- William C. Evans
This applet shows the solutions for the angles and speeds of two objects after an offset elastic collision. The lighter circle represents an initially-stationary object, of mass m2, while the darker circle is the moving object, with speed v1 and mass m1. The motion is from left to right horizontally. The grey dashed vector represents v1. The collision is controlled by the "impact parameter" b, which is the vertical distance between the circles' centers. The radii of the circles can be adjusted, independently of the masses. The "impact parameter ratio" is b/(r1+r2). The relation between r1, r2, and b will set up the geometry of the collision, while m1, m2, and v1 control the momenta and kinetic energy. The vectors represent the after-collision velocities. Their angles are measured from the horizontal, positive counterclockwise, as usual. Clicking and dragging the plot area will allow the image to be centered, as needed. The implementation has been tested, but of course not exhaustively, since so many parameter combinations are possible. (Please contact the author of this applet if any incorrect results are noted; send the exact setup, so the problem can be reproduced.) Setting b=0 will produce the usual 1D collision cases. Having the circles with the same radii is a good idea, since the circle size might easily be confused with its mass. Note that if the impact parameter ratio is greater than unity, the moving object disappears; this is a way of showing that there was no collision. The mathematics implemented in this applet was taken from a PDF (attached) found with a Google search. The author is Dr. J. B. Tatum, and this material can be found at www.astro.uvic.ca/~tatum, under "Classical Mechanics" Chapter 5. Some additional material was found in a paper by C.E. Mungan and T.C. Lipscombe, "Oblique elastic collisions of two smooth round objects", in Eur. J. Phys. 39 (2018).