First off, this is not a homework question or anything like that. I'm trying to build a catapult to launch a payload using a flywheel as an energy device!
It goes like this:
- The flywheel spins up to maximum speed. All other components are at rest.
- The catapult lever (in resting position, with a payload at the end of it) engages a tooth.
- The flywheel tooth (always extended) connects with the catapult lever tooth and rotates it over a certain angle. During this time the flywheel is slowed down a certain amount and the lever gains a great amount of speed.
- At the end of the interaction between the flywheel and the lever tooth (after some degree of rotation) the lever gets to the end of its stroke and abruptly stops, the payload continues flying upward and the remaining energy of the flywheel makes it continue to spin (it can freely "slip" past the lever tooth at the end of the movement).
I've attached a couple pictures which describe the two states, T0 and T1 (basically step 3 and 4 respectively).
My question is, how do I determine the final energy of the flywheel after this interaction given the following parameters: Moment of Inertia and initial Kinetic Energy of the flywheel, mass of payload, and the basic geometry between them. Assume the weight and inertia of the catapult lever are negligible and there is no friction between the interaction of the two moving parts.
I originally thought this problem would be as easy as assuming all the kinetic energy of the flywheel just went into the upward motion of the mass (the flywheel would come to a complete stop). However, after thinking about it for a while I realized it is probably not that simple at all...I smell some differential equations which scare me and has been a while since I've done any of that which is why I am asking for some help. Maybe it's not that complicated after all, but I am at a dead end. Anything would be appreciated.
Thanks in advance.