At a classic auto show, a 840-kg 1955 Nash Metropolitan motors by at 9.0 m/s, followed by a 1620-kg 1957 Packard Clipper purring past at 5.0 m/s. (a) Which car has the greater kinetic energy? What is the ratio of the kinetic energy of the Nash to that of the Packard? (b) Which car has the greater magnitude of momentum? What is the ratio of the magnitude of momentum of the Nash to that of the Packard? (c) Let ?F?N be the net force required to stop the Nash in time ?t?, and let ?F?p be the net force required to stop the Packard in the same time. Which is larger: ?F?N or ?F?P? What is the ratio ?F?N/?F?P of these two forces? (d) Now let ?F?N be the net force required to stop the Nash in a distance d, and let ?F?P be the net force required to stop the Packard in the same distance. Which is larger: ?F?N or ?F?P? What is the ratio ?F?N/?? ?

Solution 76P Problem (a) Step 1: Mass of Nash Metropolitan m = 840.0 Kg 1 Mass of Packard Clipper m = 1620.2Kg Speed of Nash Metropolitan v = 9.0 m1 Speed of Packard Clipper v = 5.0 2 Step 2: 1 2 Kinetic energy of Nash Metropolitan K = 1 2 m1 1 1 2 K1 2 *840*9 K = 34.02 KJ 1 Step 3: 1 2 Kinetic energy of Packard Clipper K = 2 2 m2 2 K2 1 *1620*5 2 2 K = 20.20 KJ 2 Kinetic energy of Nash Metropolitan is greater. Step 4: Ratio of the kinetic energies K 1 = K 2 = 34.02 K 20.20 K = 1.68 Ratio of the kinetic energy of the Nash to that of the Packard is 1.68 Problem (b) Step 1: Momentum of Nash Metropolitan P1 m 1 1 P = 840*9 1 P1 7560 Kg.m/s Step 2: Momentum of Packard Clipper P2= m 2 2 P2= 1620*5 P2= 8100 Kg.m/s Momentum of Packard Clipper is greater Step 3: Ratio of Momentum P1 = P 2 7560 = 8100 = 0.93 Ratio of the Momentum of the Nash to that of the Packard is 0.93 Problem (c) Step 1: Force required to stop the Nash in time t = F N Force required to stop the Packard in time t = F P P 1 FN t P 2 FP t Since force is directly proportional to rate of change in momentum F is greatP than F N F > F P N Step 2: Ratio of forces F N P 1 F P = P 2 or F N P 1 F P = P 2 = 0.93 or F = 0.93F N P Problem (d) Step 1: Force is directly proportional to work done to move the car to the distance d. Kinetic energy does a work to move the car to distance d. And the force required to stop the car is also directly proportional to kinetic energy Hence Nash Metropolitan car requires greater force to stop it. F > F N P