Size
Elastic bands can be thick or thin, and the size of a elastic band impacts its strength. Find a sturdy, stable object and put a yardstick next to it. Cut elastic bands of different sizes in half. Test them one at a time by tying one end to the stable object and the other to the end of a spring scale. Each band must be the same length when tied. Draw the scale back until the band breaks. Record the amount of force it required to break the band from the spring scale as well as how far it the band stretched. Using your records, determine which bands are strongest and whether the strength and the length the band will stretch are related. To make the experiment more complex, compare different brands or compare plain to colored elastic bands. Wear protective glasses and gloves to protect you if the elastic band snaps back at you.
Temperature
Temperature is known to affect the elasticity of rubber. You can discover if it affect strength, as well. Take several elastic bands of the same size and brand. Soak one in very hot water, one in room temperature water and one in ice water. The room temperature water is your control group. You may need to weight down the bands. Find a solid object that you can tie a band to and put a yardstick next to it. With each band, remove the band from the water and hook one end to the stable object and hook the other onto a spring scale. Be careful and do not burn yourself with hot water. Pull the band back with the scale and record both how far each stretches as well as how much force it takes to break the band. Use your results to determine if there is a relationship between temperature and strength as well as temperature and elasticity. Again, wear protective glasses and gloves to protect you if the elastic band snaps back at you.
Multiple Bands
Using elastic bands together increases their strength. Find or build an object that you can safely suspend a elastic band on. Add weight to the bottom of the elastic band until it breaks. Record how much weight was needed to break the band. Repeat the same experiment with two, then three elastic bands. Record the amount of weight each setup is able to hold and compare the results. You can continue the experiment by adding more elastic bands, or make it more complex by recording how far each setup will stretch. Again, wear gear to protect you if the elastic band snaps back at you.
Chemicals
Elastic bands are usually made from natural rubber, which is resistant to many chemicals. For instance, when dyeing fabrics, elastic bands can be used as a resist to prevent the dye from reaching certain parts of the fabric. Soak similarly sized elastic bands in different household chemicals, such as vinegar or nail polish remover. Soak one in plain water for your control group. Hook one end of each band around a stable object and the other to a spring scale, pulling back the scale to test how much tension the band will with stand. Measure how far the band stretches, as well, and record your results. Compare the bands soaked in chemicals to the one soaked in water to see if there is a difference. Rubber absorbs oils readily, so you could try the same experiment with different, common oils. Wear protective gear to prevent the elastic bands from hurting you and to protect your hands against any chemicals. Do not conduct this experiment with anything that is very caustic, like bleach or ammonia.