Key concepts

If you've ever been shot with a rubber band then you know it has energy in it—enough energy to smack you in the arm and cause a sting! But have you ever wondered what the relationship is between a stretched rubber band at rest and the energy it holds? The energy the rubber band has stored is related to the distance the rubber band will fly after being released. So can you guess one way to test how much energy a stretched rubber band contains?

No mechanical contraption would be any fun if it did not work. But "work," in the physics sense, takes energy. Consider a rope and pulley that bring a bucket up a well. The energy that makes this mechanical system work is provided by a person who pulls up the rope.

There are actually two different kinds of energy: potential energy, which is stored energy, and kinetic energy, which is energy in motion. A great example of the difference between kinetic and potential energy is from the classic "snake-in-a-can" prank. This is an old joke where you give someone a can of peanuts and tell them to open it, but inside is actually a long spring that pops out when the lid is twisted off. Because the spring is usually decorated to look like a snake, this prank usually causes the victim to jump back and shout in surprise! When the snaky spring is compressed and secured inside the unopened can, it has potential energy. But when the can is opened, the potential energy quickly converts to kinetic energy as the fake snake jumps out.

•    A long, wide concrete sidewalk, driveway or other hard surface that you can draw on with chalk (as an alternative, you can make distance markers out of paper and place them on a surface on which you cannot draw)
•    Sidewalk chalk
•    Metric ruler
•    Rubber bands (all of the same length and kind)
•    A helper
•    Metric tape measure
•    Paper and pencil or pen

•    Find a helper, gather your supplies and go outside to do this activity. You will want a place with a lot of clearance that has a concrete or other hard surface on which you can draw with chalk.
•    Your partner will draw circles around where the flying rubber bands land, so choose a person with a keen eye and some running shoes!
•    Use caution to shoot the rubber bands out in front of you—and make sure no one is in the flight path! If necessary, have an adult do the rubber band launching.

•    At the outside place you picked, stand where there is lots of clearance in front of you. With your chalk, draw a line in front of your toes. This is where you will line your feet up when you shoot your rubber bands. This is also the mark from where you will measure the distances your rubber bands have flown.
•    Your helper can stand a few meters in front of you, but off to the side, not directly in the line of fire! Make sure he or she has a piece of chalk.
•    Shoot a rubber band by hooking it on the front edge of the ruler, then stretching it back to 10 centimeters (cm) on the ruler and letting the rubber band go. Remember the angle and height at which you hold the ruler because you will need to keep it the same for each rubber band launch.
•    Have your helper draw a small chalk circle where the rubber band landed.
•    Shoot at least four more rubber bands in the same way, stretching them back to 10 cm on the ruler each time. Have your helper circle where each lands.
•    Measure the distances from your line to the circles your helper made. Write these distances down under the heading "10 cm." Did all five rubber bands land close to each other or was there a lot of variation in where they fell?
•    Shoot more rubber bands in the same way, except stretch them back to 15 cm, 20 cm, 25 cm or 30 cm. Shoot at least five rubber bands for each stretch length. After each launch, have your helper circle where they land. After launching five rubber bands at a given stretch length, measure the distances from your line to the circles. Write these distances under a heading for their stretch length (for example, "20 cm").
•    For each stretch length, did all five rubber bands land close to one another or was there a lot of variation? Did they land far from where the rubber bands landed that were launched using different stretch lengths?
•    Average your results for each stretch length and make a graph of your results by putting "Stretch Length (cm)" on the x-axis (this will be 10 cm, 15 cm, 20 cm, 25 cm and 30 cm) and "Launch Distance (cm)" on the y-axis (this will be the distances you measured). Do your data follow any type of pattern or trend? What was the relationship between the stretch length and the launch distance? What do you think this indicates about the relationship between potential and kinetic energy when using rubber bands?
•    Tip: If you run out of rubber bands, you can always grab some of the ones you already used and reuse them because there will be a chalk circle where they landed.
•    Extra: In this activity you kept the angle and height of the launch the same from trial to trial. How do these variables affect the distance the rubber band travels? Design a separate activity to test each of these variables separately.
•    Extra: You can do a very similar activity to this one by using other types of mechanical systems, such as springs and slingshots. How do the data collected using these other mechanical systems compare with that collected using rubber bands?
•    Extra: For an advanced challenge, you can use linear regression to further analyze your data. Can you define an equation that expresses the relationship between potential and kinetic energy in this system?

Observations and results
Did the rubber bands stretched to 30 cm launch farther than the other rubber bands? Did you see a linear relationship between the launch distance and stretch length when you graphed your data?

You input potential (stored) energy into the rubber band system when you stretched the rubber band back. Because it is an elastic system, this kind of potential energy is specifically called elastic potential energy. Elastic potential energy (measured in the unit joules) is equal to ½ multiplied by the stretch length ("x") squared, multiplied by the spring constant "k." The spring constant is different for every rubber band, but can be figured out (see "Welcome to the Guide to Shooting Rubber Bands" below). When the rubber band is released, the potential energy is quickly converted to kinetic (motion) energy. This is equal to one half the mass (of the rubber band) multiplied by its velocity (in meters per second) squared.

Using these equations, you can calculate the velocity of the rubber band right when it is released, and find that the velocity has a linear relationship with the stretch length. (Because the amount of time that the rubber band spends in the air is dependent on its initial height and force of gravity, and these factors should not change between your trials, then how far the rubber band flies depends on its initial velocity.) Consequently, after you graph your data, you should see a roughly linear relationship between the stretch length and the launch distance.

More to explore
What Is Energy? from Wisconsin K-12 Energy Education Program (KEEP)
Energy Conversions: Potential Energy to Kinetic Energy from FT Exploring Science and Technology
Welcome to the Guide to Shooting Rubber Bands: The Physics of Shooting by Tim Morgan
Rubber Bands for Energy from Science Buddies

This activity brought to you in partnership with Science Buddies