A ping-pong ball sits on a tiny rubber band (a rainbow loom, or hair elastic) at the end of a popsicle stick. That provides friction to keep the ball in place. A small rod, spool, or domino acts a fulcrum. The catapult is a simple lever – a rigid object (popsicle stick) rotating around a fixed point, the fulcrum. Like a seesaw, but notice the fulcrum is not in the middle. The short end gets the force, and the long end sends the ball flying!
You can use a plastic spoon, or pretty much anything with a flat or rounded surface. The greater the incline (tilt), the higher the ball can go. Too much incline though, and the ball will roll off. As in the story of Goldilocks and the three bears, engineering (and life) is a dance between too much and too little, we’re always looking for the “just right”.
The potential energy is in the position of the block that is set to fall on the short end of the catapult. The higher and heavier the block, the greater the force. Newton’s second law says that for every action there’s an equal and opposite reaction. With a lever, as one side goes down, the other side must go up (conservation of momentum) as it rotates around a fulcrum. And we exchange force for distance, so the reaction (the flying ball has lots of distance) is equal to the action (the falling block has lots of force).
All complicated machines are made from simpler parts. If you haven’t mastered this technique, or don’t yet understand it, break it down into smaller parts till you “get” each one, and then build up from there. Find or make a lever, and place a fulcrum underneath it, off-center. Place a ball (or something else lightweight and soft) on the long end. Drop something heavy on the short end. Watch it fly!