A 1200-kg SUV is moving along a straight highway at 12.0 m/s. Another car, with mass 1800 kg and speed 20.0 m/s, has its center of mass 40.0 m ahead of the center of mass of the SUV (?Fig. E8.54?). Find (a) the position of the center of mass of the system consisting of the two cars; (b) the magnitude of the system’s total momentum, by using the given data; (c) the speed of the system’s center of mass; (d) the system’s total momentum, by using the speed of the center of mass. Compare your result with that of part (b).
Solution 54E Introduction We have to find the center of mass of the two car system. Then we have to find the total momentum from the mass and velocity of the car. Then we have to find the velocity of the center of mass using the mass and the velocity of the car and finally we have to calculate the total momentum using the velocity of the center of mass. Step 1 Suppose the center of mass is1x distance away from the SUV. Hence the distance from the other car is Hence using the formula of center mass we can write that Hence the center of mass will be 24 m away from the first car. Step 2 The momentum of the first car is And the momentum of the second car is Hence the magnitude of the total momentum is