Two Dimensional Collisions


Hi Mr. Jones.

My partner and I were looking at your notes on the web and found some interesting information about momentum. Coincidentally, my partner and I are working on a project involving billiard balls. We would just like to confirm that we are interpreting your notes and equations correctly.

For the 2D equation case, we just need to use the two equations:
v1 = v1i * (m1-m2)/(m1+m2) + v2i * (2*m2)/(m1+m2), and
v2 = v1i * (2*m1)/(m1+m2) + v2i * (m2-m1)/(m1+m2)

where v1,v2 represent the change in line of sight velocity vectors. v1i and v2i can be vectors (x,y,z) formed by the initial velocities projected onto the line of sight. v1 and v2 are then added to the corresponding initial velocities.

I'd like to make sure our interpretation is correct and that we can indeed use "vectors" rather than scalars for v1i and v2i.


(My physics are a bit rusty =). It's been 3.5 years since I had a course in physics.)


Your interpretation of the equations and concepts involved in two dimensional collisions is essentially correct. Your statement "use 'vectors' rather than scalars for v1i and v2i" made me think a bit. The projection of a vector onto a particular line is not much different than a scalar. In fact the magnitudes of the projected vectors, which are scalars, are the quantities used in the equations.

You might want to check out an alternative way to model multi-dimensional collisions. In our MechLab program we create virtual objects with spherical symmetry by a representation of the potential energy resulting from their interaction and actually let them collide in model space to see what happens. This allows us to handle up to three objects in three dimensions, a situation where the geometric approach is way too messy.

This information is brought to you by M. Casco Associates, a company dedicated to helping humankind reach the stars through understanding how the universe works. My name is James D. Jones. If I can be of more help, please let me know.