ABSTRACT
In this chapter, we consider a somewhat more general case, in which two bodies experience momentum conservation while colliding in a plane. Rotational effects are not considered, which means the impact is central (contact forces pass through the centers of mass), that rotational motions are not significant, or that rotational inertia is insignificant (i.e., the bodies are particles). Each body thus has two degrees of freedom, instead of one in uniaxial collisions, or three if rotational effects are considered. Since the two bodies are taken together as a system, contact forces do not enter the picture. If forces external to the system are negligible, momentum is conserved during the crash phase. This can be expressed mathematically as
L LX X= ′ (20.1)
L LY Y= ′ (20.2)
or
m V m V m V m VX X X X1 1 2 2 1 1 2 2+ = ′ + ′ (20.3)
m V m V m V m VY Y Y Y1 1 2 2 1 1 2 2+ = ′ + ′ (20.4)
Again, the primed velocities may be considered as known, being determined during the analysis of the run-out phase. The velocities without primes are the unknowns. We see that we have four unknowns, with only two equations available from momentum conservation considerations. Again, there is a gap to be filled.
