On the Rebound: The Height Limits and Linearity of Bouncy Balls
AbstractYou might think that plants and animals have little in common with batteries, springs, or slingshots, but they actually do have something in common. Both living and non-living things store and transfer energy from one form to another. In this physics science fair project, you'll investigate this energy storage and transfer, not in a plant or animal, but in bouncy balls. You'll find out if there are limits on how much energy can be stored and if there are losses when the energy is transferred.
Kristin Strong, Science Buddies
To determine the rebound height limits and evaluate the relationship between the dropped height and the rebound height of dropped bouncy balls.
There is nothing quite as satisfying as hitting a ball with a bat right in the "sweet spot" and watching it fly into the outfield. When a bat connects with a ball, the energy of the collision is stored as a physical deformation of both the bat and the ball (mostly the ball). The stored energy is called elastic potential energy. Potential means it holds the possibility of doing work, or causing a change in energy. As the squashed ball returns to its original shape, its stored elastic potential energy is transformed into kinetic energy (motion energy) and the ball flies through the air for a home run!
You can see this same energy transfer happen in an even simpler example, too. Imagine that there is no bat. Instead, you are holding a bouncy ball above a hard surface.
Drawing shows a bouncy ball at four different stages as it is dropped and bounces off of the ground. At the start time, the ball is held by a hand above a surface, displaying gravitational potential energy about to turn into kinetic energy. At the second time frame, the ball has been released and has contacted the surface and been squashed into an egg shape, displaying kinetic energy that has been transformed into elastic potential energy. In the third time frame the ball is still in an egg shape on the ground, but is starting its rebound, the elastic potential energy is becoming kinetic energy again. In the fourth time frame, the ball has lost all its kinetic energy, returned to its spherical shape, and has reached its final rebound height, which is lower than its start height, displaying a new gravitational potential energy.
Figure 1. This drawing shows the transfers of energy that occurs when a bouncy ball is dropped onto a hard surface.
As shown in Equation 1, the ball has a gravitational potential energy that is equal to the mass of the ball, times the acceleration due to gravity, times the height above the surface.
|Gravitational Potential Energy =||Mass × Gravitational acceleration × Height|
|Gravitational potential energy is in joules (J) or newton meters (N·m).|
|Mass is in kilograms (kg).|
|Gravitational acceleration is 9.81 meters per second squared||(||
|Height is in meters (m).|
As you release the ball, that potential energy is transformed into kinetic energy (remember, the energy of motion). When the ball hits the ground, it is deformed (just as when it was hit with a bat). In this deformation, the kinetic energy gets transformed and stored as elastic potential energy within the ball. The ball then releases this stored potential energy as it returns to its original shape. The stored elastic potential energy is transformed into kinetic energy and the ball "rebounds." The kinetic energy is then gradually transformed into gravitational potential energy once again.
An ideal, perfectly elastic ball operating in a vacuum would rebound back to its original height, but real-world balls are not perfectly elastic, and, thankfully, we don't live in a vacuum. In the real world, there are small energy losses at every stage of the ball's journey. When the ball is moving through the air (both up and down), the air molecules collide with it, creating resistance to motion. This warms up both the ball and the air slightly, resulting in a small energy loss. Another energy loss arises when the ball strikes and rebounds from the ground. In both cases, the ball is changing its shape and that warms the ball slightly, producing an energy loss. In addition, during the collision with the floor, you hear that classic "bouncy sound." Creating sound also results in a small energy loss. The sum of all these small energy losses means that the rebound height of the ball cannot reach the original height of the ball. The ball follows the conservation of energy law.
In this physics science fair project, you will explore the rebound heights for different balls and determine their maximum limits. You will also see if the relationship between the dropped height and the rebound height is linear by evaluating a graph. So, let the bouncing begin!
Terms and Concepts
- Elastic potential energy
- Kinetic energy
- Gravitational potential energy
- Gravitational acceleration
- Conservation of energy
- What happens to a moving ball when it collides with a hard surface?
- How is energy stored in a bouncy ball?
- When you drop a bouncy ball, why doesn't it return to the height from which it was released?
This source provides a discussion of work, energy, and power:
- Nave, C. R. (2005). Work, Energy, and Power. Retrieved December 1, 2008.
This source provides a discussion of elastic potential energy:
- Henderson, T. (2007). Potential Energy. Retrieved December 2, 2008.
This source provides a discussion of the energy transfers that occur in dropped bouncy balls:
- France, C. (2008). Energy Transfer. Retrieved December 2, 2008.
Materials and Equipment
- Large pieces of paper (enough to cover a 6- x 2-foot section of wall)
- Tape, any kind that is safe for walls
- Chair or stool
- Measuring tape, meterstick, or yardstick
- Bouncy balls (2) of different types, such as a racquetball, tennis ball, super ball, ping pong ball, or rubber ball
- Lab notebook
- Graph paper
Preparing Your Test Wall
- Ask your parents what wall you can use for your experiment. The wall must stand beside a hard floor and you will need to use tape on the wall.
- Tape paper to the wall until an area about 6 feet high and 2 feet wide is covered.
- Using your measuring device and a pencil (and a chair or stool, if necessary), mark and label every inch of your paper, from the floor up, until you have reached the top of the covered wall area. Be careful standing on the chair.
Testing Your Bouncy Balls
- Have the volunteer hold one of the balls at the 6-inch mark on the paper. The ball should be held slightly away from the wall, so that it doesn't hit any molding when you drop it, but close enough so that you can observe the ball's rebound height based on the markings on the wall.
- Have the volunteer release the ball while you observe the ball's collision with the floor and observe its rebound height. Record the rebound height in a data table, like the one below. Repeat two more times, so you have a total of three trials. Can you see a deformation?
- Have the volunteer hold the same ball at the 12-inch mark on the paper. Repeat step 2.
- Have the volunteer move up the paper 6 inches at a time, and repeat step 2 until the top of the paper is reached.
- Repeat steps 1–4 for the second ball and record your results in a second data table.
Ball 1: Rebound Heights Data Table
|Drop Height (in)||Trial 1 Rebound Height (in)||Trial 2 Rebound Height (in)||Trial 3 Rebound Height (in)||Average of the Rebound Heights (in)||Average Rebound Height to Drop Height Ratio|
Analyzing Your Data Tables
- For each drop height, calculate the average of the rebound heights and record your calculations in the data tables.
- For each drop height, calculate the ratio of the average rebound height to the drop height and record your calculations in the data tables. Can this ratio ever reach the number 1?
- For each ball, plot the drop heights on the x-axis and the average rebound height to the drop height ratio on the y-axis. Is the graph linear? Is it linear over a certain range of drop heights and not over others? Did the balls bounce highest when released from their highest point? Was there a point at which the rebound height reached a maximum? If so, what do you think explains this limit?
Ask an Expert
- Investigate the rebound heights when the same balls are dropped on different flooring materials.
- Investigate how cooling the same balls in a freezer or refrigerator affects their rebound heights.
If you like this project, you might enjoy exploring these related careers: