Calculating trajectory of ball rolling down slope and off launch ramp
Good news: I did all the calculations and they come up with sensible numbers.
Bad news: I needn't have done so as the machine will never work. Newton's laws dictate that all the balls will end up in exactly the same place. Think about it, they are all identical except mass and the only external force is that of gravity; everything boils down to a ratio of F=ma. They all leave the lauch ramp at the same velocity and they all hit the ground at the same place.
It's a shame I wasted your time and mine working out the calculations for, what is in fact, an obvious answer!
Thanks all the same for your help, I did learn a couple of lessons:
- Relationship between energy and motion
- Relationship between angular and linear velocity
- Don't ignore basic principles
Damn that Gallileo! :)