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Message No. 13707, Started by rubinho on 04/20/04
 Calculating trajectory of ball rolling down slope and off launch ramp I am having some trouble with calculating the distance travelled and maximum height gained by balls rolling down a slope and off a lauch ramp.   There are 3 different types of ball, 100% steel, 100% nylon and 50% steel (by diameter) surrounded by 50% nylon.  They are all 20mm diameter.   The balls are released at the top of a ramp of height h1 at angle a1 and they are launched from the end of a launch ramp of height h2 and angle a2.  I have started tackling the problem by splitting it into two halves, one to calculate the velocity of the ball at the bottom of the first ramp and then to use this velocity as the start velocity of the second ramp trajectory calculation.  For ease of calculation I have assumed that there is negligible loss of velocity through the curve that will obviously (in real life) sit between ramp 1 and ramp 2.   The balls will be rolling down and up the ramps so their accelerations (hence velocities) will be related to their moments of inertia, this is where I am having the trouble.   I think I will be fine working out the trajectory once I know the velocity at the end of the launch ramp (I am assuming air resistance is negligible).   Can anyone suggest where I might start looking for equations to solve the velocities at the end of each of the ramps?   Have I covered all the bases here or are there some other factors I have not taken into account?   Thanks in advance.
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Follow-up Messages (17)
 I'll accept that if the ramp is sufficiently large and the balls are suffic... No. 13777, Posted by b1ueshift on 04/28/04, 20:16 PST. If you're money's on the hybrid, you can just make the check out to me... No. 13764, Posted by acroduster1 on 04/27/04, 13:05 PST. That sure is some fancy figuring. My money is still on the hybrid. No. 13757, Posted by b1ueshift on 04/26/04, 22:48 PST. Acro, You stated: "This would imply that the steel ball would travel 17% ... No. 13749, Posted by rorschach on 04/26/04, 10:40 PST. Bravo, rubinho - you did it right! Neglecting friction, the energy equatio... No. 13747, Posted by acroduster1 on 04/26/04, 06:06 PST. Actually the point of the exercise seems to be understand that the nylon ba... No. 13741, Posted by b1ueshift on 04/25/04, 17:39 PST. rubinho, if all the balls are falling in EXACTLY the same spot, you've made... No. 13732, Posted by rorschach on 04/23/04, 10:40 PST. Good news: I did all the calculations and they come up with sensible number... No. 13731, Posted by rubinho on 04/23/04, 10:12 PST. b1ueshift is exactly right. I'll set up the equation here: First, you h... No. 13723, Posted by acroduster1 on 04/22/04, 07:05 PST. You seem to be a little off track. The change in gravitional potential e... No. 13720, Posted by b1ueshift on 04/21/04, 23:58 PST. Bear with me here but I'm trying to digest your last post. The ball is... No. 13718, Posted by rubinho on 04/21/04, 11:21 PST. The variables that I can think of for the ramp problem are as follows: I... No. 13716, Posted by acroduster1 on 04/21/04, 06:38 PST. another way to skin this cat is to have two counterbalanced levers in serie... No. 13715, Posted by rorschach on 04/21/04, 05:41 PST. Rubinho I think that u might get some projectile in free air equations f... No. 13711, Posted by yesyouretheone on 04/20/04, 19:48 PST. Disregarding drag, the landing position of the balls is solely dependent on... No. 13710, Posted by rolschwarz on 04/20/04, 12:19 PST. It is homework, but not as you might expect. We have been assigned a desig... No. 13709, Posted by rubinho on 04/20/04, 11:58 PST. Do we get partial credit for helping you with your homework? No. 13708, Posted by rolschwarz on 04/20/04, 11:14 PST.