pressure for the basketball during games. Research Question:What is the relationship between the internal pressure and the rebound height of a ball?Background Information:Elastic potential energyElastic objects such as basketballs can change their shape when they make contact with another surface such as a floor. When they change their shape by either being squashed or stretched, energy is used. This energy is stored in these objects such as a basketball is known as elastic potential energy.Kinetic energyEvery moving object has kinetic energy. Kinetic energy is proportional to velocity and mass, which can be derived from its formula. Example 1 – The bouncing ballSeveral energy transfers happen when a basketball makes contact with the floorWhen a basketball is held stationary from a point above the floor, its gravitational potential energy (GPE) is at a maximum. At this point of time, the basketball has no kinetic energy (KE), or elastic potential energy (EPE).When the basketball falls from the point (i.e. no longer stationary), its GPE is transferred to KE. This is when the ball accelerates at around 9.81 ms-2, which is the Earth’s acceleration of gravity of a free fall object. When the basketball makes contact with the ground, this KE is now transferred to EPE as the ball makes contact with the ground, and its shapes changes due to the force of the impact.The reason the ball bounces back up is because this EPE converts back into KE, and the ball bounces upwards. When the ball reaches the maximum height of its rebound, the KE transfers back to EPE.The reason why the rebound height is lower than the original drop height is because some energy from the ball is either transferred as heat and/or sound energy and/or is lost to the surroundings.High upGPE – maximumKE – noneEPE – noneFallingGPE – decreasingKE – increasingEPE – noneOn tableGPE – minimumKE – noneEPE – maximum(“GCSE Bitesize: Potential Energy and Kinetic Energy.”)PressureA ball that is pressurised has elasticity and also bounces because that air molecules which are in the ball are at a larger volume than in the surrounding atmosphere. Thus, when there is more air pressure in a ball, is bounces more and becomes more elastics higher because there are more air molecules in the ball and the ratio of air molecules in the ball versus the air molecules in the outside atmosphere increases, allowing more molecules to collide with each other inside the ball due to more being present. Ground ContactAccording to Wesson, before a ball makes contact with the ground, air pressure is constant throughout the ball. However, when the ball makes contact with the ground, it deforms and the air pressure around the deformed area increases, as well as throughout the ball’s interior. In addition, the constant pressure during the rebound increases due to the volume of the ball being reduced when contact with the floor was made. (Parrish, Rogue. “How Does Air Pressure Affect the Bounce of a Soccer Ball?”).Hypothesis:I think that if the air pressure inside the basketball increases, then the rebound height of the basketball will also increase. I think this because when there is more air pressure inside a basketball, there are more molecules of air in the basketball. Thus, the molecules become more packed together inside the basketball, leading to more force exerted on the interior walls of the basketball. Thus, when a basketball lands on a surface, the more air pressure there is present inside the basketball, the less distorted the shape becomes when it makes contact with the surface, meaning that it has less energy lost. This is because the potential energy of the ball which is equal to mgh, was converted to elastic energy when it impacts the surface, in this case the ground. With that, there is also some friction (both inside the ball and between the ball and the surface) which will dissipate energy. Therefore, when there is more air pressure inside the basketball, there is more elastic energy in the ball, which allows the ball to rebound at a higher height. Moreover, I think that the there is an positive correlation between the two variables; independent and dependent variable, as one increases, so does the other variable. Variables:Independent VariableI am changing the air pressure inside the basketball, hPa, by using a pump to make the air pressure 1000 hPa, and then using an air pressure gauge to decrease the pressure by 100 hPa each time. Therefore, my first trial will be at 1000 hPa, and my 8th trial (last trial), will be at 300 hPa.Dependent VariableI will be measuring the rebound height of the basketball (first bounce) when it is dropped by a controlled height of 92 cm, which is measured by a ruler. The rebound height will be measured by using a slow-mo video camera and a meter ruler, and looking at the replay and the corresponding height on the ruler. Control VariablesHow?Why? Height of Initial DropBy dropping the basketball from a height of 92 cm, measure from the bottom of the basketball for each trial. Because, according to the potential energy formula which is P.E. = mgh, if height changes, then potential energy also changes, meaning that the amount of potential energy that is converted into elastic and kinetic energy changes, affecting the rebound height of the basketball. Atmospheric PressureBy doing the experiment in the same classroom each time, so that the level I am conducting the experiment at is constantly at the same height above sea level, keeping atmospheric pressure constant. At higher altitudes, the air is less dense and/or thinner than air at lower altitudes. When the air is thinner, objects are not as affected by factors such as air resistance while they are in the air. Thus, atmospheric pressure affects the rebound height of a basketball, and thus should be kept constant. Materials/Equipment: MaterialQuantityBasketball1Air Pump1Milton Air Pressure Gauge1iPhone 7 (a phone that can record slow-mo)1Clamp Stand2Meter Ruler1Method: Be cautious of your surroundings when carrying the experiment (dropping the basketball), to ensure that no damage is done to other objects, especially the device that you are recording with. Pump a basketball as hard as you can, so that there is high amount of air pressure in the basketball. Insert an air pressure gauge into the basketball. The air pressure gauge should read that the pressure inside the basketball in greater than 1000 hPa. If it is less than 1000 hPa, repeat step 2. Using the air pressure gauge, adjust the pressure of the basketball into it is at 1000 hPa, by pressing the button on top of the gauge to release air pressure. Tape a meter ruler to a wall, ensuring that the bottom of the meter ruler is touching the ground. Also, set up two clamp stands and tape your slow-mo recording device to the two clamp stand so that it able to record the meter ruler properly. The height can be adjusted by adding objects such as books below the clamp stand as the rebound height will differ with different pressures. Ensure that the meter ruler can be seen clearly with the recording device.If it is hard to read the numbers on the meter ruler, use a marker to darken the lines which increase in 10’s, starting from zero (i.e. 10, 20, 30, etc). Press record on the slow-mo device and drop the ball without exerting any external/extra force, from a height between 90-100 cm (the bottom of the ball) so that the rebound height of the basketball should be around the middle and middle upper portion of the meter ruler. Rewatch the video to determine the rebound height, by pausing the video where the basketball is at the highest height after its first bounce and record the data in a data table. Measure the height of the bottom of the basketball. Do 2 more trials with the same pressure, ensuring that the basketball is dropped at the same height as the previous trial and that the slow-mo device is operating. Repeat steps 4, 8-10 but instead, using the air pressure gauge to change the air pressure inside the basketball by a reduction of 100 hPa each time, until you have 8 datasets of different air pressures.Safety Measurements:Ensure that you are cautious of your surroundings, so that you do not damage anything valuable with the basketball. Ensure that your recording device is at a same distance from the area the basketball is dropped, but close enough to be able to see the meter ruler clear enough.Be cautious towards the experiment.Tie your hair back if you have long hair so it doesn’t get in the way. Act sensible when conducting the experiment. Make sure the work area is tidy and clean. Ensure you are aware of your surroundings and other people who are conducting the experiment. Diagram:(Effect of Pressure on Elastic Rebound of a Basketball), www.tuhsphysics.ttsd.k12.or.us/Research/IB08/ScotKern/index.htm.Raw Data Table:The data table showing the relationship between the change in pressure, hPa, of a basketball and its corresponding rebound height, cm, when dropped from a controlled height of 92 cm, and reducing the pressure of the basketball by 100 hPa each time using an air pressure gauge. Pressure / hPa± 5Rebound Height / cm± 0.1Trial 1Trial 2Trial 3Average100069.570.570.570.290067.067.567.567.380065.565.064.064.870062.063.062.562.560059.061.559.059.850056.558.057.057.240055.554.555.055.030053.052.552.552.7Processed Data Table:The data table showing the relationship between the change in pressure, Pa, of a basketball and its average corresponding rebound height, m, when dropped from a controlled height of 0.92 m, and reducing the pressure of the basketball by 10000 Pa each time using an air pressure gauge. Pressure / Pa± 500Rebound Height / m± 0.001Average1000000.702900000.673800000.648700000.625600000.598500000.572400000.550300000.527 Uncertainties Length 0.001 m(0.1 cm)±0.001m was the uncertainty of the one meter ruler that was used to measure the rebound height of the basketball. Air Pressure of Basketball500 Pa(5 hPa)The uncertainty of 5 hPa (500 Pa) is the uncertainty of the air pressure gauge which was used to measure the internal air pressure of the basketball. Table of Random ErrorEquipmentCalculationsPercentage uncertaintyAir Pressure (in Pa)500100000 x 100 0.5%Ruler (in meters)0.0011 x 100 0.1%Total uncertainty 0.6% Graph:(Note: Graphs are made by using Microsoft Excel 2016). Calculations (using the formula y=210-6x+0.4507):Air Pressure / PaRebound Height / my=210-6x+0.4507y=210-6(100000)+0.4507y=0.6507y=210-6(90000)+0.4507y=0.63070.6507 0.6307y=210-6(80000)+0.4507y=0.61070.6107y=210-6(70000)+0.4507y=0.59070.5907y=210-6(60000)+0.4507y=0.57070.5707y=210-6(50000)+0.4507y=0.55070.5507y=210-6(40000)+0.4507y=0.53070.5307y=210-6(30000)+0.4507y=0.51070.5107 ConclusionThe main point of this experiment is to find out the relationship between the internal air pressure of a basketball and the corresponding rebound height. The relation between the two variables; independent variable and dependent variable can be represented by the equation y=210-6x+0.4507, which was derived from the gradient of the line when graphing the two variables. This equation was used to do sample calculation which can be seen above and proved to be quite accurate to the results which were obtained during the experiment. When using the equation, the variable y is the rebound height and the variable x is the air pressure of the ball. For example, when the air pressure of the basketball was 30000 Pa, the experimental value was 0.527 metres, and the calculated value was 0.5107 metres. Also, when the air pressure of the basketball was 100000 Pa, the experimental value was 0.702 metres and the calculated value was 0.6507. These two results for the rebound height at both 30000 Pa and 100000 Pa are quite close to each other, thus making the experiment accurate due to a minor difference between the experimental values and calculated values obtained. The major reason for the difference between the calculated and experimental values is because of uncertainties that occurred during the experiment. These uncertainties included measuring both the internal pressure of the basketball and the rebound height of the basketball. There was uncertainty when measuring the internal pressure due to the instrument which was used to measure it, which was the air pressure gauge. The uncertainty comes from the instrument itself with it being stated on it at 5 hPa. There was uncertainty when measuring the rebound height of the ball because of two things. The first was that the meter ruler itself has an uncertainty of 0.001 meters (or 0.1 cm), which was decided manually. The reason it was 0.1 cm is because of the second reason which was the iPhone. In order to get the result of the rebound height, a replay of the bounce in slow-mo was used to determine the rebound height and from the videos, 0.1 cm of uncertainty seemed appropriate. It was important to carry out this experiment because as someone who takes a significant interest in basketball, the pressure of the ball can change the whole aspect and outcome of the game. It is also very important for players, officials, and the league (i.e. NBA) to decide and acknowledge a specific pressure for the basketball for every game for fair play and also to prevent cheating. The reason for this is because different internal pressures of a basketball can affect certain factors such as flight time, the amount of power you need to use, and the feel of the ball. These factors can affect the outcome of the game as it can be used to players advantage or disadvantage, depending on their preferences. However, by having one set pressure for a basketball during every game eliminates any kind of cheating along this line and also prevents anything being used against the league/officials along this line. Take Tom Brady from the New England Patriots in the NFL who was was conspired for deflating the balls for example, and how much controversy and confusion that caused. EvaluationAccuracy of data collection:(Describe in detail the difficulties or limitations in collecting data. )Improvements to future collection of data:(Describe how you can realistically change the experiment to collect more accurate data.)In order to know what the rebound height was of the basketball, a slow mo camera was used, as looking for where the ball rebounded at on the ruler was too fast for the naked eye. Thus, the replay would be looked at to determine where the the highest point at which the bottom of the ball was against the ruler after one bounce. However, it was quite difficult and time consuming to get the phone into a position so that it could record the ball and the ruler as I had to tape it to a clamp stand, but as well as determining and pausing the video at the exact point at which the ball was at the highest point after one bounce. This could have led to inaccurate results due to not picking the time where the ball was at the highest height above the ground after one bounce. This however, was accounted for by the uncertainty of the ruler. By having two people doing the experiment, so that one person can hold the phone and record, saving a lot of time, and getting a second opinion on which point the ball was at the highest point after one bounce from your partner. At the beginning of each trial, the pressure was set to a certain number, which is indicated in the table (i.e. 100000 Pa), however I noticed that after the three trials were done and I was going to use to gauge to set the pressure to a lower figure, it would be lower than the original amount which it was set to (i.e. 100000 Pa), which was due to the ball losing pressure when it was bouncing during the three trials which could have affected the accuracy and reliability of the results. By using the air pressure gauge to check the internal air pressure of the basketball after each trial, and if it is lower than the set pressure/desired pressure, then pump it back to that pressure. Thus, all three trials for a specific pressure will be all be done at that specific pressure. Further experiments:Changing the drop height of the basketball as opposed to changing the pressure of the basketball and measuring the rebound height that follows.Calculating the coefficient of restitution.Changing the atmospheric pressure of where the experiment is conducted and measuring the rebound height. Changing the temperature of the basketball and seeing how it affects rebound height. Bibliography”GCSE Bitesize: Potential Energy and Kinetic Energy.” BBC, BBC, www.bbc.co.uk/schools/gcsebitesize/science/add_aqa_pre_2011/forces/kineticenergyrev2.shtml. Parrish, Rogue. “How Does Air Pressure Affect the Bounce of a Soccer Ball?” LIVESTRONG.COM, Leaf Group, 11 Sept. 2017, www.livestrong.com/article/428414-how-does-air-pressure-affect-the-bounce-of-a-soccer-ball/Effect of Pressure on Elastic Rebound of a Basketball www.tuhsphysics.ttsd.k12.or.us/Research/IB08/ScotKern/index.htm.