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Longer Path, Shorter Time

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Author: s_noonan

Group: Technical

Filesize: 6.48 kB

Date added: 2012-05-06

Rating: 6.1

Downloads: 870

Views: 443

Comments: 6

Ratings: 3

Times favored: 0

Made with: Algodoo v2.0.1 Edu


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What kind of curve results in the fastest time?

See The Brachistochrone Problem .
Last edited at 2016/07/02 20:59:53 by s_noonan
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ok... i am like totally confused right now. can anybody explain to me why this happens?

My thought was that the faster ball "borrows" potential energy and converts it to kinetic energy at the first bend and then and then "returns" the potential energy by converting kinetic energy to potential energy at the second bend. The borrowed energy gives it faster speed.

There must be a another explanation. I would like to hear it. Anyone?
my initial thought was because the downward ramp was steeper than the upward ramp, giving more energy to the ball than was removed (which still is correct) however if I rotate the device -5 degrees (so it is horizontal), and apply a 5 m/s impulse to the two balls, the blue ball still travels the same distance faster than the green ball, great find, Noonan:D, I will do further research on this
This event only happends on a GLOBE, or an object with GRAVITY... out in space with no effects of gravity, given the same initial velocity, they will arrive at their destination at precisely the same time.
2 dirtrider08,

I agree that this event only happens only with GRAVITY, but...

If no gravity, then the balls won't follow the tracks. The initial velocity of each ball is zero, so they would never arrive at their destination.

Here's a thought... Two balls in space, one has 10X the initial velocity as the other, both start out at the same position, the faster ball gets to the destination 10x faster, both balls use the same amount of energy (zero) because no friction and no speed change.

So you're probably thinking that you need more energy to accelerate the faster ball. OK, so we can accelerate the ball with a spring attached to the ball and when we reach our destination we can reverse the process by compressing the spring and slowing the ball in the process. If the spring starts and ends with the same compressed length, then the net energy usage is zero.

Do you concur?