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#1




Physics: ball launch using gravity
OK, before I get into what I'm looking for, here's my assignment:
I have to build a device that will launch a ball approximately 10 grams in weight to a 10 cm wide hoop 1 meter away and 1 meter high. Now, what I really want to do is build a ramp system that will use gravity to accelerate the ball and then redirect its direction so that it will launch high and far enough to get into the hoop. In my thinking, if I build it just right, it should work 100% of the time. Question is, how do I successfully transfer the vertical motion of the ball at start into horizontal and vertical motion good enough to get the ball into the hoop? Thoughts? Other suggestions are really welcome. Joe [edit] in the case that this involves complex math and you must use it, I'm currently enrolled in a precalc class. So go for it. [/edit] 
#2




Re: Physics: ball launch using gravity
Using conservation of energy, you should be able to determine from what height you will need to start rolling the ball down a "ski jump" in order to achieve enough velocity to launch the ball at some angle to make it through the hoop. Don't forget to include the rotational energy of the ball in your calculation...

#3




Re: Physics: ball launch using gravity
Quote:
Total energy is a system is constant. Code:
Potential Energy (U) = (mass) * (height) * (acceleration of gravity) Linear Kinetic Energy (T) = 1/2 * (mass) * (velocity ^ 2) Rotational Kinetic Energy (K_{R}) = 1/2 * (moment of inertia) * (velocity ^ 2) I for a sphere: 2/5 * Mass * Radius^2 E_{A} = E_{B} (E is total energy, A and B are arbitrary points in time.) E = T + U + K_{R} Once you have your needed velocity and launch angle, figure out how much kinetic energy it will have at launch. Plug the velocity, mass, and Moment of Inertia (I) into the equations above, and add the 2 values together to find net kinetic energy. Then, set that equal to the potential energy (You can assume this if your reference frame has the balls launch point as (0,0) and the ball is starting from a stop, aka no kinetic energy.) So now you have U = T + K_{R} and U = mgh. Simply solve for U, and divide by 0.098 (g * m) to find how high (in meters) your ball should start in the y direction above the launch point. Voila. 
#4




Re: Physics: ball launch using gravity
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Joe 
#5




Re: Physics: ball launch using gravity
Quote:
http://www.chiefdelphi.com/forums/sh...5&postcount=19 Have fun... 
#6




Re: Physics: ball launch using gravity
It's been a while since I posted here, but a few things have changed with the project, which is working quite well. First, here's the criteria for the ball launcher from the sheet my physics teacher gave:
Quote:
The device consists of a vertically standing PVC pipe that is 1.9 meters long. It provides the ball gravity acceleration. At the end of the pipe, I have 2 'hotwheels' flexible tracks that end about .75 horizontal meters away, pointing the ball 4555 degrees to the hoop. I need to know how exactly to measure the curve, circular or not. It was never drafted, and was tweaked SEVERAL times that any rough/initial draft with any accuracy would be no longer accurate. Pictures are attached of the device, or should I say ramp. As far as calculations are concerned, I know that I can get the speed and force before the ball hits the curve using v = gt and f = ma respectively since it's a relatively straight vertical drop. It's the curve that I need measured, and the angle I can get easily. Thanks again, and any ideas on how to get the ball just a wee bit higher would be really great. Joe Last edited by JoeXIII'007 : 03022006 at 02:10 PM. 
#7




Re: Physics: ball launch using gravity
Joe:
Does your calculation of drop height consider the rotational kinetic energy of the ball? (If not, this would explain why you are coming up short.) You may also be losing some energy due to flexure of those "hot wheels" tracks and perhaps some friction losses as well. So, you will need to drop the ball from a greater height to offset some of these loss factors. If you need the ball to go higher, you can increase the angle (with loss in distance traveled). 
#8




Re: Physics: ball launch using gravity
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Neglecting friction, the problem of finding the curve of steepest descent rate (which would maximize velocity at the bottom) is called the brachistochrone problem. The solution is a cycloid curve. The problem can be generalized using calculus of variations to include friction, rotational KE, etc. The descending section of your Hot Wheels track appears to be very close to a cycloid. 
#9




Re: Physics: ball launch using gravity
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Increasing the angle I have tried, but the loss of xdistance is too great. And yes, I have been trying to stiffen the tracks so that they would not absorb energy needed to launch. As far as height, we have considered going to the second floor and drilling a hole large enough to do that, but I do not think the administration and especially the custodial staff would like that. The top of the pipe is 1015 cm from the drop ceiling though, and perhaps if I could convince someone to let me move the tiles... hmm... yes. I'll have to do some good old fashined negotiating. Quote:
Interesting stuff though, can't wait until I learn it all, and thank you very very much for the insight. Joe PS: I wonder what my partner in this project is going to think of all this... Last edited by JoeXIII'007 : 03022006 at 06:41 PM. 
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