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