Firing Q - Loading Pivot Origin Trebuchet Diagram This simplified system is based on the rotation of a 51 feet long lever arm that weighs 3.2 pounds per foot, with the 8250-pound counterweight's center of mass a distance 7 feet from the hinge of the trebuchet. The counterweight is a solid sphere of radius 5 feet. For optimal operation, the counterweight just Assume that the payload is a projectile of mass 10.5 and fires horizontally. Video: Optimizing a Trebuchet * The original Chinese trebuchets were human powered lever arms that required a large crew of soldiers to pull down on the siege engine in unison. ** Prior to the invention of the cannon, town walls were quite thin. Catapults, onagers or trebuchets, did not break walls down, they tossed things over the walls. Like chickens. Cannons tore through the medieval walls when they came into common use a few centuries after the introduction of the trebuchet. Part 1 of 5 - Initial Vectors To begin, you need to translate the initial situation into mathematical form. In the this case, the important points to keep track of are: 1. The Pivot Point 2. The Center of the Counterweight 3. The Position of the Payload We need to find this points in both the loading and the firing positions. I. Loading Positions Where are the three important points relative to the origin? Calculate them using the data above and vector reasoning. (a) What is the initial position of the pivot point? P = y + 2 (b) What is the initial position of the payload? R = y + (c) What is the initial position of the counterweight? C = y + (d) What is the initial position of the lever arm? L = y + II. Position at Launch You will be using energy conservation to solve this problem, so you will have to have to know the positions of the various objects at launch in order to make the comparisons. (e) What is the launch position of the pivot point? P = y + (f) What is the launch position of the payload? R = y + (9) What is the launch position of the counterweight? C = 2 (h) What is the initial position of the lever arm? L = y +