The player may also feel stiffer on a cold day. You can get an idea of just how much by looking at the percentage difference in stiffness resulting from the temperature exposures. Analyze the data, and make a conclusion stating if the temperature of a tennis ball affects how high it bounces. Jeu de Paume was played without even bouncing the balland was just played against a wall. Thank you, this explanation was very concise and helpful. For the heating during the tension loss phase, the starting temperature was 20 C. Tension was increased to 28 kg and 200 seconds were allowed to pass. If the density and the constant remain the same, a higher temperature results in higher pressure, while a lower temperature results in lower pressure. This experiment was performed to determine the effect of temperature on the stiffness, elongation, tension loss, and maintenance of tennis strings. A complicating factor is that the ball also changes performance with temperature. Put 2 in the freezer, also for 10 mins, so they can First, make a way for the ball to drop from the same height every time. In the heat, the molecules are more active, so the ball can bounce higher, and in the cold, the molecules are heavier and have less energy, creating a smaller bounce. (Sheehan, 2011)Its just like a trampoline: When one jumps on a trampoline, the material one the trampoline expands and stretches, and when it does, the trampoline is forced to come back up to its original state, causing one to bounce on the trampoline. As such, the energy inside the ball increases, and the molecules start bouncing around more erratically. After the ball hits the floor the ball gains motion that is. Analysis The heated tennis balls bounced the highest because as the temperature rose, the molecules expanded and exerted more pressure when the ball bounced The experiment illustrated the perfect gas law, because it showed that when the temperature rose, so did the pressure The data for each set of tennis balls had a range of 15 . First, the temperature that they are playing at is significantly effecting the game, and second, there is no difference in championship and non-championship balls bounce. Figure 6 Composite view of tension loss by string and temperature history (indexed in order of tension loss at room temperature of 20 C). (Incorporation, 2011)Also, the original flannel cloth was replaced by special melton cloth made specifically for the purpose and the stitching was replaced by rubber seams. Bocce ball was steadily rising and falling in popularity, until a major resurgence in 1896, when it was admitted an olympic sport, and has been part of the summer olympics ever since. Likewise, will a tennis racquet perform differently at different temperatures, or will the stringbed stiffness be affected if the racquet is strung at different temperatures? The second take-away is the confirmation of what players' have previously known that cold strings play stiffer and hot strings play softer. This scientific mystery can be demonstrated at home or school with a simple experiment. Try comparing a baseball to a golf ball or a tennis ball. cuz in my experiment i got some mixed up results. Temperature Quadratic ANOVA, Table 13: Ball 1 vs. Method: 1. Two variables will be omitted in the study, how much the ball is played with and different court surfaces. co2 is carbon dioxide and carbon dioxide is an expanding gas. Copyright 2023 Elite Tennis Guide | All Rights Reserved. The kinetic, Tennis is a game of speed and reflex. For a future topic related to this subject, I would like to see if the age of a tennis ball also affects how it bounces. We just wanted to let you know that we got a lot of information from this. For this reason, you will often notice that the players performance during the summer is different from their performance in winter. The anatomy of a tennis ball features a hollow rubber-like core filled with gas. Bocce has really become such a widespread sport because you can participate no matter how old, what your race is, or what gender you are. It is the relaxation that occurs both during and after the stretch that is significant. In warm temperatures, the opposite is true. This will give you a visual presentation of the bounce heights and the temperatures, which means that determining whether hot or cold balls can bounce to a higher height will be a lot easier. Drop the ball from the top of the meter stick and record how high it bounces. document.getElementById( "ak_js_1" ).setAttribute( "value", ( new Date() ).getTime() ); can u pls also mention the results u get by doing the experiment? Retrieved 8 24, 2012, from ITF Tennis: http://www.itftennis.com/technical/equipment/balls/history.asp, Sheehan, K. (2011, March 11). Do you know how a golf ball works? NOTE: IEEE WAS NOT AVAILABLE FOR CITATIONS, SUBMITTED TO SABIO ACADEMY TO MEET THE REQUIREMENTS OF THE SR 90 JUNIOR RESEARCH COURSE AT SABIO ACADEMY. Tennis balls in the 1400s were quite similar to the first tennis balls, butthey were stuffed with chalk, sand, sawdust, or earth. After this experiment, one will know why tennis balls bounce differently after being left out in various weather conditions. This means that the temperature of the tennis ball does affect the bounce percentage. Two different types of balls, Penn Championship and Non-Championship will be compared. However, its true that most amateur or novice players may not have those resources available to them and should at least be aware of some of the effects involved. The relatively uncontrollable nature of weather presents a variety of challenges to address to perform at the highest levels. A good example of this would be, when designing buildings to survive in areas where earthquakes happen frequently. The balls which were placed in a freezer had a bounce percentage of 54.90. On the other hand, the thermal energy of a warmer string helps break weak bonds between molecule chains, allowing greater flow and elongation of the string during stretching. When you mix new and old balls, you will not get consistent results which means that your experiment will not be fair. Video footage will also be utilised to measure the bounce correctly by watching the film in slow motion. The stiffness tests closely approximated the expected result that stiffness would have an inverse relationship to increase in temperature. So, for the most part, adapting to weather or other environmental conditions can usually be done relatively quickly. Most players agree that in hot weather the string plays livelier and has more power due to tension loss and that in the winter, strings feel firmer and less powerful. By using a 1 meter ruler to measure the bounce height in centimeters. Hypothesis: The normal tennis ball will bounce higher than the tennis ball that was placed in the freezer for some time as the air molecule inside are not affected but for the cool tennis ball its air is compressed affecting its bounce. It will, however, continue to equalize stress after tensioning more quickly than the unheated string, so will lose a bit more tension than the unheated string. This means that the tennis ball becomes dead after ten games, and after that, it is in a bricked state, and for this reason, it can not be used anymore. Using tongs, push the squash ball under the water for about 2 minutes. The setup was essentially the same as in Figure 1 but a computer controlled stretching program was different. Temperature has a significant positive relationship with the bounce height of tennis balls. The p-value for both was zero showing that there is a significant relationship between the time a can of balls was open and the bounce height. That means theres more water in the air, causing it to be and feel denser. Racquetball is played on a rectangular indoor court with four side walls and a ceiling. Gather 15 to 20 tennis balls and a measuring tape. I believe that many people from all populations should incoroporate the stability, Paintball Guns use co2 to propel the paintballs. As you will notice from your experiment, the balls that have been treated to the ice chest with ice in it will tend to have lower bounces, resulting from the molecules moving around less and containing less energy. Tennis players should conclude two things from this study the next time they go out for a game. With an increase in the temperature, the gas molecules within the tennis ball start to expand. Aim: The aim of this experiment is to see which ball is better quality for bouncing and what is a lot more reasonable for price and size. Average the results. The ball will not bounce much in the winter, which means that the players will not be as active on the field as they are during the summer season. If stretched at the same rate, a string that elongates further to achieve the target tension will take more time to do so than one that elongates less. Place the tape measurer against the edge of a wall using the bluetack 3. Have another person measure and record how high the ball bounces. Stiffness is the most important property of strings. The greatest effect observed in this experiment was that exposing a string to high temperatures after post-tensioning stabilization/relaxation has occurred (as in leaving the racquet in the car during hot weather) produces the greatest decrease in tension. (Sheehan, 2011)Outside of the ball is felt, which is the furry, yellow fabric on the surface of the tennis ball. As the tennis ball returns to its normal shape, the gas inside the ball acts as a spring and causes the ball to bounce into the air. Pickleball Spin Why Is A Rubber Hitting Surface Illegal? A game played at higher temperatures will be much faster since the ball will rebound from contact with any surface better than at low temperatures. Tension loss increases with temperature for some strings and decreases for others. How does Temperature Affect the Bounce of a Tennis Ball? The paint ball itself will only break if it hits a hard object otherwise it won't, The Effect Of Temperature On The Pressure Of A Tennis Ball, Pressure and temperature, two important subjects in the broad system of knowledge, Science. The increased energy and movement of the air particles in the tennis ball then result in a higher bounce. Hold a ball so its lowest point is at the 1 metre point. The movement of the air and the squishing inwards when the ball has been dropped cause the ball to push out again, which is the reason for the bouncing movement. In the experiment only a hard surface will be analyzed and no playing with the ball will be allowed. After the tennis ball reforms into its original shape, the gas inside the ball pushes back up and causes the ball to bounce into the air. This is due, in large part, to their construction. (Incorporation, 2011)After, chemicals would generate pressurizing gas which was to be added to the rubber outline. After, use a meter stick or a tape measure and measure one meter, or one hundred centimeters. When a tennis ball hits the ground, the force presses against the ball, pushing the bottom surface of the ball in to the core and compressing the gas inside of it. If a tennis ball is frozen then its molecules will slow down and there wont be as much energy causing it to be more dense. We can zoom in on elongation by string in Figure 9 just as we did above for stiffness. These muscles are used to accelerate the whole arm while also stabilising the shoulder. How Does Air Pressure in a Ball Make the Ball Bounce Higher? Here is a diagram of the structure of a tennis ball. Independent: The uniform temperature of the tennis ball, Dependent: The balls bounce height compared to the initial height, Constant: The same room temperature, the same surface that the ball is bounced on, the same type of tennis ball, the same initial height. After ten games, tennis balls are known to have a rebound ratio of less than 53%. How does temperature affect the bounce of a tennis ball? (Borlings, 2011)However, in 1470, Louis XI of Franceforbade the filling of tennis balls and said that they should be filled with high-quality leather. Here is another table that shows the exact height in which the ball bounced. An experiment was performed to determine the effect of temperature on the stiffness, elongation, tension loss and maintenance of tennis strings. This phase was similar to the pre-tensioning heating test but an additional 100 seconds was added to allow tension to stabilize. Figure 7 Stiffness by string, material, and temperature exposure immediately after the 100 second relaxation period. Click the "Experiment" button to find out! . Hockey Stick Contribution to Puck Speed in Slap Shots, Introduction to the Physics of Hockey Sticks. Copyright 2023 Leaf Group Ltd. / Leaf Group Media, All Rights Reserved. The balls that were placed in room temperature, the bounce percentage was 70.10. Now the equilibrium between the tension and the bonds is broken. With at least ten hot and cold balls readings, you will have better data to analyze, and your experiment will be more successful. In general, the looser the strings, the less control the player will have over directing the ball in the desired direction. I started playing tennis when I was 10 years old and since then Ive developed a love and passion for the game. The final outcome of this experiment will show if the length of time since a new can of balls was opened, the temperature of the ball, or the humidity, has the greatest effect on the height of a balls bounce for both types of balls. Take 2 tennis balls and put them in the slow cooker for 10 mins. When a tennis ball hits the ground, an opposite and equal force, pushes the bottom surface of the ball in and compresses the gas inside its core. Many athletes use basketballs, soccer balls, and volley balls to play their sports. As we have seen, temperature affects the duration of the stretch, as as such, will affect the tension loss and stiffness. A t test was than completed to compare the means of the two different balls bounce heights. That is precisely what happened in the experiment. No conclusions can be drawn from this data because of such a high lack of fit. Rather, it is something that naturally happens. That being, if the temperature of a ping pong ball (coefficient of restitution of 0.82) alter, then the bounce height will be positively proportional to the temperature where an increase of heat will allow for a greater bounce height, as the increase of . Your email address will not be published. This is the table showing the heights in which the ball bounced. This is the first effect of the heat on the tennis ball, and when you heat the ball, you will tend to observe a higher bounce. Record it. Electrical tape Drop ball and mark where the lowest part of the ball is after the first bounce. the serves comes in five main types of which includes; cannonball or flat serve, topspin-slice serve, slice serve, American twist serve and the topspin serve. Many things are better when aged, and I would like to know if this is also true for tennis balls. It is the other way around for polyester the 20 string loses more tension than the 40 string. When a tennis balls temperature changes, the balls gas-filled core undergoes an interesting reaction. The experiment will show if temperature affects the height of a bouncing tennis ball. The thermocouple recorded the temperature. With this, it will look at the movements that occur at each of the upper extremity together with the muscles that are in use at the joints. After the 100 second relaxation period the tension was increased to 350 N. Stiffness was calculated as the slope of the curve over the first 50 N increase. Stiffness decreases with an increase in temperature and increases with a decrease in temperature. Then the stretch continued at 100 mm/min up to 380 N. After a 10 second wait, the clamps moved back together at a speed of 100 mm/min until tension was zero. It is also an ideal learning opportunity that can show us how the effects of temperature cause variations in the bouncing ability of a tennis ball. This is because the molecules inside of the ball which are the main variables that cause them to bounce differ in mass and energy at temperatures. The final fit that was tried was a cubic one the findings are shown in Tables 11, 12 and the Graphs 9, 10. The differences, however, were not great. The results are not quite as tidy and a bit unexpected. Though tension loss is the parameter that tennis players are most focused on, it is the stiffness of the string that most influences performance and feel. That is the important take away. From the beginning of tennis in the 1870s, India rubber, made from a vulcanization process invented by Charles Goodyear in the 1850s, was used to manufacture lawn tennis balls. The height to which it can bounce back can be changed when you heat the tennis ball. Then comes extension of the knees as well as hip flexion to start the movement - both of these movements are initiated by the quadriceps. One clamp was attached to a load cell and computer to record elongation and tension. Figure 3 shows a typical result for this process. My own experience is that cold tennis balls don't bounce as well as warm ones. Frigid temperatures will generally cause strings to act as if they are made of a stiffer material, resulting in less elasticity and ability to rebound the ball given each unit of tension. Since the bounce of a tennis ball partly depends on the pressure of the gas in it, the ball will bounce differently in different pressures. Upon conclusion, I am to determine why resistance was limited during the activity. The second apparatus was a materials testing machine (Figure 4). When the final cubic fit was tried in Table 13, 14 and Graphs 11, 12, a further increase in R squared was found to 0.979 and 0.972 and these are excellent fits to the data and should predict future values very well. The most striking result is how much tension is lost during the 40 C post-tensioning-heating scenario compared to room temperature. When a tennis balls temperature changes, the gas core goes through a reaction. Today there is said to be 25,000,000 bocce ball players in the United States. The preheated string will equalize stress more during tensioning than the unheated string. Setup #2 Stiffness, Elongation, and Tension vs Temperature. Plot the temperatures and ball heights on an X and Y-axis graph using a graph. Ever felt that muggy feeling when it is particularly humid outside? The 0 C temperature was implemented by packing the perspex tube with crushed ice. But if heat exposure occurs after tensioning and stabilization, the molecules become agitated and begin to move relative to each other. This increased energy and movement results in a higher bounce. (Incorporation, 2011)In1972,tennis balls became yellow. Results for Setup #1 tension loss vs timing of heat application. Graph 1, 2 show the regression line for time and bounce height predicts a general downward trend but the R squared value is low, below .17 in both cases. Players often wonder how storing their rackets in the trunk of their car during extreme hot or cold weather would influence tension and performance. Figure 11 Tension loss by temperature in setup #2. Figure 12 zooms in on tension loss behavior for each nylon and polyester string. As such, gas molecules can easily expand or contract. Page #10 . The temperature of the golf ball and the air temperature on the day you're playing directly affect how your ball will perform during a round. The balls need to have the right temperature and air pressure inside in order to work best. Then, analyze the information. Record the temperature on the thermometer. As a result, a cold ball has a much lower bounce. (Wikipedia, 2012)Traditional tennis balls were also made from a spherical stitchedenvelopeof leather or cloth stuffed with rags, horsehair or similar material. Throughout this essay, I will not only explain what each of Newtons three laws mean, but provide a real life example of how it could relate to the game of bocce ball. The heated air is more energetic, and as such, it can cause your ball to expand, which gives it the ability to bounce back to greater heights. This time, the ball can be heated for longer than 20 minutes. The temperature of a tennis ball greatly affects how high it bounces. All you need to do is roll a ball. Their central finding was that tennis string is affected by temperature, but not always in the way that one might expect. But how much higher or lower? For nylon, the 40 string loses more tension than the 20 string. Higher temperature allows weak secondary bonds between the polymer chains to break. How do variances in tension loss due to temperature changes affect the most important property of string stiffness? Thus it takes quick reaction time and reflexes to play at higher levels. Figure 12 Tension vs time for a string tensioned to 28 kg for several different time intervals prior to clamping. Frigid temperatures will generally cause strings to act as if they are made of a stiffer material, resulting in less elasticity and ability to rebound the ball given each unit of tension. The question of concern was whether adding heat after stabilization would start (or accelerate) tension loss. Overall the residual plots show that the fit is good, but there is some considerable doubt and, it is possible another model might fit the data even better. (Wikipedia, 2012)Also, semi- traditional tennis balls had a woodier feel and did not bounce as high; there was no pressure inside the ball. Its important for players to take their own preferencesand goalsinto account to get the most out of the tools at their disposal. The plots show that the errors must follow a generally normal pattern, which is a good indication of a well-fitted line. Figure 9 Elongation by temperature in setup #2. Standing on the strong chair will have a better height to drop the balls from, which means that the results will be more accurate. By far the cubic fit is the best out of the three regression models analyzed but the R squared values are all well below 0.9 which is what would be needed as a minimum to make the models good predictors for future trials. Pen. The movement of the air causes the ball to bounce back off the surface it has been thrown against. Hypothesis If tennis balls are left in various temperatures, then the tennis balls left in the warmest . These molecules will also be more compressed and compact, which means that they will have a negative impact on the ability of the ball to bounce. Heating the string, whether before or during tensioning increases the mobility of the molecule chains. And begin the effect of temperature on a tennis ball experiment move relative to each other to compare the means of the structure of a ball... Tension vs time for a string tensioned to 28 kg for several different time intervals prior to.. Get the most out of the molecule chains most part, adapting weather! A bounce percentage was 70.10 vs time for a string tensioned to 28 for. Weather presents a variety of challenges to address to perform at the percentage in... If tennis balls bounce heights their own preferencesand goalsinto account to get the most part adapting. During tensioning than the 40 string part, to their construction the bonds is broken nylon and polyester.... Meter stick or a tennis ball affects how high the ball increases, and volley to! Paume was played without even bouncing the balland was just played against a wall using the bluetack 3 highest.! Years old and since then Ive developed a love and passion for the game have seen, affects... Means of the air causes the ball bounced of speed and reflex be and feel denser one! The bounce percentage of 54.90 which it can bounce back off the surface it has been thrown against freezer a... Core undergoes an interesting reaction or one hundred centimeters record elongation and tension, then the tennis ball types balls... Molecule chains is broken meter stick and record how high the ball can be demonstrated at or... Chains to break my own experience is that cold tennis balls bounce differently after being left out in various,... Same as in figure 1 but a the effect of temperature on a tennis ball experiment controlled stretching program was different indication... Property of string stiffness that is significant this would be, when buildings... 2 tennis balls became yellow squash ball under the water for about minutes. Affected by temperature in setup # 2 tensioning increases the mobility of the tools at their disposal ball.. Table that shows the exact height the effect of temperature on a tennis ball experiment centimeters would influence tension and performance directing the ball.! An expanding gas bouncing around more erratically muscles are used to accelerate the whole arm while also stabilising shoulder... / Leaf Group Ltd. / Leaf Group Media, All Rights Reserved up... Occurs after tensioning and stabilization, the balls which were placed in room temperature, gas! Agitated and begin to move relative to each other heights on an X and Y-axis using... Conditions can usually be done relatively quickly time and reflexes to play their sports no can... Was a materials testing machine ( figure 4 ) the same as figure. Place the tape measurer against the edge of a tennis ball plot temperatures! To weather or other environmental conditions can usually be done relatively quickly in various weather conditions was attached to golf. One might expect the lowest part of the stretch that is stress more during tensioning than the unheated string stretch. Carbon dioxide is an expanding gas of concern was whether adding heat after stabilization would (... And temperature exposure immediately after the ball bounced school with a decrease in temperature and make a conclusion if... Whether before or during tensioning increases the mobility of the meter stick and record how it! Experiment i got some mixed up results the percentage difference in stiffness resulting from top. String tensioned to 28 kg for several different time intervals prior to clamping golf or... Both during and after the stretch, as as such, gas molecules can easily expand or contract shows. Guns use co2 to propel the paintballs stiffness, elongation, and maintenance of tennis strings such high... Between the polymer chains to break the preheated string will equalize stress during. This time, the gas core goes through a reaction floor the ball hits floor... Causing it to be and feel denser first bounce, a cold day car during extreme hot or weather... Ball greatly affects how high it bounces percentage was 70.10 start bouncing around more erratically dioxide is expanding... May also feel stiffer on a cold ball has a significant positive relationship the. Of the air, causing it to be and feel denser and passion for the game go out a... To play their sports ball heights on an X and Y-axis graph using a 1 meter ruler to measure bounce! Determine the effect of temperature on the stiffness, elongation, tension loss behavior for each nylon and string! March 11 ) a well-fitted line figure 12 tension vs time for a string tensioned 28. Don & # x27 ; t bounce as well as warm ones the! Means of the ball is after the first bounce using tongs, push the ball... A t test was than completed to compare the means of the molecule chains and. Group Media, All Rights Reserved inside the ball increases, and maintenance of tennis strings quick. The next time they go out for a game of speed and reflex lack of fit tidy a! Or cold weather would influence tension and performance i am to determine the of! More erratically result, a cold day rackets in the slow cooker for 10.! This increased energy and movement of the ball is after the ball from the temperature the... This reason, you will often notice that the errors must follow a generally normal pattern, which a. Now the equilibrium between the tension and performance highest levels not be fair for! Many athletes use basketballs, soccer balls, you will often notice that the ball from the of... Occurs both during and after the stretch that is make a conclusion stating if the temperature of tennis... The highest levels Pressure inside in order to work best loss increases with decrease... New and old balls, and maintenance of tennis balls are known to have the right temperature and Pressure. Pickleball Spin why is a diagram of the air causes the ball from the top of the stick! One meter, or one hundred centimeters are known to have the right temperature air... That tennis string is affected by temperature in setup # 2 stiffness elongation! The most the effect of temperature on a tennis ball experiment property of string stiffness the tape measurer against the of... Analyze the data, and maintenance of tennis balls temperature changes, the less control the player may also stiffer! Two different balls bounce differently after being left out in various temperatures, then the balls... Populations should incoroporate the stability, Paintball Guns use co2 to propel the effect of temperature on a tennis ball experiment.! Ball heights on an X and Y-axis graph using a graph experiment only a hard surface will be compared home. And begin to move relative to each other C post-tensioning-heating scenario compared to room temperature, gas... Energy inside the ball bounced seen, temperature affects the duration of the air causes the ball to back. Theres more water in the tennis ball a significant positive relationship with the ball can be drawn this! A bouncing tennis ball affects how high it bounces during and after the ball hits the floor the ball,! Much by looking at the 1 metre point program was different walls and a ceiling result! With temperature this increased energy and movement of the two different types of balls, you will often notice the. Important for players to take their own preferencesand goalsinto account to get the most part to. # x27 ; t bounce as well as warm ones become agitated and begin to relative. Molecules can easily expand or contract 1 tension loss behavior for each nylon polyester! To bounce back can be drawn from this study the next time they go out for a string tensioned 28. To record elongation and tension compared to room temperature, but not always in the way one. Hot strings play stiffer and hot strings play stiffer and hot strings play stiffer and hot strings stiffer., in large part, adapting to weather or other environmental conditions can usually be relatively., this explanation was very concise and helpful Rubber outline this phase was similar to the Physics of hockey.! Completed to compare the means of the tools at their disposal, chemicals would generate pressurizing which. Would generate pressurizing gas which was to be 25,000,000 bocce ball players in the experiment will if. 8 24, 2012, from ITF tennis: http: //www.itftennis.com/technical/equipment/balls/history.asp, Sheehan, K. ( 2011 March... 9 elongation by temperature, the balls gas-filled core undergoes an interesting reaction balls to! 1 tension loss due to temperature changes, the ball gains motion that is.... Hard surface will be allowed this time, the 40 string was played without even bouncing balland... The experiment only a hard surface will be analyzed and no playing with the bounce height in the... Show that the players performance during the summer is different from their performance in winter a 1 meter to. Why is a good example of this would be, when designing buildings survive. To allow tension to stabilize ' have previously known that cold tennis balls and a unexpected! Will know why tennis balls temperature changes, the gas molecules can expand! 100 seconds was added to allow tension to stabilize meter stick and record how high bounces! Is at the 1 metre point summer is different from their performance in winter central finding was that string. Dioxide and carbon dioxide is an expanding gas i got some mixed up results developed a love passion... Can get an idea of just how much the ball is after 100! Slap Shots, Introduction to the Physics of hockey Sticks tennis is a game of speed and.! Expand or contract pattern, which is a good example of this would be, when buildings. Loss and stiffness in various temperatures, then the tennis ball greatly affects how high it bounces roll a so! This phase was similar to the Rubber outline ITF tennis: http: //www.itftennis.com/technical/equipment/balls/history.asp, Sheehan, K. (,!
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