Investigating the Bounce of a Tennis Ball after It Has Been Dropped From Certain Height
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Aim To investigate how high a tennis ball will bounce back after it has been dropped from a certain height How a Tennis Ball Bounces As the ball is elevated the ball gains gravitational potential energy equal to the ball's weight multiplied by its change in height1. When the ball is dropped, the height decreases, and therefore so does the gravitational potential energy. At the same time, the velocity of the ball increases due to gravity, and therefore the kinetic energy increases, as kinetic energy half the mass of the object (in this case the falling ball) multiplied by velocity squared (Source: Physics for You GCSE textbook). When the ball hits the floor the kinetic energy goes into deforming the ball from its original round shape to a squashed, oval shape. A tennis ball contains a rubber shell, which is filled with compressed gas. The ball is most stable in a round shape, so the gas inside expands to push the ball back to form the round shape. This forces the outside of the ball to push out and therefore bounce back up2. However, the ball will not bounce back to its original height due to it losing energy as heat and sound energy when hitting the floor. Relevant Variables The independent variable in this investigation is the height that the ball is dropped from. The dependent variable that will be measured is the height that the ball bounces back. The control variables that will need to be kept constant if the results are to be as accurate as possible are: 1. The weight of the ball; we will use the same ball throughout the experiment to ensure that the results are as accurate as possible. 2. Material of the ball; as the ball is the same one used, this will be kept the same also. 3. How to Cite this Page
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Temperature of the ball; if the ball is cooler or hotter, it may
bounce up to a less or greater distance. As the temperature of the ball is not easily controllable we left approximately a minute between each drop to ensure the ball had returned to room temperature. 4. Air pressure (acting on the ball). Although this is not easily controllable, we can assume the air pressure is kept fairly constant as the experiment was conducted in the same classroom. Prediction I predict that the higher the ball is dropped from the higher it will bounce back. This is due to the fact that the higher the ball is elevated, the greater its gravitational potential energy, the greater amount of kinetic energy it will gain when falling, and therefore the greater the energy the ball has to bounce back with. I predict that the ball will never bounce back to its original height, due to the energy the ball loses as mentioned above. The ball will not back at all when it is "dropped" from a height of 0cm, as there is no gravitational potential energy gained by the ball. Due to this when I plot a graph of The Height the Ball is dropped from against the average height that the ball bounces back I expect that the line of best fit will look something like this: [IMAGE] The line of best fit will go through (0,0) indicating direct proportionality. Preliminary Work A preliminary experiment was carried out to enable us to predict and to make the actual experiment as reliable as possible by adapting the method suitably. Preliminary Method Equipment List * Meter ruler * Retort stand and clamp * Tennis Ball Method 1. Attach the clamp to the retort stand 2. Clamp the ruler so it stands vertically, as parallel to the retort stand as possible to ensure that the readings are accurate. 3. One person will hold the ball at 100cm, and when the second person knows that the ball is about to be dropped, they will drop the ball. 4. The second person will, as accurately as possible, read the height at which the ball bounced back to. 5. This will be repeated twice more, and an average found of the results for greater accuracy. 6. This method will then be repeated at 90cm, 80cm, 70cm, 60cm, 50cm, 40cm, 30cm, 20cm, 10cm and then left at 0cm. Safety Precautions The experiment is fairly hazardfree, although bags and stools were removed from the vicinity of the experiment, to ensure that any injury caused by tripping etc was prevented. Results Height Dropped (cm) Height Bounced Repeat 1 (cm) Height Bounced Repeat 2 (cm) Height Bounced Repeat 3 (cm) Average Height of Bounce (cm) 0 0 0 0 0 10 7 7 7 7 20 13 13 14 13 30 18 18 18 18 40 22 23 24 23 50 26 28 27 27 60 33 33 32 33 70 37 39 38 38 80 44 41 43 42 90 49 48 48 48 100 54 53 52 53 As predicted, the graph's best fit line goes through the origin, indicating direct proportionality between the height from which a tennis ball is dropped, and the height at which it bounces back to. There were no blatant anomalies in my results, so I decided to use the same, unchanged method for my actual experiment. Results Height Dropped (cm) Height Bounced Repeat 1 (cm) Height Bounced Repeat 2 (cm) Height Bounced Repeat 3 (cm) Average Height of Bounce (cm) 0 0 0 0 0 10 7 7 6 7 20 12 11 13 12 30 17 18 17 17 40 22 23 23 23 50 27 27 28 27 60 33 31 33 32 70 36 38 38 37 80 43 43 44 43 90 49 50 47 49 100 52 53 54 53 Analysis Through our investigation I confirmed my theory that the greater the height a ball is dropped from, the greater the height it will bounce back to, the straight best fit line on t both the graphs passing through the origin also confirm this. As the line of best fit is straight we can also deduce that the smaller the height the ball is dropped from the smaller the height the ball will bounce back to. I thought about what happens after the ball has bounced once, and whether or not it continues to bounce infinitely at smaller and smaller heights. However this could not happen, as eventually the ball loses energy through friction with the air and the material, heat, and sound energy, causing the ball to eventually stop bouncing. Relevant Extensions To extend the experiment, there a number of investigations we could go through. For example: 1. The bounce back heights of different balls, of different materials. 2. The number of bounces a ball will make before stopping. 3. Carrying out these experiments in a vacuum, and testing whether or not air resistance affects some balls. By using the coefficient of restitution, we can measure how much bounce there is, or in other words, how much of the kinetic energy of the colliding objects before the collision remains as kinetic energy of the objects after the collision. With an inelastic collision, some kinetic energy is transformed into deformation of the material, heat, sound, and other forms of energy, and is therefore unavailable for use in moving. A perfectly elastic collision has a coefficient of restitution of 1. Example: two diamonds bouncing off each other. A perfectly plastic, or inelastic, collision has c = 0. Example: two lumps of clay that don't bounce at all, but stick together. So the coefficient of restitution will always be between zero and one3. To measure the coefficient of an object falling to the floor the formula is: [IMAGE] Where c is the coefficient, h is the height the ball bounces back and H is the height that the ball is dropped from. I worked out the coefficient of restitution for the both the preliminary experiment and the main experiment. Results Preliminary Experiment: Coefficient of Restitution of the tennis ball used = 0.76 Main Experiment: Coefficient of Restitution of the tennis ball used = 0.74 Although the exact same ball was used for both the experiments, by the second time, the ball's coefficient of restitution was less. This could be perhaps due to air seeping out of the ball between to the experiments, which is why tennis balls sometimes lose their 'bounciness'. For this reason, tennis balls come in pressurized containers, the pressure exerted on the outside of the ball being equal to the pressure of the inside of the ball, to prevent any gas seeping out. By comparing these coefficients of restitution to what the manufacturers claim their balls coefficients of restitution to be (0.75) we can see that our ball is still quite "bouncy". Evaluation I feel that the experiment went very well, with no anomalies, and both experiments confirming my previous predictions. The accuracy of the experiment was maintained throughout, with constant control variables, and averages found wherever possible, to give the greatest accuracy. Improvements To give greater accuracy, although it is not needed to confirm my predictions, there are a number of things that could be done. For example: 1. Increasing the range of the measurements to 0cm  200cm 2. Using digital imaging to get an exact height at which the ball bounces back, instead of using our eyes and reactions. 3. Doing more repetitions, and finding averages. Sources and Bibliography 1 Physics for You GCSE textbook 2 Factors Affecting A Bouncing Tennis Ball website. Address: http://van.hep.uiuc.edu/van/qa/section/Making_Stuff_Move/Bouncing_Bumping_and_Crashing/20011228194353.htm) 3 Coefficient of Restitution website. Address: http://www.racquetresearch.com/coeffici.htm 
