Irodov Problem 1.174

The velocity vectors of masses m1 and m2 are given by (v1 i + 0 j) and (o i + v2 j) respectively. The velocity of the center of mass is then given by,


The velocities of the particles relative to a frame fixed to the CG are given by,














Thus, momenta of either particles as seen from the center of mass will be




The kinetic energy of the entire system as seen from CG will be given by,

Irodov Problem 1.173

As there are no external force the total momentum of the system before and after impact must be conserved at all times. So we have,




The change in kinetic energy between before and after collision is given by,


The fractional change is thus .

Irodov Problem 1.172

Let v be ball 1's initial velocity and let the velocities of balls 1 and 2 after the collision be v1 and v1. Since there are no external forces on the system, the momentum must be conserved. So we have,



The kinetic energy after collision decreases by a fraction we have,















Since v1 > v2 is not possible (for this ball 1 would have to pass through ball 2 and move ahead) we choose . This also means that v1 will always be positive, in other words it will not change its direction.