Something I used to love using as a kid was a slingshot. It's so fascinating that a mechanism as simple as one of these can shoot something so fast. I thought I'd go through some of the physics behind this.
As the elastic band is stretched, the potential energy stored is similar to that of a spring. However, the longer you take to aim the slingshot, the more potential energy you lose due to heat loss (aim fast!). If you happen to be making your own slingshot you would think that using a thicker band would have a higher spring constant and thus a larger exertion of force on whatever object is being flung, right? Against what your initial beliefs might be this is in fact not true, as a tapered band will be faster than a thicker band because it is more efficient when converting the potential energy into kinetic energy for some reason. The other interesting part about a slingshot is that, like we discovered in class with the egg drop, rubber does not obey Hooke's Law that says the Force of a spring system is equal to the product of the spring constant and the displacement. The force required actually increases in a curved, exponential fashion, whereas if you graphed Hooke's law it would be linear. If you wanted to find the force of a non-hookean solid then you could, however there are several other things to consider, such as a shear modulus or a bulk modulus, that just makes it difficult and much more complicated. Using a slingshot is fun, however make sure you use it for good and not evil.