- #1

luckis11

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By the angle θ they mean some angle before or during the collision, or after the collision?

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- Thread starter luckis11
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- #1

luckis11

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By the angle θ they mean some angle before or during the collision, or after the collision?

- #2

Dale

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It is the angle before the collision

- #3

luckis11

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Any drawing that shows that angle?

- #4

A.T.

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Have you looked at reference the Wikipedia article is based on?Any drawing that shows that angle?

https://archive.org/details/mechanics00land/page/46/mode/2up

- #5

luckis11

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- #6

luckis11

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https://www.plasmaphysics.org.uk/collision2d.htm

where he says:

"

So, I examined whether Θ is Wikipedia's θ, with a particular example with numbers. And I saw that either Θ is not θ, or the solution they found violates the conservation of momentum.

- #7

sophiecentaur

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At the risk of repeating this idea (Wiki says it all, actually): Initially, angles have to be relative to the line of centres. For circles / spheres, the two faces can only have normal incidence. And, of course, because you don't know the answer yet, you start with the angle of incidence and work out the final angle. The difference will be the scattering angle. (Re-arrange the equations if necessary to get out what you want)

By the angle θ they mean some angle before or during the collision, or after the collision?

Classic school problem (at simplest level - I did loads of those in A level applied maths) You just consider momentum conserved along line of centres and assume that velocity, perpendicular to line of centres is not changed (no friction).

If you are finding some apparent conflict between sources, ignore it and start from basics. No conservation violation then.

- #8

cmb

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For any particle to take or drop 'out of plane' net energy would involve energy via some intermediary, I think, such as an imposed torque from a spinning particle and a friction impulse/nuclear force/EM interaction, and thus always not elastic?

A multi-body collision, one would probably have to resolve one collision pair before another.

I suppose there is a class of electrostatic interactions where one particle might approach a pair of particles already interacting, but one would assume the 2D to be between the one particle and the centre of mass/charge of 'the others', however many, so still a calculation in a 2D plane?

- #9

- #10

luckis11

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Here at the drawing it seems that Θ is an angle AFTER the collision, and it has the same equations as Wikipedia's where Θ=θ. ΤΗΕΝ, Dale gave me the wrong answer, as well as this friend here who says:

"

https://www.plasmaphysics.org.uk/collision2d.htm

΅where at his drawing you can see that

- #11

Dale

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I did not give you the wrong answer. You asked specifically about the Wikipedia article where it clearly and specifically says “θ1 and θ2 are their movement angles, that is, ##v_{1x}=v_{1}\cos \theta _{1},\;v_{1y}=v_{1}\sin \theta _{1}##”. Where they are writing post collision quantities with primes and pre collision quantities without. My answer was correct.Here at the drawing it seems that Θ is an angle AFTER the collision, and it has the same equations as Wikipedia's where Θ=θ. ΤΗΕΝ, Dale gave me the wrong answer

Other sources may use different variables, but that does not make my answer wrong. Don’t go criticizing me here.

- #12

luckis11

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Excuse me but θ1 and θ2 are the angles of the two dx's with the axis of x, AFTER the collision.

- #13

Dale

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No, they are not. Read the text.Excuse me but θ1 and θ2 are the angles of the two dx's with the axis of x, AFTER the collision.

- #14

luckis11

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https://phys.libretexts.org/Bookshe..._Collisions_in_Center-of-Mass_Reference_Frame

v2f is clearly a velocity after the collision, as well as θ2f.

- #15

Dale

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I am glad that you have found a better reference. Please use the better reference instead of Wikipedia. But please do not call me out by name and claim that I specifically gave you a wrong answer when I did not.

- #16

luckis11

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- #17

Dale

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It does bother me. I did not give you a wrong answer. Simply telling me to not be bothered doesn’t fix that.do not bother whether you gave me a wrong answer or not

- #18

luckis11

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OK, I take it back, I do not know whether you gave me a wrong answer or not because I am stupid. But whoever are really interested in the topic can respond to my last post.

Last edited:

- #19

Dale

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Thank you. I appreciate that. Although, I did not call you stupid.OK, I take it back, I do not know whether you gave me a wrong answer or not because I am stupid. But whoever are really interested in the topic can respond to my last post.

I will compare the plasma physics and libretext pages

- #20

Dale

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I didn't see any clear mistake. A definition like ##\alpha = (\pi - \Theta)/2## cannot be wrong, it is true by definition.the professor at plasmaphysics.com says a mistake by saying thatα=(π-Θ)/2, because the "center-of -mass scattering angle Θ"is what they mean at phys.libretexts.org by saying "The angle ΘcmΘcm between the incoming and outgoing velocities is called thecenter-of-mass scattering angle"and that has NOTHING to do with his "α".

That said, I found the plasmaphysics presentation very difficult to follow. They really should use LaTeX to make their site readable. I would recommend sticking with the libretext page instead regardless of whether or not there is an actual mistake on plasmaphysics.

- #21

luckis11

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- #22

Dale

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Sure, but he can always define a quantity ##\alpha## to be whatever he wants. There is nothing wrong with him defining it to be whatever.And he is not true by definition because by Θ he clearly states that he means what the others mean by Θ.

- #23

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Actually, I think the wiki page (at least) switches to the COM frame, in which the two velocity vectors are in opposite directions by definition. It makes the maths easier, and you can always switch back to your desired frame afterwards.I am not any more interested in the solution of Wikipedia and libratexts, because I just found out they ignore the angle of impact α.

- #24

sophiecentaur

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Why would you expect them to? If you are doing more than A/B comparison of different articles about this topic then I'd assume that you can derive your own equations with your own terminology.But at that simulator they do not say the equations.

You should remember that the

The Maths is very straightforward.

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