(13%) Problem 3: A banked highway is designed for trafc moving at v = 85 kin/h. The radius of the curve r = 346 In. 50% Part (3) Write an equation for the tangent of the highway's angle of banking. Give your equation in terms of the radius of curvatl speed of the turn v, and the acceleration due to gravity g. tau-1(6) = v2/( r g ) I/ Correct! $3 50% Part (b) What is the angle of banking of the highway? Give your answer in degrees. 6 = 0.16295l D: P( (13%) Problem 2: Part of riding a bicycle involves leaning at the correct angle when making a turn; the rst gure in the image carousel shows a rider leaning the bicycle at an angle 0 from the vertical. To be stable, the net force exerted by the 2 I 2 ground where it contacts the tire must be on a line passing through the center of gravity. The forces have been summarized with a free-body diagram, as seen in the second gure in the image carousel. The ground exerts a normal force which is equal L: in magnitude to the combined weight of the bicycle and the rider. The ground additionally exerts a force due to static friction which is parallel to the ground, causing the bicycle to move in a circle, F. - ' 3 1 I7 I I i LL?\" 9/ ' ~ A '1 i L9 O 50% Part (a) Enter an equation for the tangent of the angle between the bicycle and the vertical in terms of the speed of the bicycle, v, the radius of curvature of the turn, r, and the acceleration due to gravity, g. tan(9) 2 v2/( r g ) I/ Correct! $8 50% Part (b) Calculate 6 , in degrees, for a turn taken at 9.87 m/s with a radius of of curvature 43.3 In. Grade Summary 0 = 0.23l Deductions Potential 100% ankmhmannn ,V,/\\ H,\" x,,,/\\ | ml II | a | n | n | "mm