- #36

TonyCross

- 66

- 12

I never imagined when I asked this question it would be so complex. Thanks for putting this effort, it must have taken you ages..TSny said:I attempted to use Mathematica to numerically solve the equations of motion and generate some animations.

The tube is represented by a semicircle. I varied the mass ratio M/m, where M is the mass of the tube and m is the mass of the ball. The animations start at the instant the particle enters the tube on the left.

Here is the choice M/m = 2

View attachment 272194

The ball makes it all the way through the tube. The final angular velocity of the tube is zero. I found this to be the case whenever the ball makes it all the way through the tube. The red dot is the center of mass of the system. The small black dot is the center of mass of the tube.The next case is for M/m = 1/3.

View attachment 272195

Now the ball does not make it all the way through the tube. It exits the same end of the tube in which it entered. The final angular velocity of the tube is not zero.There is a critical value of the ratio M/m equal to ##\large \frac{4\pi-\pi^2}{\pi^2-4} \normalsize\approx 0.46## where the ball gets stuck at the apex of the tube.

View attachment 272196

Of course, all of the above depends on the correctness of the equations of motion and the programming.