Two automobiles A and B, of mass mA and mB, respectively,

Chapter 14, Problem 14.35

(choose chapter or problem)

Two automobiles A and B, of mass \(m_{A}\) and \(m_{B}\), respectively, are traveling in opposite directions when they collide head on. The impact is assumed perfectly plastic, and it is further assumed that the energy absorbed by each automobile is equal to its loss of kinetic energy with respect to a moving frame of reference attached to the mass center of the two-vehicle system. Denoting by \(E_{A}\) and \(E_{B}\), respectively, the energy absorbed by automobile A and by automobile B, (a) show that \(E_{A} / E_{B}=m_{B} / m_{A}\), that is, the amount of energy absorbed by each vehicle is inversely proportional to its mass, (b) compute \(E_{A}\) and \(E_{B}\), knowing that \(m_A=1600\mathrm{\ kg}\) and \(m_B=900\mathrm{\ kg}\) and that the speeds of A and B are, respectively, 90 km/h and 60 km/h.