Bounce a ball off a round post: where does it go?

[Drmarshall]

I am writing a QBASIC program that simulates the game of Bagatelle

The scattering of He nuclei by gold ions is a famous formative experiment and the ion beam is deflected thru angle theta= 2 times anctan(K/s)
But my target (the post) is NOT of zero radius - it is radius R
And my ions are radius r
So they "collide" when distance r+R apart
I can simulate this by doing a repulsion calculation as inverse 12th power distance (from collision distance), but what I want to do is the "simpler" (!) mechanical "bounce off the tangent mirrer" task.

After two days work I am still stuck

help! (please)

 

[Whovian]

Dunno if this answers your question (no offence, but I couldn't make perfect sense of this,) but I have two things that might help.

First, a pointlike object bouncing off a surface of sorts, assuming it bounces off instantaneously, should behave like a pointlike object bouncing off of the tangent plane to that surface. Basic geometry, or, if you prefer, calculus, though it's harder to do it that way, give you a way of finding this.

Second, how can you relate a tennis ball of radius r bouncing off a cylinder of radius R to a pointlike object bouncing off a tennis ball of radius r+R?

 

[my_wan]

Instead of collision detection your program can simply test for proximity. If proximity = r+R then you can assume a collision is occurring. At this point you can then treat the recoil as if the ion had a zero radius and collided with a zero radius post at the center position of the ion.

 

[Drmarshall]

Instead of collision detection your program can simply test for proximity. If proximity = r+R then you can assume a collision is occurring. At this point you can then treat the recoil as if the ion had a zero radius and collided with a zero radius post at the center position of the ion.

No, part of my difficulty is I am not SURE this assumption -that everyone says is obvious! - is right.

Suppose the projectile radius R passes by the target post at grazing incidence (Distance R+r)
Then it suffers NO deviation.

On a "direct hit" path it suffers 180 deg deviation

Somewhere in between it suffers 90 deg deviation
This 90 deg is FROM a point for which the line joining centres is 45 deg at instant of impact.
So it is for a projectile that WOULD HAVE passed (were the target removed) at a distance (R+r)/sqr(2) from where the target centre was.
It gets deviated BEFORE it reaches the 90 deg line thru the target and thus hits the next post at a position that depends on BOTH this position AND the deflection.

 

[my_wan]

If at the point of impact you draw line A from center point r to center point R, then at the center of the ion draw line B perpendicular to A. Then the ion will recoil as if recoiling off a wall at B.

 

[Drmarshall]

If at the point of impact you draw line A from center point r to center point R, then at the center of the ion draw line B perpendicular to A. Then the ion will recoil as if recoiling off a wall at B.

Yes that is right
The ion SEEMS to have come NOT from the centre of the target but from a position that VARIES with the direction into which it was deflected.

 

[Simon Bridge]

The ion SEEMS to have come NOT from the centre of the target but from a position that VARIES with the direction into which it was deflected.

(a) that's not what he's saying though is it?
(b) you said you only needed a simulation - so "seeming" is good enough.

Why would anyone expect the projected point of collision to coincide with the center of the target: the target has an extent in space?

At what level of detail do you need your model to operate at?
You seem to be describing programming tasks that have solution code in physics libraries.

 

[Drmarshall]

(a) that's not what he's saying though is it?
(b) you said you only needed a simulation - so "seeming" is good enough.

Why would anyone expect the projected point of collision to coincide with the center of the target: the target has an extent in space?

At what level of detail do you need your model to operate at?
You seem to be describing programming tasks that have solution code in physics libraries.

The "well known" solution that the beam is deflected 2atn(k/s) is only ONE PART of the answer.
To know where it goes we need MORE that a mere direction.
We need one point on its path.
For a real target etc this point is NOT the centre of the target.
It changes with the position of the point at which instantaneous contact is made.

As you point out, this is obvious. So how is it related to the beam incident direction and contact-with-target position?

 

[Nugatory]

Try this... First identify the point of contact. That's easy to do if you're tracking the cener of the ball, it'll be the point of intersection at the moment that the center of the ball a distance r+R from the center of the post. Then calculate the tangent plane of the post at that point, construct another plane parallel to that tangent plane and passing through the center of the ball. Now treat the center of the ball as a point particle bouncing off that second plane.

 

[Simon Bridge]

At what level of detail do you need your model to operate at?

You don't answer questions you cannot get good help.

i.e. do you need to model the actual trajectory as of a coulomb repulsion as in Rutherford scattering or do you just want the ball-bounce model?

The "well known" solution that the beam is deflected 2atn(k/s) is only ONE PART of the answer.

I never said anything about that - I said that the code that solves your described problems exists in programming libraries. Look up "physics engine".

To know where it goes we need MORE that a mere direction.
We need one point on its path.
For a real target etc this point is NOT the centre of the target.
It changes with the position of the point at which instantaneous contact is made.

Of course it does - but you know the geometry of the target don't you?
Nugatory keeps telling you how to do it.

You have the initial direction and position - the geometry and position of the target?

 

[Drmarshall]

You don't answer questions you cannot get good help.

i.e. do you need to model the actual trajectory as of a coulomb repulsion as in Rutherford scattering or do you just want the ball-bounce model?

The ball bounce.
We are playing Bagatelle - as I said at the biginning.

 

[Simon Bridge]

Then why do you keep going on about Rutherford scattering and beams?
You've established that you cannot model the ball hitting the stick the same way as rutherford scattering so why keep bringing it up?

Do you need the ball to be tracked throughout the fine detail of the bouce - i.e. the deformation, spin etc. or is it good enough to get the rebound trajectory right?