Relationship between Drop Height and a Ping-Pong ball’s Half-Life while Bouncing

IB Physics IA

Brandon Dupreez

Word Count: 1606  

 

Table of Contents: Return to Research

Introduction

Method

Data

Graphs

Analysis

Conclusion

Links

Introduction

 

As a kid, I was always interested in mathematical puzzles. For me, the focus was always on the puzzles themselves and the methods used to solve them. It was this part that always fascinated me the most. One of these formulas was the power function. This function can be found throughout physics, with some examples being acceleration, periods of oscillators, escape velocity, and SUVAT derived equations. My project asks; At what rate will a ping-pong ball bouncing on a table lose energy and will it lose energy at a constant rate. Due to the fact that the ball’s energy is proportional to how high it bounces, I believe that increasing the drop height will decrease the rate at which the ball loses energy. As the drop height increases, the potential energy stored in the ball would increase, thus making the amount of time that passes between the first and fifth bounces larger as well. I assume that an increase in drop height would cause this effect.

 

Method

The values calculated from this experiment were times when the ball bounces on the surface for the first and fifth times as well as how high the ball bounced on its first and fifth bounces. The bounce times are measured in seconds while the height is measured in centimeters. The ball is dropped from heights ranging from 5 to 100 centimeters above the surface. Each drop height is given 3 trials. Then, taking the average of these three trials for both the first and fifth drop heights, I will subtract the latter from the former to find the average time between the two. This should allow me to find if the rate of decay is constant or not. A simple meter stick will help me measure the distance, while a microphone hooked up to a computer will gather the data for me. The acceleration of gravity and the weight of the ping pong ball will remain constant regardless of my intervention or not. Likewise, I can’t see any possible safety concerns that could arise from this project. I chose the amount of trials and variations I did because it made it easy to measure with a meter stick and because it was enough to account for possible deviations inherent to each individual trial. 

Independent Variable: Drop height (in meters)

Dependent Variable: The Average Time Between the Fifth and First Bounces

Constants: Acceleration of Gravity, Weight of Ping-Pong Ball

Objects in Diagram:

Ping Pong Ball

Meter Stick

Microphone

Table

Computer

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Data Collection Example:

Capture1.PNG

 

Data and Graphs:

 

 

First

Bounce

Time

 

 

 

Fifth

Bounce

Time

 

Height (m)

 

 

Time in Seconds

 

 

Height (m)

 

 

Time in Seconds

 

 

(+/-0.1ccm)

Trial One

Trial Two

Trial Three

Average

Uncertainty

(+/-0.1m)

Trial One

Trial Two

Trial Three

Average

Uncertainty

5

0.0756

0.1176

0.1360

0.1097

0.0302

5

0.0875

0.8834

0.9286

0.6332

0.4206

10

0.0736

0.2320

0.1964

0.1673

0.0792

10

1.1000

1.2550

1.2120

1.1890

0.0330

15

0.3152

0.2776

0.1680

0.2536

0.0736

15

1.5200

1.4730

1.3840

1.4590

0.0445

20

0.0256

0.2518

0.0272

0.1015

0.1131

20

1.4890

1.6150

1.4640

1.5227

0.0755

25

0.0848

0.0132

0.1518

0.0833

0.0693

25

1.6880

1.5740

1.7330

1.6650

0.0795

30

0.1876

0.4394

0.3254

0.3175

0.1259

30

1.7870

2.0330

1.9140

1.9113

0.0609

35

0.2700

0.4624

0.0290

0.2538

0.2167

35

1.9210

2.1010

1.8310

1.9510

0.1350

40

0.0978

0.2946

0.4096

0.2673

0.1559

40

1.9710

2.0170

2.1390

2.0423

0.0610

45

0.0840

0.4832

0.5232

0.3635

0.2196

45

2.0440

2.2710

2.3170

2.2107

0.0532

50

0.0792

0.2922

0.0938

0.1551

0.1065

50

2.1000

2.3190

2.1240

2.1810

0.0975

55

0.1862

0.1306

0.0914

0.1361

0.0474

55

2.2970

2.2110

2.1960

2.2347

0.0194

60

0.1048

0.1282

0.1524

0.1285

0.0238

60

2.2870

2.2910

2.3270

2.3017

0.0180

65

0.0952

0.1332

0.1302

0.1195

0.0190

65

2.3210

2.3710

2.3660

2.3527

0.0092

70

0.1112

0.3682

0.1566

0.2120

0.1285

70

2.4270

2.7070

2.4410

2.5250

0.1330

75

0.1068

0.1408

0.1392

0.1289

0.0170

75

2.4490

2.4680

2.4920

2.4697

0.0120

80

0.1822

0.1592

0.1604

0.1673

0.0115

80

2.5820

2.5640

2.5530

2.5663

0.0067

85

0.2144

0.1950

0.2946

0.2347

0.0498

85

2.6690

2.6410

2.7340

2.6813

0.0465

90

0.2732

0.2016

0.2982

0.2577

0.0465

90

2.7720

2.6990

2.8030

2.7580

0.0520

95

0.2708

0.2314

0.1734

0.2252

0.0487

95

2.7850

2.7610

2.6870

2.7443

0.0370

100

0.4094

0.2196

0.2622

0.2971

0.0949

100

2.9790

2.8050

2.8350

2.8730

0.0340

 

 

 

 

       Difference

 Between Fifth And

                                                                          First Bounces

 

 

 

Time in Seconds

 

 

Trial One

Trial Two

Trial Three

Average

Uncertainty

0.0119

0.7658

0.7926

0.5234

0.39034

1.0264

1.0230

1.0156

1.0217

0.0054

1.2048

1.1954

1.2160

1.2054

0.0056

1.4634

1.3632

1.4368

1.4211

0.0368

1.6032

1.5608

1.5812

1.5817

0.0212

1.5994

1.5936

1.5886

1.5939

0.0054

1.6510

1.6386

1.8020

1.6972

0.0817

1.8732

1.7224

1.7294

1.7750

0.0754

1.9600

1.7878

1.7938

1.8472

0.0861

2.0208

2.0268

2.0302

2.0259

0.0047

2.1108

2.0804

2.1046

2.0986

0.0152

2.1822

2.1628

2.1746

2.1732

0.0097

2.2258

2.2378

2.2358

2.2331

0.006

2.3158

2.3388

2.2844

2.3130

0.0272

2.3422

2.3272

2.3528

2.3407

0.0128

2.3998

2.4048

2.3926

2.3991

0.0061

2.4546

2.4460

2.4394

2.4467

0.0076

2.4988

2.4974

2.5048

2.5003

0.0037

2.5142

2.5296

2.5136

2.5191

0.008

2.5696

2.5854

2.5728

2.5759

0.0079

 

 

 

Capture4.PNG 

Data File:.Excel .:. Text

 

Capture2.PNG

Data File:.Excel

 

 

 

Capture3.PNG

 Data File:.Excel

 

Analysis:

 

            For the data, I chose to take three trials for each drop height before finding their average and uncertainty. Following this, I subtracted the times of the first bounce from the times of the fifth bounce and found their average and uncertainty, providing me with the data I’ll use for my graph.

As an example: I got times of 0.0756, 0.1176, and 0.1360 for my three trials at five centimeters of height (first bounce) and times of 0.0875, 0.8834, and 0.9286 for my three trials at five centimeters of height (fifth bounce). The average of the former is 0.1097 and the latter, 0.6332. Subtracting 0.1097 from 0.6332 will give me an average difference of 0.5235.

In order to prove my hypothesis that the difference will increase at a non linear rate, I will used the equation , an equation derived from the SUVAT based equation. S=

a = Acceleration of Gravity ()

s = Drop Height (5-100 cm)

t  = time (Seconds)

Solving for t then gives us

h =

2h =

Plugging the values given for h and g into this formula gives us

Chart

The graph created from this is a square root graph, just like the raw data graph derived from my experiment, proving that my guess was correct.

 

Conclusion:

 

            The data gathered confirms that the graph does increase overtime at a non-linear rate. Proof of this is that the graph is also a square root graph, just like the graph predicted using the equation. The deviations in my data were likely caused by the ball frequently drifting to the side while falling, causing it to bounce out of the detection range of the microphone or for the ball to collide with the microphone, ruler or other objects on the table. Furthermore the measurement of how high the ball was dropped and measured by hand, which resulted in the wide error margins seen in my graphs. To alleviate these basic flaws, I would use a modified tube to prevent the ball from moving in any direction but vertically and use a more precise way to decrease the range of error in the drop height. These simple changes should be enough to eliminate the largest sources of error. If I was to conduct this experiment again, I would redo the experiment with other bouncing objects of different mass and density to see if they also follow similar mathematical patterns. 

Related Links:

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Since my project required little prior research to complete, these links go to sites containing mundane details about Ping pong balls. The Bottom two link to other, more advanced studies on similar topics to my project.

https://www.theguardian.com/notesandqueries/query/0,5753,-4149,00.html#:~:text=What%20were%20the%20balls%20made%20of%3F,-Rafael%20Holt%2C%20Lima&text=Ping%2Dpong%2C%20or%20table%20tennis,the%20remnants%20of%20the%20meal.

Gives a brief history of how ping-pong balls and table tennis were invented.

 

https://www.education.com/science-fair/article/ball-bounce-higher-dropped-greater-height/#:~:text=When%20the%20ball%20hits%20the,energy%2C%20the%20higher%20the%20bounce!

A basic experiment that compares the elasticity of various types of balls (including ping-pong balls)

https://easyscienceforkids.com/ping-pong-balls-video-for-kids/

A small collection of fun facts about ping-pong balls and table tennis.

https://www2.montgomeryschoolsmd.org/siteassets/schools/high-schools/r-w/rmhs/departments/science/ping-pong-ball-sample-ia.pdf

Another IA on the same topic I did

https://www.markedbyteachers.com/gcse/science/the-bouncing-ball-experiment.html

Another experiment covering bouncing ping-pong balls.