Movement of a ball on curved trajectory

[chronicx]

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

 

[jedishrfu]

Welcome to PF.

This looks like a homework assignment. You need to follow the homework template. We can't do your work for you can give you hints to get going.

Homework Statement

Homework Equations

.[/B]

The Attempt at a Solution

 

[chronicx]

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.

 

[ratchettrack]

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

 

[jedishrfu]

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.

 

[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.

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

 

[jbriggs444]

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.

 

[chronicx]

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?

 

[ratchettrack]

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