Movement of a ball on curved trajectory

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Discussion Overview

The discussion revolves around the motion of a ball on a vertical parabolic ramp, specifically whether the ball will travel all the way from point A to point B or stop halfway due to its motion characteristics. Participants explore the physics involved, considering factors such as friction, rolling motion, and energy conservation.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants propose that without any resistance, the ball will travel all the way to point B and oscillate back and forth between points A and B.
  • Others argue that the ball will roll down the ramp, converting some energy into rolling motion, which may affect its ability to reach point B.
  • A participant suggests that if the ball transitions from not rotating to rotating, it would eventually stop at the bottom center of the ramp due to energy dissipation.
  • Another participant challenges this by stating that rotational motion does not inherently dissipate energy.
  • One participant questions whether the ball, when released from rest near point A, would still reach point B under the assumption of no resistance and no initial velocity.
  • It is noted that if there were no rotation and no resistance, the ball would return to a height equal to the distance it fell.

Areas of Agreement / Disagreement

Participants express differing views on the effects of rolling motion and energy conservation, leading to unresolved questions about the ball's ultimate behavior on the ramp. There is no consensus on whether the ball will reach point B or stop midway.

Contextual Notes

The discussion includes assumptions about the absence of friction and external forces, as well as varying interpretations of energy dynamics in rolling motion. These factors remain unresolved within the conversation.

chronicx
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http://i47.tinypic.com/mt55s7.jpg

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You drop a ball on this vertical parabola with point A as starting point and point B as ending point. What is the expected natural movement of the ball that is set into motion with no external force assuming no friction? Would it go all the way from point A to point B or halfway to point B and come to rest at the middle of the curve?

I am also trying to find some evidence or literature from some text to confirm of such expected motion.. however most of the examples I see are more related to an object falling in a downward parabola or other examples on a downward projectile.

Many thanks
 
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The Attempt at a Solution

 
Its not exactly homework question. I am working on a academic proposal and need to understand the physics on such ramp for stimuli. So i wanted to know about this question in general terms.. i am not looking for any calculations as such. So posted in general section. Just need some explanation or some pointing to certain source.
 
chronicx said:
http://i47.tinypic.com/mt55s7.jpg

-See for image

You drop a ball on this vertical parabola with point A as starting point and point B as ending point. What is the expected natural movement of the ball that is set into motion with no external force assuming no friction? Would it go all the way from point A to point B or halfway to point B and come to rest at the middle of the curve?

I am also trying to find some evidence or literature from some text to confirm of such expected motion.. however most of the examples I see are more related to an object falling in a downward parabola or other examples on a downward projectile.

Many thanks

Without any resistance to slow it down, its going to go all the way to B. It would then continously go from A to B back and forth.

Ratchettrack
 
ratchettrack said:
Without any resistance to slow it down, its going to go all the way to B. It would then continously go from A to B back and forth.

Ratchettrack

I think you need to consider that it will roll down the track and as a result some energy will be in the rolling motion. So the next question would be if there's any resistance to the rolling.
 
jedishrfu said:
I think you need to consider that it will roll down the track and as a result some energy will be in the rolling motion. So the next question would be if there's any resistance to the rolling.

Your right. With the ball having to go from not rotating to rotating to not rotating...
It would eventually stop in the bottom center of the shape. Even if it was a mass on a sled, there would still be rotation. Only if the mass didn't rotate and there wasn't anything to inpede its movement, would it go on forever.

Ratchettrack
 
ratchettrack said:
Your right. With the ball having to go from not rotating to rotating to not rotating...
It would eventually stop in the bottom center of the shape. Even if it was a mass on a sled, there would still be rotation. Only if the mass didn't rotate and there wasn't anything to inpede its movement, would it go on forever.

This is incorrect. There is nothing inherent in rotational motion that dissipates energy.
 
I understand that as the ball goes down the ramp, it acquires some energy and it carries itself to point B. Assuming (a) no resistance from the ramp (b) no initial velocity - the ball isn't being let go from a certain height. It is just being held near the point A and let go. without any added manipulations and based just due to gravity, would it still go all the way to B?
 
chronicx said:
I understand that as the ball goes down the ramp, it acquires some energy and it carries itself to point B. Assuming (a) no resistance from the ramp (b) no initial velocity - the ball isn't being let go from a certain height. It is just being held near the point A and let go. without any added manipulations and based just due to gravity, would it still go all the way to B?

If there was no rotation and resistance, the ball will go back up a distance equal to what it fell.

Ratchettrack
 

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