# Help Needed - Catapult Lever system

1. Sep 28, 2013

### ChrisLarabee

I have here a class 1 lever style catapult built using leaf springs (A Da Vinci design) which relies on the stored energy in the springs to apply torque over a certain distance which is the length of the arm. Of course, for max distance the arm will stop at 45 degrees or pi/4 RAD. Now here is my question. How do I determine the displacement or range of my projectile given mass and its shape.

I realize this depends on the force or energy exerted on the projectile which is then transferred into kinetic energy when it begins flight off the catapult arm. My question IS: What does this force depend on? the length of the arm? angular velocity? linear velocity? moment of inertia (I)? The more I read the more I am confused. I keep thinking a longer arm will increase angular velocity but not linear velocity but then I question how, as it is still travelling pi/4 RAD over a given time.

The way I think is that if I apply a force A (10N) on a class 1 lever the force B at 1/2 the length from the fulcrum that Force A was exerted at will be greater but due to conservation of energy this is true:
(w=f*d 10N x 2m = 20J= Fb x D= Fa x d ... all relative) so less force over more distance moves the other terminal end of the class 1 lever at an increased force over shorter distance. therefore I determine that a longer arm would hold the reverse in the style of my catapult and actually decrease the force or torque in this case applied.. but that makes NO SENSE to me.

I don't care how complicated this gets I just want to build a bad a** catapult for 4U physics(GR.12)