A car of mass M, traveling with a velocity V, strikes a parked station wagon, whose mass is 2M. The bumpers lock together in this head-on inelastic collision. What fraction of the initial kinetic energy is lost in this collision?
A) 1/4
B) 1/3
C) 2/3
D) 1/2
E) 1/9

Question

Quizplus · Accepted Answer

In an inelastic collision, kinetic energy is not conserved. The initial kinetic energy is (1/2)MV^2. After the collision, the combined mass is 3M and the velocity is V/3 (from conservation of momentum). The final kinetic energy is (1/2)(3M)(V/3)^2 = (1/6)MV^2. The fraction of kinetic energy lost is (initial - final)/initial = [(1/2)MV^2 - (1/6)MV^2] / (1/2)MV^2 = 2/3.

A Car of Mass M, Traveling with a Velocity V