4. Exam-style Question: Banksy (6 points) If a car is traveling at a certain speed 1;, it is possible to bank a curve at just the right angle so that no friction at all is needed to maintain the car's turning radius; the car can then safely round the curve even in the slickest conditions. (Bobsled racing also depends on this.) (a) Your engineering rm plans to build a banked turn with radius R so that a car moving with chosen speed 1; can safely make the turn even with no friction. Draw a free body diagram of the forces on the car and sketch a vector to represent the net force on the car on your diagram. (Hint: Which way does an object's acceleration point during circular motion? Revisit your Lecture 5 notes for a reminder.) (b) At what angle [3 should the curve be banked? (Hint: Remember from Lecture 5 that the magnitude of acceleration of an object in circular motion is a = %). (c) If the road isn't icy and has a coefcient of static friction as, what is the maximum speed the car can have while rounding the bend without losing traction