Maximizing Projectile Range on a Class 1 Lever Catapult: Tips & Tricks

[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 traveling 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)

 

[LightHero]

and I need some help.The key factor in determining the range of your projectile is the kinetic energy it has when it leaves the catapult arm. The kinetic energy depends on the force and speed with which the projectile is launched. The force is determined by the amount of torque applied to the arm, which in turn is determined by the length of the arm, the spring constant of the leaf springs, as well as the angle of the arm (45 degrees or pi/4 RAD). You can use the equation KE = 1/2 * m * v^2 to calculate the kinetic energy, where m is the mass of the projectile and v is its velocity. To calculate the velocity of the projectile, you can use the equation v = Torque x Angular velocity, where Torque is equal to Force x Length of the arm, and Angular velocity is the angular displacement divided by time. The angular displacement is equal to pi/4 RAD. Once you have calculated the velocity of the projectile, you can calculate the range of the projectile by using the equation Range = Velocity x Time. The time is determined by the time the projectile spends in the air (which depends on factors such as air resistance). I hope this helps!