It is assumed that each of the two automobiles involved in the collision described in Prob. 14.35 had been designed to safely withstand a test in which it crashed into a solid, immovable wall at the speed v0 The severity of the collision of Prob. 14.35 may then be measured for each vehicle by the ratio of the energy it absorbed in the collision to the energy it absorbed in the test. On that basis, show that the collision described in Prob. 14.35 is (mA.mB)2 times more severe for automobile B than for auto mobile A.
Reference to Problem 14.35:
Two automobiles A and B , of mass mA and mB , 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 EA and EB , respectively, the energy absorbed by automobile A and by automobile B (a) show that EA/EB= MA/mB , that is, the amount of energy absorbed by each vehicle is inversely proportional to its mass, (b) compute EA and EB , knowing that mA= 1600 kg and mB= 900 kg and that the speeds of A and B are, respectively, 90 km/h and 60 km/h.
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