(Solved): 3. (15 pts) You are traveling at 25mph along a banked horizontal curve with a radius of curvature o ...

3. (15 pts) You are traveling at $25\mathrm{mph}$ along a banked horizontal curve with a radius of curvature of $p=160\mathrm{ft}$. a. (7 pts) Determine the minimum bank of the curve needed so that you do not slip without the aid of friction. Compare this value to a bank angle of approximately $4.6^{?}$ for $25\mathrm{mph}$ used by the Department of Transportation (DOT) in designing roads. Keep in mind that friction may play a role. Hint: the car is coming toward you out of the page; you may need a third axis. b. ( 8 pts) Now, you are traveling around the same curve at $45\mathrm{mph}$ in your Audi A6 that weighs 4 kip, which includes yourself and your cargo. What is the friction force needed to keep you from slipping? What is the approximate coefficient of friction between the tires and the road?