Fire Away!

The goal of this project was to build a catapult or trebuchet which would launch a small projectile as far as possible. We constructed our launchers individually, and could build them any way we liked. However, they had to be easily modifiable, because throughout the build process we conducted experiments to determine what changes to make in order to maximize the distance the projectile traveled. For instance, our group conducted an experiment which showed that increasing the ratio of [distance from the projectile to the pivot point] to [distance from the pivot point to the weight/energy source] would increase the distance that the projectile flew (up until a physical maximum determined by the machine's constitution — see the proof of efficacy document below for more).

In my machine, I used a yardstick as the main arm. I used weights and rolls of pennies for the energy source, attached to one end of the arm. The arm was able to rotate about a piece of PVC pipe while still staying attached due to a rubber-band construction. This mechanism provided a small amount of spring energy as well, because it resisted the arm when it was in the retracted position. Finally, the projectile itself was two metal marbles held together by tape. This was restrained in a milk cap on the end of the machine's arm opposite the weights, so that it did not release at the wrong angle. For more information on the machine's design, see the proof of efficacy document below.

Proof of Efficacy Document

Core Concepts

Spring Constant

The spring constant, denoted k, is how "rigid" an elastic mechanism is. In other words, it is how resistant to expanding or contracting it is. k can be calculated using the formula k = F / d, where F is the force applied to the spring and d is the distance it moved (by applying the force). Thinking intuitively, we see how this formula arises: the smaller the distance moved is, the lower the constant (the spring moved less, so it is more rigid), while applying more force increases the constant (you've had to apply more force to get it to move, so it is more rigid). The unit for k is N / m (newton per meter), which can be clearly derived from the formula.

In my machine, the total spring constant for the rubber band assembly was ~71.43N/m. This means that you would have to apply 71.41 newtons of force to get them to move a meter. (Here we see the meaning of the units.) Obviously, they won't move a full meter, so the force required to stretch them (and more importantly, the force they will exert when stretched) is lower.

Spring Potential Energy

Spring potential energy is the "stored energy" that a spring or other elastic mechanism possesses. It is clearly related to the spring constant, and this is echoed in the formula SPE = 1/2 · kx², where k is the spring constant of the mechanism and x is the distance it has been stretched to. In my machine, the rubber bands stretched to 0.05m before the arm was released, so their potential energy was 0.05 · (71.43)(0.05^2) = ~0.089J.

Reflection

In this project, I think I did well with critical thinking because I put a lot of thought into the modifications. And, each modification yielded very measurable performance gains, so that was confirmation that I had made the right choices. Additionally, I feel that I did well with my communication. I made everything as clear as possible in my proof of efficacy document and provided figures as evidence for all of my claims. I structured the document in a logical fashion and went into detail about every aspect of the project. However, I feel that I also could've done better with communication in some areas. The "measurements and calculations" section and the "calculation table" reiterated a lot of the same facts — I feel that there could've been a better way to present that information. Additionally, I feel that I could've done better with conscientious learning. I feel that I didn't explore this project as deeply as I could've — while I did meet all the requirements and do everything that was needed, I didn't delve into this project as fully as I have with other projects.