Ready to Start an Office Siege war? Paper can be used for your physics project, or cubical conundrum.

Materials:

Paper (I used 120 pound card stock)
Glue (I used gorilla wood glue, see build step)
Source of energy (I used an exercise band)
Counterweight (paper doesn't weigh much, my assembled catapult weighed approx. 18 oz)
Projectile (my catapult was designed to launch tennis balls)

Total cost for mine: 10$

Info:

For a school project over the past 9 weeks we had to build a catapult capable of launching tennis balls with accuracy. Being the overachiever I am I decided to make my catapult unique, by creating mine out of paper.

Paper is one of the most versatile materials I know of, forming anything from writing paper to cardboard, my own goal was to make a Sudo-wood that could outperform traditional wood. I went a little too far with my design and it ultimately failed, but the guide is here for future catapults.

My catapult consisted of principles from the 3 classes of catapult recognized by "Punkin' Chunkin'," Torsion (rubber band), trebuchet (sling, this was the fail point), and Centrifugal (the arm rotates beyond 360*). In the end I overlooked the design of a sling, they use what is called a finger to release the sling at about 45*, doesn't work when your arm is spinning around 7 times before it is ready to launch. If I had had time I could have installed an electric trigger but I didn't.

Step 1: Design

First thing you will want to do is sit down with a sketchpad or graph paper and create your catapult. I have included my Sketchup file and blueprint made from it of my design. My design changed as I constructed it (simplified) but the principle is still the same. The catapult is constructed from overlapping "planks", 14 sheets of paper thick, some cut paper long ways, some short.

I tested the strength of glues as follows:

I glued 2 strips of paper together with one of 4 adhesive, I left 2 strips unglued for a control
Allowed glue to set for 36 hours between 2 clipboards.
After removing the planks from the boards (wood glue took some clipboard with them :P, using wax paper makes sure glue wont stick to things it shouldn't) I creased the planks in the middle and allowed them to sit against gravity.
12 hours later the results were clear, see picture, gorilla glue didn't budge.

Later planks take didn't break/snap under conditions a similar piece of wood did so my sudo-wood outperformed, perfect.

Step 2: Build

This step is by far the most time consuming, gluing planks together; luckily they make 1" sponge brushes that make gluing 1" by 11" or 8.5" planks a breeze. 50 planks and 1 gear, totaling at 700 strips of paper, 30 gear cutouts, around 95 sheets of paper later, the planks were ready to take shape. Using a wooden dowel for the fulcrum. (didn't trust paper there) Assembly was unique (ever drilled and/or sawed paper?) As stated in the intro paragraph this is as far as construction went, my sling concept could not have worked (tried for 6 hours to fix it).

Step 3: Enjoy

My catapult in its current form will never launch a tennis ball due to a principle I overlooked about a trebuchets sling, but don't let that discourage you. Paper can be used to make a very capable white catapult.

Attached I have a video of my first test fire, skip to 0:35 for the action.

Good luck in your cardstock catapult endeavors.