Frictionless impact refers to short interactions when there is no noticeable effect due to friction.
The free-body diagram of the two particles during the collision is The impulse momentum for each particle is Where and are the externally applied forces. The general impulse momentum relation for this system will be An empirical relation is used to account for the loss of mechanical energy in the impact. This relation is between the relative speed that the particles approach each other and the relative speed that they separate from each other. This relation is , where e is the coefficient of restitution , an empirical constant between 0 and 1. In an elastic collision the magnitude of the normal component of the relative velocity before and after the collision is the same.