The action of a catapult uses tension, torsion and gravity. Like the catapults in Peter Jackson’s movie the “Return of the King,” catapults are siege weapons that hurl projectiles at an enemy target without the use of explosives. Crucial during the Medieval ages and even earlier, these simple machines make use of stored energy to release a projectile, or payload.
TL;DR (Too Long; Didn't Read)
Catapults employ basic physics to function. The first catapult, a ballista, simulated the action of a crossbow, firing an enormous arrow as its missile. The device got its name from the Greek word ballistes, which means to throw. Despite the accuracy of this siege weapon, it lacked the power found in the trebuchet and mangonel catapults.
If you've used a crossbow or seen one fired, you can envision how a ballista works. Like a mangonel, it employs twisted ropes to create torsion, or tension, about the axis of rotation. Instead of having one arm that rotates through a vertical plane, it uses twin arms that move through a plane elevated above the horizontal to an angle of its crews' choosing. This device can fire stones like other catapults but is especially suited to firing enormous darts and spears.
The most efficient and accurate type of catapult, a trebuchet makes use of a heavier counterweight than the payload to provide the energy for launch. The apparatus is set up like a see-saw, with the pivot point much closer to the counterweight end at the front than to the payload and sling at the rear. As an example of the principle of mechanical advantage, the linear velocity of the sling -- in this case the speed with which the payload traces out its arc just before it is launched -- is more than that of the counterweight, simply because of the larger mass of the latter.
Sciencing Video Vault
The most familiar type of catapult, the mangonel fires projectiles at lower angles than does a trebuchet, making it better suited for destroying walls rather than firing objects over them. In physical terms, tension is created in opposing directions by ropes, one in the direction of launch and the other toward the ground beneath the payload. When soldiers cut the rope lashed to the ground, the arm of the mangonel accelerates quickly toward the target and the payload flies. The potential energy itself originates in the elastic properties of device: the flexible wood joins the pivot arm to the rest of the apparatus.
Build your-own table-top, mangonel-style catapult -- also called a siege engine in the old days -- using easily found parts and tools. You'll need a dozen or more pieces of wood six to 12 inches long, a supply of small nails or screws, wood glue, a few tough elastic bands, a pair of eye-hook screws, a 6-inch long metal bar, and a piece of cardboard about 4 inches square. For a special challenge, try assembling these without instructions.