Puzzle Time - Rolling Balls
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wrote on 22 Nov 2020, 17:23 last edited by
Four identical ball on four different tracks are released at the same time. Which of the tracks - bent, straight, circular, or cycloidal - will deliver the ball to the end of the slope the fastest?
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wrote on 22 Nov 2020, 18:11 last edited by Klaus
Interesting. I remember very little physics. But the total energy of the balls must stay the same. The initial energy is something like m* g * h if I remember correctly. This gets translated into a mix of rotational energy (how fast the ball rotates) and translational energy (how fast the ball moves). So I'd say the fastest ball is the one that rotates the slowest. I presume that the shortest track - the straight line - yields the slowest rotation, hence I'd go with that one.
My confidence: About 40%.
We are supposed to ignore heat, rolling resistance etc., right?
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wrote on 22 Nov 2020, 18:32 last edited by
||Cycloidal, because that allows the fastest acceleration in the early phase of the roll.||
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wrote on 22 Nov 2020, 18:36 last edited by
Cycloidal (guessing the initial gravity/greater acc) Are they in order, right to left?
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wrote on 22 Nov 2020, 19:58 last edited by
Wrong.
||we can’t we enough of the graph to know||
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wrote on 22 Nov 2020, 20:05 last edited by
||Cycloidal. I know enough physics to work out a proof but the fact that high end skate pipes are cycloids tells me someone else already did.||
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Interesting. I remember very little physics. But the total energy of the balls must stay the same. The initial energy is something like m* g * h if I remember correctly. This gets translated into a mix of rotational energy (how fast the ball rotates) and translational energy (how fast the ball moves). So I'd say the fastest ball is the one that rotates the slowest. I presume that the shortest track - the straight line - yields the slowest rotation, hence I'd go with that one.
My confidence: About 40%.
We are supposed to ignore heat, rolling resistance etc., right?
wrote on 22 Nov 2020, 20:23 last edited by@Klaus said in Puzzle Time - Rolling Balls:
Interesting. I remember very little physics. But the total energy of the balls must stay the same. The initial energy is something like m* g * h if I remember correctly. This gets translated into a mix of rotational energy (how fast the ball rotates) and translational energy (how fast the ball moves). So I'd say the fastest ball is the one that rotates the slowest. I presume that the shortest track - the straight line - yields the slowest rotation, hence I'd go with that one.
My confidence: About 40%.
We are supposed to ignore heat, rolling resistance etc., right?
Oh, I just see that I misread the question.
You are asking for which ball reaches the end of the slope the fastest. I believe Jon is right about that one. Isn't that a famous historical problem?
I somehow read your post as asking for which track yields the highest terminal speed, and I still guess that the straight line has that property.
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||Cycloidal. I know enough physics to work out a proof but the fact that high end skate pipes are cycloids tells me someone else already did.||
wrote on 22 Nov 2020, 21:37 last edited by@jon-nyc said in Puzzle Time - Rolling Balls:
||Cycloidal. I know enough physics to work out a proof but the fact that high end skate pipes are cycloids tells me someone else already did.||
||Same. Acceleration's relationship to movement vectors and time is a thing.||
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wrote on 22 Nov 2020, 21:50 last edited by
This question is what defines a cycloid.
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wrote on 22 Nov 2020, 22:07 last edited by
@Horace said in Puzzle Time - Rolling Balls:
This question is what defines a cycloid.
It is defined as the path shape which yields the fastest traveling time for a rolling ball.
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wrote on 23 Nov 2020, 01:13 last edited by
@AndyD @Axtremus @jon-nyc @Aqua-Letifer
Good job guys!!!