r 1. A concrete highway curve of radius r is banked at an angle a A rubber-tired car of mass m drives along this curve, with friction, at maximum speed without siiriing. (Here use p... and In as the known coefcients of friction, and g for the acceleration due to gravity.) Free-body diagram for car on a banked curve c} Please apply Newton's second law to this system and write down appropriate expressions. What is the condition related to friction that yields the maximum speed without slipping? a) Please draw a freebody diagram of the car on this banked curve, labeling all the forces. b) Please explain why we should choose an \"rm" coordinate system for this problem, with a horizontal radial axis and a vertical 2 axis, instead of tilting the axes to match the plane. d) Using one of the above equations, please show how to derive that the normal force, in this \"18 cos El ~ y, sin 9 particular case, is given by: n = e} Use the above expression for the normal force a to solve for the maximum speed v in terms of the known variables given above. TFiLA check:_ 0 Please calculate a numerical value for this velocity, if the car has a mass of 1500 kg and the highway curve of radius 60 In is banked at a 15 angle. (Here please use g = 10 misz, p, = 1.0 and in = 0.3 for rubber on concrete, and tan 15 = '13.) Does your estimated answer also make sense in mph? Were there any known quantities that you did not use in your solution