3 ms·
The article explicitly discusses the fact that this is possible specifically because of the shape of the dome, and does not work on a hemisphere, precisely for
by xyzzyz 3y ago
The article explicitly discusses the fact that this is possible specifically because of the shape of the dome, and does not work on a hemisphere, precisely for reason you bring up.
- kergonath 3y agoThe article explicitly discusses this without demonstrating anything. On it’s face this argument has the weight of these demonstrations.
- eesmith 3y agoYou are right - I misread it. The next step would be to verify that the paths always stay on the surface. The mathematics shown says the point always follows the surface, but I don't see a demonstration that that's true. I no longer have the skills to easily do this calculation. EDIT: Oh man, I used to be a lot better at this. I remember the mgh = 1/2 m v^2 and the slope calculation, but can't figure out how tell when the falling point mass detaches from the slope. If it detaches at h=0 then there's no physically viable reversed path on the surface.