PHYSICS · Subjective · AP · Physics C: Mechanics · Linear Momentum · Linear Momentum
Problem
Two identical smooth steel balls A and B, each of mass m, lie on a perfectly smooth horizontal table. Ball A is projected with speed u along the +x–direction while ball B is at rest. The balls undergo a perfectly elastic collision and afterwards move freely on the table.
(a) Taking the centre of mass of the two-ball system as an inertial frame, write the momentum conservation equations along mutually perpendicular x and y axes.
(b) By eliminating the magnitudes of the final velocities, prove mathematically that the directions of motion of the two balls after collision are perpendicular to each other.
(c) Establish that the kinetic energy of the system remains the same before and after the collision.
(d) Comment, with reasons, on how the result in part (b) would change if the masses of the two balls were unequal.