Puzzle Time - Rolling Balls

[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?

[Axtremus]

||Cycloidal, because that allows the fastest acceleration in the early phase of the roll.||

[AndyD]

Cycloidal (guessing the initial gravity/greater acc) Are they in order, right to left?

[Loki]

Wrong.

||we can’t we enough of the graph to know||

[jon-nyc]

||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.||

[Klaus]

@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.

[Aqua Letifer]

@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.||

[Horace]

This question is what defines a cycloid.

[Klaus]

@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.

[taiwan_girl]

@AndyD @Axtremus @jon-nyc @Aqua-Letifer

Good job guys!!!