Timeline for Bouncing a ball down the stairs
Current License: CC BY-SA 3.0
15 events
| when toggle format | what | by | license | comment | |
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| Nov 4, 2015 at 15:45 | history | edited | Jeff Strom | CC BY-SA 3.0 |
deleted 1 character in body
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| Jun 24, 2014 at 0:37 | answer | added | Brendan McKay | timeline score: 8 | |
| Jun 23, 2014 at 23:16 | comment | added | Jeff Strom | Rolling it down will put a bunch of energy into the spin, so it would be going slower at any given depth. I'm proposing to bounce the ball, either down a slope or down some stairs. | |
| Jun 23, 2014 at 20:44 | comment | added | Ryan Budney | It seems to me, in that case the limiting situation would be the ball making very shallow collisions with rather infrequent stair corners. So I think it should be faster than a roll down a straight slope. | |
| Jun 23, 2014 at 20:31 | comment | added | Jeff Strom | @ryan: yes, that's my idea. | |
| Jun 23, 2014 at 20:07 | comment | added | Ryan Budney | "Bounces" are instantaneous mirror reflections of the velocity vector? Basically a completely elastic collision with a rigid, frictionless disc, and an immovable staircase? | |
| Jun 23, 2014 at 17:04 | comment | added | Jeff Strom | Yes, this model eliminates friction, hence spin, for simplicity. | |
| Jun 23, 2014 at 16:33 | comment | added | Victor Protsak | Direct observation shows that a bouncing ball inevitably spins forward. So it is not just the question of the motion of the center of mass. | |
| Jun 23, 2014 at 16:05 | comment | added | Jeff Strom | @BenBarber Right! and then sometimes it hits flat or almost flat and gets very little forward thrust. Then meanwhile the ball on the ramp gets the "same" proportional forward thrust each time. So this is some kind of averaging question. | |
| Jun 23, 2014 at 15:45 | comment | added | Ben Barber | I've often bounced cricket balls down stairs. If the ball catches the corner of a step just right then it can suddenly shoot forward very quickly. I don't know if this model captures enough of the physics to have the same behaviour. | |
| Jun 23, 2014 at 14:57 | history | edited | Jeff Strom | CC BY-SA 3.0 |
grammar
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| Jun 19, 2014 at 11:43 | comment | added | Joseph O'Rourke | Just a tangent: When the ball has friction and can spin, a ball thrown down the stairs can actually climb up a bit. See this MO question, and especially this figure. | |
| Jun 19, 2014 at 3:00 | comment | added | The Masked Avenger | Now that I've seen that the ball has large enough radius, I suspect the answer is that it will be faster, because the ball will tend to impact the stair at a shallow angle and so receive more of a propelling force than a retarding force. I'm curious as to what a simulation would reveal. | |
| Jun 19, 2014 at 2:53 | comment | added | The Masked Avenger | On a (likely with probability 1) set of conditions, the ball will go slower, because the forces it receives from the staircase will be more in opposition to gravity than those from a ramp of similar slope. (This may be true even for balls of large radius, but is less clear.) The only time the ball might go faster is if it hits the corner of the stair in a way that the force is directed more horizontally than it would be from the ramp. This depends strongly on the ratio of ball radius to stair step dimensions. | |
| Jun 19, 2014 at 0:59 | history | asked | Jeff Strom | CC BY-SA 3.0 |
