# Elastic collision considering the angle of impact

luckis11
https://www.plasmaphysics.org.uk/collision2d.htm

This is the only one I found, but when I plug in the numbers of his example I get a wrong result. Do you know any others who solved it i.e. considering the angle of impact? Angle of impact I name the angle that is shaped between the initial dx with the surface that separates the 2 balls at the time of impact (the other ball is still before the impact).

Homework Helper
Gold Member
Please be more specific. What is the question you are trying to answer? What numbers are you plugging in and what result do you get? Why do you say that the result is wrong? The angle of impact is defined in the link you posted and presumably the equations in the link are based on that definition. I am not sure whether your definition is the same because I don't understand it.

luckis11
The only thing I asked is if you know other sites that solved the same problem as he did. I do not know if he solved it correctly, I just find it impossible to understand it better (and thus get correct results), so the only solution is another site.

luckis11
Fred Wright
The only thing I asked is if you know other sites that solved the same problem as he did. I do not know if he solved it correctly, I just find it impossible to understand it better (and thus get correct results), so the only solution is another site.
You can down load Landau and Lifshitz "Mechanics" for free. Google " Landau and Lifshitz Mechanics pdf". Read pages 44-46 which is a derivation of the problem in center of mass coordinates.

Staff Emeritus

Legally? Lots of things are on the web that aren't exactly legal.

At the time of the collision it's most convenient to take a coordinate system with one axis (the ##x##-axis, say) parallel to the line of centres of the two spheres. Then, resolving the two initial velocities ##\mathbf{u}_1 = (u_{1x}, u_{1y})## and ##\mathbf{u}_2 = (u_{2x}, u_{2y})##, and similarly for the final velocities ##\mathbf{v}_1## and ##\mathbf{v}_1##, you can write one equation using that the coefficient restitution ##e=1##, $$u_{1x} - u_{2x} = v_{2x} - v_{1x} \ \ \ (1)$$then one equation by conserving the ##x##-momentum,
$$m_1 u_{1x} + m_2 u_{2x} = m_1 v_{1x} + m_2 v_{2x} \ \ \ (2)$$and those two equations can be easily solved given ##u_{1x}## and ##u_{2x}##. Further, since the impulse either exerts on the other has only an ##x##-component, you can write down ##u_{1y} = v_{1y}## and ##u_{2y} = v_{2y}##.
Here, the equations of this, where are they. And they took in account the angle of impact or they theorized that it is 45 degrees?
I don't think "45 degrees" is a relevant number for that simulation!

luckis11
You must be kidding me. Think it over.

@luckis11 that is not very nice, so I will not help you any more. [Also, this thread really ought to be "B" level, it is a fairly common school-level maths question in the UK at least.]

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