Physics: ball launch using gravity

[Richard Wallace]

Originally Posted by JoeXIII'007

Thanks again, and any ideas on how to get the ball just a wee bit higher would be really great.

-Joe

This may be a bit late in your project and a bit too abstract to be useful, but..

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.

[JoeXIII'007]

Originally Posted by David Brinza

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).

Actually, the 1.9 meter length of the pipe was arbitrary, because I bought over at a hardware store, and they cut it there. I do have the other half, however. I have actually gone the experimental route in developing the launcher.

Increasing the angle I have tried, but the loss of x-distance 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 10-15 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.

Originally Posted by Richard

This may be a bit late in your project and a bit too abstract to be useful, but..

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.

I'm studying Pre-calc, not calculus quite yet, that's a problem. But if I were to sit down and take some time with it, maybe I could figure it out. Otherwise I do not need to bother my physics teacher with more stuff to read over, since he was assuming everyone was going to build a simple catapault or trebuchet. Plus, he's got a hockey team, robotics team, TV productions, and this physics class to handle (a lot of people need help on simple physics stuff, I always try to help out). SO, I'll have to ask him what exactly he would like as far as calculations for the device.

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...