• #1
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Introduction
This article follows on from the previous on an alternate approach to solving collision problems. In that article, we determined the equal and opposite collision impulse to have magnitude ##\mu \Delta v## for perfectly inelastic collisions, ##\mu(1+e) \Delta v## for semi-elastic collisions and ##2\mu \Delta v## for elastic collisions which will be the focus here. Reduced mass ##\mu=\frac{m_1m_2}{m_1+m_2}## – where ##m_1## and ##m_2## are the colliding masses – and ##\Delta v## is their relative velocity along the line of collision. e is the coefficient of restitution.
Since the previous article focused on 1-dimensional collisions, the aim here is to develop a method of solving 2-dimensional elastic collision problems using a Cartesian plane in which the x and y axes are defined to be respectively parallel and perpendicular (normal) to the line of collision. The latter is defined by the post-collision direction of the stationary mass since it cannot attain momentum...

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Likes PhDeezNutz, Hrishikesh Edke and Greg Bernhardt

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  • #2
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If you are looking at the elastic collision of two bodies, shouldn't you be solving for the transient elastic deformation of the bodies during the collision using Theory of Elasticity, involving Young's modulus, density, and Poisson ratio of the two bodies?
 
  • #3
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Thanks for the comment / query but I'm really not doing much more than follow the basic theory of 1-dimensional elastic collisions in which transient deformation is not usually dealt with. For example a bouncing ball deforms when it hits the floor but the energy is lost and then immediately regained. Very specifically in this article we are dealing with fully elastic 2D collisions (coefficient of restitution = 1). Have requested the graphic being used gets changed as it may create the wrong impression - car collisions are not at all elastic! Gravitational slingshots might be more pertinent examples of what's being described here.
 
  • #5
edguy99
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Great article, never thought about the relationship between refraction and momentum. Another amazing relationship is to apply a wave function to one of the particle sizes. Let one of the particles expand and contract at a certain frequency which adds to the dynamics of the collision (ie. if expanding or contracting, the particle will have another aspect to the collision). This extends the refraction/momentum model to include diffraction around edges.
 
  • #6
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Thanks for your kind comment - what I had been trying to do is see if somehow the theory can be adapted for Compton scattering. But haven't made much progress as yet. Can't quite figure what ##2 \mu \Delta v## (elastic collision impulse) looks like when we're talking about a photon/electron collision.
 

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