Bounce Height of a Tennis Ball

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Fahad Saeed

Abstract

The experiment seeks to identify whether the temperature and thenature of the surface used will influence a bouncing tennis ball.More specifically, it will depend on two experiments with the firstone evaluating if temperature plays a major part while the secondexperiment will highlight the effect of the surface on the bouncingtennis ball. It will also analyze the data from the experiment toprove that the hypothesis heated tennis balls and those tennis ballsbouncing on the hard court both will reach higher heights.

At times, various activities might need the bouncing of tennis balls, but the participants will proceed without acknowledging factors that influence the bouncing of tennis balls. Some of these factors include the temperature as well as the surface that the tennis ball will be bouncing on. In this experiment, two procedures will prove whether the temperature and nature of a surface are influential in the bouncing of the balls. Evidently, such knowledge is essential in those that might often use the tennis balls for various activities in the community.

  1. Materials and Methods

    1. Materials

The experiment will need the presence of four tennis balls, a clamp, a measuring ruler, a table, heater, freezer, hard court and the grass surface too.

    1. Experimental Procedure

More generally, the experiment had two experiments that all aimed at determining if the temperature and the nature of a surface will influence the height a bouncing ball will reach when released on the two surfaces.

    1. Experiment One

The first experiment had a first tennis ball being heated for twenty minutes while second was frozen for a period of an hour as the third one remained at the room temperature. After that, each of the tennis balls was dropped from a height of 200cm. The steps were repeated two more times in order to achieve the accuracy needed for the experiment. Later, the results for each ball were recorded including the multiple times the heated, frozen and normal tennis balls were dropped.

    1. Experiment Two

The second experiment will evaluate the impact of the nature of surface on influencing the height a tennis ball will bounce when released from a point above. The experiment will need the only one tennis ball that will be released on the grass surface and the hard court. The presence of the measuring ruler will help in identifying the height the tennis ball will reach

when released on a grass surface. Other than that, the procedure is repeated with the ball being dropped two more times before determining the accurate results needed. After the first steps, the same steps are repeated but using the hard court in this case.

    1. Analytical Methods

Evidently, the use of heating, freezing and normal temperature of the tennis balls help in reaching diverse outcomes. The use of the different surfaces also determines the impact of the surfaces in the bouncing balls as well.

  1. Results and Discussion

Table 1: The findings of Experiment One

Trials

Heated

ball (cm)

Frozen ball

(cm)

Normal ball

(cm)

1

107.22

53.31

94.24

2

106.20

53.54

93.30

3

106.34

53.29

92.34

4

106.54

53.29

94.21

5

106.50

53.35

92.35

6

106.68

53.42

93.30

7

107.16

53.41

93.33

8

106.34

53.51

93.26

9

106.33

53.30

93.28

Average (cm)

106.59

53.38

93.29

The findings of the first experiment show that the temperature plays a major role in determining the height that a bouncing ball will reach. The heated tennis ball ended up reaching an average higher height of 106.59cm as the frozen tennis ball reached the average lowest of 53.38cm. The one that was at room temperature bounced to the average height of 93.29cm instead. From the data, the sole reason for the difference of the heights the bouncing balls reached arises from the pressure gas within the tennis balls. The equation p=rRT with “p” being pressure, “r” the density, the “R” is constant related to the gas while the “T” represents the temperature (Stewart, 2015). More specifically, as the density remains constant and the temperature keeps rising, it will amount to higher pressure as well. A decrease in the temperature will result in the

reduction of the pressure and make the ball smaller and also bouncing a lot lesser than expected (Myers, 2006).

Table 1Effects of Nature Surface on the Bouncing Height

Trials

Grass Surface (cm)

Hard Court Surface (cm)

1

42

54

2

43

55

3

42

56

4

42

54

5

43

56

6

42

55

7

43

54

8

43

56

9

42

55

The data reveals the way that tennis balls behaved on the different surfaces. The ball bounced to an average height of 42.33cm while on the grass surface as it reached to 55cm while bouncing on the hard court surface. The cause of the difference in the two surfaces arose from the way each of the surfaces had different abilities in absorbing kinetic energy (Harriman, 2012).

One-way ANOVA: Heated ball (cm), Frozen ball (cm), Normal ball (cm)

Source DF SS MSFP

Factor2 13803.01 6901.50 35268.73 0.000

Error244.70 0.20

Total26 13807.70

S = 0.4424R-Sq = 99.97%R-Sq(adj) = 99.96%

Individual 95% CIs For Mean Based on

Pooled StDev

Level N Mean StDev -+-+-+-+

Heated ball (cm) 9 106.590 0.368 *

Frozen ball (cm) 953.380 0.096 (*

Normal ball (cm) 993.290 0.665 *

-+-+-+-+

60 75 90 105

Pooled StDev = 0.442

ANOVA analysis from MINITAB, the effect of heat is clearly shown. With a mean of 106.59, heated ball bounces highest. The difference between the heated ball and the frozen ball is big with a margin of 44.21 cm.

Figure 1: Residual Plots for Heated ball (cm), Frozen ball (cm), Normal ball (cm)

The normal distribution graph shows the points close to the normality line. This is a clear indication that it was a random experiment. There is a need to conduct a random experiment to eliminate the chances of having predetermined results.

Figure 2: Individual Value Plot of Heated ball (cm), Frozen ball (cm), Normal ball (cm)

In the individual value plot above, the effect of temperature on the bounce of a tennis ball is made clear. The heated ball records the highest bounce with the frozen ball recording the least. Temperature, therefore, clearly affects the extent to which a tennis ball bounces. When the temperatures increase, the gas molecules inside the tennis ball expand. As they expand, it is believed that their energy increases resulting in increase of their ability to interact and bounce (Harriman, 2012). The increased energy and movement results into a higher bounce (Stewart, 2015). On the other hand, when the temperatures decrease, the gas molecules contract and move around slowly and sluggishly.

One-way ANOVA: Hard Court Surface (cm) versus Grass Surface (cm)

Source DF SS MS FP

Grass Surface (cm)1 0.450 0.450 0.57 0.476

Error 7 5.550 0.793

Total 8 6.000

S = 0.8904R-Sq = 7.50%R-Sq(adj) = 0.00%

Individual 95% CIs For Mean Based on Pooled StDev

Level N Mean StDev -+-+-+-+

42 5 54.800 0.837 (-*)

43 4 55.250 0.957(–*–)

-+-+-+-+

53.90 54.60 55.30 56.00

Pooled StDev = 0.890

The ANOVA analysis from MINITAB compares the means and calculates the standard deviation. From the ANOVA, it is clear that there is a significant difference in the bounce of the tennis ball in the two surfaces.

Figure 3: Boxplot of Heated ball (cm), Frozen ball (cm), Normal ball (cm)

Due to this, the ball will hence bounce slowly as shown in the boxplot above.

Description of Experiment Number#2

The second experiment was to the effect of the nature of a surface on the height of a bouncing tennis ball. For this experiment, only one ball is used, but the ball is dropped on two different surfaces. To carry out the test successfully, a measuring ruler is capped and placed on a grass surface and then a ball is dropped from 100cm height to the grass surface and then the bounce height is recorded following the measurement of the height using a ruler. To achieve more accurate results, the ball is dropped two more times for the purpose of accuracy. The above procedure is also repeated but, this time, round using a hard court surface and then the results are recorded.

The ANOVA analysis from MINITAB compares the means and calculates the standard deviation. From the ANOVA, it is clear that there is a significant difference in the bounce of the tennis ball in the two surfaces.

Figure 4: Residual Plots for Hard Court Surface (cm)

The normal probability plot above show the residue points being closer to the normality line. This is a proof that the calculated significance value does not differ greatly from the expected significance value. With this in mind, boxplot of hard surface and individual value plots were developed using MINITAB.

Figure 5: Boxplot of Hard Court Surface (cm

Figure 6: Individual Value Plot of Hard Court Surface (cm) vs Grass Surface (cm)

The above figures show that the tennis ball bounces more on the hard surface than on the grass surface. This is so because the grass surface absorbs much of the kinetic energy of the ball meaning that more energy will be absorbed when we compare this surface with the hard court surface. Moreover, it has been scientifically proven that once a ball is dropped, it dents. The grass surface is in a position to receive much of the ball denting hence making the bouncing height to be less. Analysis using Minitab showed that there is a significant difference in the two surfaces. The normal probability show the plots being close to the normality line. This is an indication of the significant difference of the bounce in the two surfaces.

  1. Conclusion and Future Works

In conclusion, the data proves that temperature as well as a type of a surface all help in influencing the height that a bouncing ball will reach. In this case, activities that involve the use of tennis ball should keep in mind the weather conditions since it will influence the temperature that will also affect the bouncing of the tennis ball. The surface also has an impact on the kinetic energy that will make the tennis ball behave in a way that will be much normal as well. The future of the research will be based on other factors that might influence the bouncing of the ball. In the process, it will be much easier to determine other factors such as the age of the tennis in influencing the height that the bouncing ball will reach.

References

Harriman, D. (2012). The Temperature of Tennis Ball. Retrieved March 9, 2016, from Livestrong: Hobby, N. (2015, December 27). What is the effect of Temperature on Tennis Ball. Retrieved March 9, 2016, from Tennis ball:

Myers, R. L. (2006). The basics of physics. Greenwood Publishing Group.

Stewart, D. (2015). A Science Project Using Cold Vs. Hot Tennis Balls. Retrieved March 9, 2016, from Aeronautics Internet Textbook: