Introduction: (Initial Observation)
When dropped on a solid surface, not even a super ball bounces back as high as its initial height, but some balls do bounce a lot better than others. Even a specific ball may bounce different heights at different times or different locations. Such variations in the bounce of a dropped ball rise questions that demand some research and investigation.
In this project we will try to find out what factors affect the bounce of a dropped ball.
Information Gathering:
Find out about the physics of a dropped ball. Read books, magazines or ask professionals who might know in order to find out the factors that affect the movements of a dropped ball. Keep track of where you got your information from. Following are some sample information that you may find:
Background Information
Everyone has played with balls that bounce, but few people truly understand the physics behind a bouncing ball. When you hold a ball above a surface, the ball has potential energy. Potential energy is the energy of position, and it depends on the mass of the ball and its height above the surface. The formula for gravitational potential energy is PE = mgh where m is the mass of the ball measured in kg, g is the gravitational acceleration constant of 9.8 m/se c2 , and h is the height of the ball in m. As the ball falls through the air, the potential energy changes to kinetic energy. Kinetic energy is energy of motion. The formula for kinetic energy is KE=1/2 mv 2 , where m is the mass in kg and v is the velocity in m/sec 2 . Both potential and kinetic energy have units of Joules (J).
As the ball falls through the air, the Law of Conservation of Energy is in effect and states that energy is neither gained nor lost, only transferred from one form to another. The total energy of the system remains the same; the potential energy changes to kinetic energy, but no energy is lost. When the ball collides with the floor, the ball becomes deformed. If the ball is elastic in nature, the ball will quickly return to its original form and spring up from the floor. This is Newton’s Third Law of Motion- for every action there is an equal and opposite reaction. The ball pushes on the floor and the floor pushes back on the ball, causing it to rebound.
On a molecular level, the rubber is made from long chains of polymers. These polymers are tangled together and stretch upon impact. However, they only stretch for an instant before atomic interaction forces them back into their original, tangled shape and the ball shoots upward.
…
Information Part 1:
Why if you drop a ball from say 2 meters does it bounce higher than a ball dropped from 1 meter?
If you follow the motion of either ball, you’ll realize that there’s a moment halfway through its bounce when the ball is perfectly motionless in contact with the floor. At that instant, how does the ball “know” how high it should bounce? Something about its situation then must determine its rebound, but what?
The answer lies in how far the ball has dented inward due to its collision with the floor. As it falls, the ball converts energy stored in the force of gravity—gravitational potential energy—into energy of motion—kinetic energy. By the time it reaches the floor, the ball is traveling quickly and it hits the floor hard. It pushes downward on the floor and the floor pushes upward on it. Because of these forces, both the ball and floor deform inward. This denting extracts energy from the ball’s motion and stores much of it in the elastic surfaces of the floor and ball. Because the ball is softer than the floor, it does most of the denting and stores most of the energy. By the time the ball comes briefly to a stop, most of its missing energy has been stored in its dented surface.
The ball then rebounds: it undents and tosses itself up into the air to a good fraction of its original height. That height fraction is equal to the fraction of energy that the ball successfully stored and returned during its bounce. Thus a typical ball bounces to 60% of its original height because it stores and returns 60% of the energy it had before the bounce. Conveniently enough, this fraction of returned energy is nearly independent of how much energy the ball had to begin with. It depends only on the elasticity of the ball itself—a super ball returns a large fraction while a beanbag returns a tiny fraction.
When you drop a ball from a greater height, it has more kinetic energy just before it hits the floor and stores more energy during the bounce—it dents farther as it comes to a stop. When the ball rebounds, its stored energy reappears and it leaps higher into the air than it would have had you dropped it a shorter distance.
Schematic diagram of two balls dropped from different heights. The balls are shown at rest, about to bounce back up.
Information Part 2:
How well a ball bounces deals with its coefficient of restitution. This coefficient of restitution, e, is actually the ratio of the velocity of recession (upwards after the bounce) to the velocity of approach (downward before the bounce). For a perfectly elastic bounce (the ultimate super ball), e =1; and for an inelastic bounce (like clay dropping on the floor), e =0. So an imperfect ball loses some energy on each bounce.
Information Part 3:
Kinetic energy
Kinetic energy means energy associated with motion. It is the most basic kind of energy.
It is defined as KE = ½mv2
where m is the mass of the moving object, and v is the velocity of the moving object.
We can go back to our table of velocities, square each one, then multiply by 1/ 2 * 0.044 kg to find the kinetic energy at each moment.
Gravitational potential energy
Gravitational potential energy means energy that an object has based on where it is located in a gravitational field.
It is defined as GPE = mgh
where g is the gravitational acceleration (9.8 m/ sec 2 at the Earth’s surface), and where h is the height of the object, measured with respect to any convenient “zero- level”.
Total mechanical energy
For a dropped ball, the total mechanical energy is defined as the sum of its kinetic energy and its gravitational potential energy. So once you know how to calculate KE and GPE, it is simple to calculate their sum, E.
E= ½mv2+mgh
Mechanical energy is conserved
KE of a dropped ball changes as it falls. GPE also changes as the ball falls.
The sum of the two, mechanical energy, stays the same (” is conserved”.)
As the ball is falling toward the ground it’s Kinetic Energy is increasing because it’s speed is increasing. Also it’s Gravitational Potential energy is decreasing because it’s height is decreasing.
Information Part 4:
Balls: Terminal Speed and Coefficient of Restitution.
Last updated on March 17, 1999
| ball | weight (lb) | diameter(in) | terminal speed(mi/hr) | CoR at 15 mi/hr | CoR at 55 mi/hr |
| 16 lb shot | 16 | 4.72 | 325 | ||
| football | 0.91 | 11.1 x 6.8 | 100 | ||
| baseball | .32 | 2.9 | 95 | 0.57 | 0.55 |
| golf ball | .1 | 1.68 | 90 | 0.60 | 0.58 |
| softball | .4 | 3.82 | 80 | 0.55 | 0.40 |
| handball | .14 | 1.88 | 75 | 0.80 | 0.50 |
| tennis ball | .13 | 2.56 | 70 | 0.70 | 0.50 |
| squash ball | .07 | 1.77 | 55 | 0.52 | 0.40 |
| soccer ball | .94 | 8.75 | 55 | 0.75 | 0.65 |
| basketball | 1.31 | 9.47 | 45 | 0.75 | 0.64 |
| volleyball | .59 | 8.43 | 35 | ||
| ping-pong ball | .006 | 1.47 | 20 | 0.80 | 0.70 |
| superball | 0.90 | 0.85 |
CoR = coefficient of restitution = (speed after collision)/(speed before collision)
The CoRs apply to balls dropped or thrown at a rigid wooden surface. Adapted from Plangenhoef, Patterns of Human Motion.
The CoR can be measured directly by velocity measurements but often it is handier to measure the height of rise of the ball after it bounces relative to the height that it fell. Since v2 = 2gh, the CoR = v’/v = sqrt(h’/h) where h’ is the height of the bounce and h is the height from which the ball is dropped. For example a regulation tennis ball is dropped from about 1 meter. The relative height of the bounce should be h’/h = CoR2 = 0.72 = 0.49. The selection of balls for official games in most sports (esp. tennis and baseball) includes the CoR test.
The terminal speed is the maximum speed reached when an object is dropped from a great height. A thrown or batted ball may travel faster than the terminal speed, but it will experience a large drag force from the air which is greater than it’s weight. At the terminal speed, the drag force = the gravitational force. With no net force, the acceleration = 0 and the ball falls at a constant velocity.
http://wings.avkids.com/Curriculums/Tennis/index.html
Question/ Purpose:
The purpose of this project is to find out what factors affect the bounce of a dropped ball.
Identify Variables:
When you think you know what variables may be involved, think about ways to change one at a time. If you change more than one at a time, you will not know what variable is causing your observation. Sometimes variables are linked and work together to cause something. At first, try to choose variables that you think act independently of each other.
Variables that may affect the bounce of a dropped ball are:
- The height from which we drop the ball
- The air pressure inside the ball
- Hardness of the bounce surface
You may study the effect of any of these variables on the bounce of a dropped ball.
If you choose to study on the effect of air pressure inside the ball, your variables will be defined like this:
Independent variable (also known as manipulated variable) is the ball’s air pressure.
Dependent variable is the height that the ball bounces.
Constants are the release height, the bouncing surface, the type and the size of the ball.
Controlled variables are air temperature, air flow, air pressure where you perform your tests.
Hypothesis:
Based on your gathered information, make an educated guess about what types of things affect the system you are working with. Identifying variables is necessary before you can make a hypothesis.
This is a sample hypothesis:
The bounce of a dropped ball has a direct relation with the air pressure inside the ball. So if we double the air pressure, we will get double bounce height.
If you choose to study on any other variable, following are samples of hypothesis.
- The bounce of a dropped ball has a direct relation with the release height. So if we double the release height, we will get double bounce height.
- An elastic surface such as rubber and a very hard surface such as concrete will result the highest bounce level. As elasticity and hardness decreases, part of the ball energy will be used to permanently dent or misplace or vibrate the surface, so ball will have less energy to bounce.
It is always good to have an explanation for choosing any hypothesis. For example this is a sample explanation.
My hypothesis is based on my observation of balls that are not well inflated. These balls do not bounce as well as balls with high air pressure.
Experiment Design:
Design an experiment to test each hypothesis. Make a step-by-step list of what you will do to answer each question. This list is called an experimental procedure. For an experiment to give answers you can trust, it must have a “control.” A control is an additional experimental trial or run. It is a separate experiment, done exactly like the others. The only difference is that no experimental variables are changed. A control is a neutral “reference point” for comparison that allows you to see what changing a variable does by comparing it to not changing anything. Dependable controls are sometimes very hard to develop. They can be the hardest part of a project. Without a control you cannot be sure that changing the variable causes your observations. A series of experiments that includes a control is called a “controlled experiment.”
Each of the following experiments tests a different hypothesis. Experiment 2 is for testing the effect of air pressure.
Experiment 1:
In this experiment you will measure the bounce of a dropped ball for different release heights. Perform this test in a Gym or anywhere else where you have a hard surface and an accessible wall. In this experiment the only variable that we modify is the release height and we keep all other variables unchanged.
Preparation: Draw a ruler with high visibility on a roll of paper about 8 inches wide and 6 feet tall. Tape the ruler to the wall. You will need an assistant, so one person will drop the ball and the other person stands about 20 feet away and records how high it bounces. You can drop the ball from your hand or you can make a stopper for the ball to hold it only from the sides with a little pressure.
Procedure:
Hold the ball at 6 feet height and release it. Your assistant will record the bounce. For each height repeat the test 3 to 5 times and record the most reliable result. If you get more than one value, calculate and record the average.
Repeat your tests 9 more times and each time lower the release height for 6 inches. Record the results in a table like this:
| Release height (feet) | Release height (Inches) | Bounce height (inches) | Bounce/Release |
| 6 | 72″ | ||
| 5.5 | 66″ | ||
| 5 | 60″ | ||
| 4.5 | 54″ | ||
| 4 | 48″ | ||
| 3.5 | 42″ | ||
| 3 | 36″ | ||
| 2.5 | 30″ | ||
| 2 | 24″ | ||
| 1.5 | 18″ |
Divide the bounce height of each row by the release height of the same row and write the result in the last column. “Bounce/Release” is the relation of bounce height to the release height.
Experiment 3:
In this experiment you will test the bounce of a dropped ball for different surface hardness. Perform this test in a Gym or anywhere else where you have a hard surface and an accessible wall. In this experiment the only variable that we modify is the type or flexibility of bounce surface and we keep all other variables unchanged.
Preparation: Draw a ruler with high visibility on a roll of paper about 8 inches wide and 6 feet tall. Tape the ruler to the wall. You will need an assistant, so one person will drop the ball and the other person stands about 20 feet away and records how high it bounces. You can drop the ball from your hand or you can make a stopper for the ball to hold it only from the sides with a little pressure.
Procedure:
Hold the ball at 6 feet height and release it on a hard concrete surface. Your assistant will record the bounce. Then change the surface material by covering it with different material and repeat the test. Material that you may test are:
Carpet, Rubber matte, ply wood, sponge, Styrofoam, another ball, …
Repeat your tests for each different type of bouncing surface and record the results in a table like this:
| Bounce Surface | Release height (Inches) | Bounce height (inches) | Bounce/Release |
| Concrete | 72″ | ||
| Carpet | 72″ | ||
| Rubber matte | 72″ | ||
| Plywood | 72″ | ||
| Sponge | 72″ | ||
| Styrofoam | 72″ | ||
| 72″ |
Materials and Equipment:
- Several balls, medium-sized super balls, hollow rubber balls, solid rubber balls, tennis balls, golf balls, baseballs, and whatever other types of balls are available. For testing air pressure you will need one ball that is inflatable such as a basketball ball.
- Several meter sticks for measuring the height of the bouncing ball or drawing a larger meter stick.
- Several smooth hard flat horizontal surfaces suitable for bouncing balls—floors, lab tables, sidewalks, and the like.
- Additional list of material can be extracted from the experiment section.
Results of Experiment (Observation):
Experiments are often done in series. A series of experiments can be done by changing one variable a different amount each time. A series of experiments is made up of separate experimental “runs.” During each run you make a measurement of how much the variable affected the system under study. For each run, a different amount of change in the variable is used. This produces a different amount of response in the system. You measure this response, or record data, in a table for this purpose. This is considered “raw data” since it has not been processed or interpreted yet. When raw data gets processed mathematically, for example, it becomes results.
Calculations:
You may need to calculate the average of bounce height. It is also good to calculate the coefficient of restitution of your ball using the formula CoR = v’/v = sqrt(h’/h).
Summary of Results:
Summarize what happened. This can be in the form of a table of processed numerical data, or graphs. It could also be a written statement of what occurred during experiments.
It is from calculations using recorded data that tables and graphs are made. Studying tables and graphs, we can see trends that tell us how different variables cause our observations. Based on these trends, we can draw conclusions about the system under study. These conclusions help us confirm or deny our original hypothesis. Often, mathematical equations can be made from graphs. These equations allow us to predict how a change will affect the system without the need to do additional experiments. Advanced levels of experimental science rely heavily on graphical and mathematical analysis of data. At this level, science becomes even more interesting and powerful.8
Conclusion:
Using the trends in your experimental data and your experimental observations, try to answer your original questions. Is your hypothesis correct? Now is the time to pull together what happened, and assess the experiments you did.
Related Questions & Answers:
What you have learned may allow you to answer other questions. Many questions are related. Several new questions may have occurred to you while doing experiments. You may now be able to understand or verify things that you discovered when gathering information for the project. Questions lead to more questions, which lead to additional hypothesis that need to be tested.
1. Does a ball bounce higher or lower in moon (Less Gravity), while all other conditions are constant?
Possible Errors:
If you did not observe anything different than what happened with your control, the variable you changed may not affect the system you are investigating. If you did not observe a consistent, reproducible trend in your series of experimental runs there may be experimental errors affecting your results. The first thing to check is how you are making your measurements. Is the measurement method questionable or unreliable? Maybe you are reading a scale incorrectly, or maybe the measuring instrument is working erratically.
If you determine that experimental errors are influencing your results, carefully rethink the design of your experiments. Review each step of the procedure to find sources of potential errors. If possible, have a scientist review the procedure with you. Sometimes the designer of an experiment can miss the obvious.
References:
Try to find more information from physics or mechanics books. Find sections related to potential energy, elasticity and springs. Your bibliography must contain sources that are available to you (at your school or local library). Specially look for parts that discuss the gas pressure and physical properties of gases.
http://wings.avkids.com/Curriculums/Tennis/index.html
The format you use to write your bibliography may look like this:
- An Introduction To Mechanics
by Daniel Kleppner and Robert Kolenkow
Hardcover – Mar 1, 1973 - Course of Theoretical Physics : Mechanics (Course of Theoretical Physics)
by E M Lifshitz and L D Landau - Engineering Mechanics – Dynamics (11th Edition)
by Russell C. Hibbeler
Jul 7, 2006
Related Attachments:
Are you ready for more advanced ball drop projects?
The following is a college level project, but some grade 9 to 12 students can also complete this with no problem.
Experiment:
In this experiment you will drop a ball on a hard surface such as table and record the sounds it makes when it bounces using a computer and any sound recorder program. You will be able to precisely measure the time intervals between bounces. You will then take your bounces and their respective time intervals to a spread sheet. Your challenge will be to find a way to determine your ball’s ‘ e’, and the initial height of the ball when you first dropped it.
Data Collection Instructions:
Use a racquetball, a golf ball or any kind that bounces well and makes a nice crisp sound when it bounces. It’s a good idea to bounce it on a level surface, and don’t release from too great a height, or while bouncing, the ball will wander away from the sound recorder range. About a foot above the table top is plenty.
If you are using windows sound recorder program, you can view the recorded waves with an accuracy of 0.01 second. To do that use the scroll button to start, then use arrow keys to move your wave 0.1 second left or right. or hold Ctrl and then use arrow keys to move the wave 0.01 second left or right. Locate the peaks and record the time for each peak.
The spikes are bounces.
Collecting Time Data:
You will next need to record your bounces and their respective times.
You are now ready to enter your data on a spread sheet and get to work. Specifically, you are tasked to determine:
A.) ” e” for your ball.
B.) the initial height of your ball when you released it.
Lab Report:
1. Discuss specifically how you developed your ” e” and initial height values.
2. Do you think ” e” is constant for your ball? Why or why not?
3. What is happening to the ball’s energy with each bounce?
Notes:
It will be important to keep track of what times go between what bounces.
Here’s another sample run:
Here’s an example of an Excel spread sheet that analyzes what’s going on:
Here’s a graph of energy vs. bounce from the spread sheet:
This is a sample on how to write the results, conclusion and make charts.
How High a tennis ball will bounce
Experimental Design:
Purpose: To determine how high a tennis ball will bounce when dropped from a specific height.
Hypothesis: If a tennis ball is dropped from a specific height then the ball will bounce to the same height.
Materials: meter stick, tennis ball
Independent Variable: The height from which the ball is dropped.
Dependent Variable: The height of the bounce.
Constants: the same person takes all of the measurements, the same materials are used in every trial
Procedure: One group member drops a tennis ball from a specific height, while the other group member notes how high the ball bounces. This is repeated three times at 5 different heights. The three trials at each height are then averaged, and the average bounce height is graphed versus the drop height.
Data Collection:
Data Table 1: Group Data
|
Drop Height (cm) |
Bounce height (cm) Trial 1 |
Bounce height (cm) Trial 2 |
Bounce height (cm) Trial 3 |
|
20 |
9.0 |
11 |
8.0 |
|
40 |
17 |
22 |
19 |
|
60 |
28 |
30. |
31 |
|
80 |
37 |
40. |
42 |
|
100 |
52 |
51 |
49 |
Data Analysis:
Data Table 2: Average Bounce Height at Each Height:
|
Drop Height (cm) |
Bounce height (cm) Trial 1 |
Bounce height (cm) Trial 2 |
Bounce height (cm) Trial 3 |
|
20 |
9.0 |
11 |
8.0 |
|
40 |
17 |
22 |
19 |
|
60 |
28 |
30. |
31 |
|
80 |
37 |
40. |
42 |
|
100 |
52 |
51 |
49 |
Data Analysis:
Data Table 2: Average Bounce Height at Each Height:
|
Drop Height (cm) |
Average Bounce Height (cm) |
|
20 |
9.3 |
|
40 |
19 |
|
60 |
30. |
|
80 |
40. |
|
100 |
51 |
Graph 1: Height of Ball drop versus Height of ball bounce:
Sample Calculations: m = Dy / Dx
m = (40-30) / (80-60) = 10 / 20 = ½ = .5
Results & Conclusions:
Our data indicates that the hypothesis was incorrect. Data table 2 indicates that on average tennis ball bounced to a lower height than it was dropped from. The reason for our error was that we thought that the tennis ball might be specially made to bounce to the same height. The results of our experiment show that this probably is not the case. However, the tennis ball we used may be a very old one, and to definitely prove that our hypothesis is wrong for most tennis balls we would need to repeat the experiment with many different tennis balls.
The purpose of our lab was fulfilled. Our lab group was able to determine the relationship between drop height and bounce height. Additionally we were able to practice reading a lab, taking data and making a graph.
Possible sources of error include several types of measurement errors. It was difficult to accurately measure the height of the bounce. We also noted after we finished the experiment that the student taking measurements sometimes stood above the height when taking the measurement and sometimes kneeled on the floor so they had a different angle on the meter stick, which may have affected the measurement.
This experiment might have been improved if we had developed a method for more accurately measuring the tennis ball’s bounce height. For example, we could have used a ruler on the top to help us read how high up the tennis ball bounced, and we could have made sure the partner taking measurements did so from a consistent height.
Summary of Lab Questions:
The slope of the line in graph 1 was found to be 0.5. This calculation is shown in the data analysis section above. This slope tells us how “bouncy” the ball is. It tells us that the ball consistently bounced to half of its drop height.
Using the slope and graph, we can estimate that the ball would bounce to 0.75 m if dropped from 1.5 m and bounce to 1 m if dropped from 2 m.
It is difficult to say with certainty that a ball dropped from 100 m would bounce to 50 m. That is because the heights we dropped the tennis ball from were all under 1 m, and at a much greater distance there may be other factors that would contribute to the bounce height. For instance, air resistance would slow down the tennis ball much more when it is dropped from 100 m than when dropped from 1 m. This difference in impact speed would probably affect the bounce height. Another experiment would be necessary to determine this for certain.
