A race-car of mass m negotiates a right hand 90o turn at constant speed v on a banked road that makes an angle θ with respect to horizontal. The radius of the turn is given by r and the time the car takes to go around the banked turn is t . The car makes the turn at high speed and, after making the banked turn, the car continues down a straight segment of road.
(A) Draw a free-body diagram which shows the forces acting on the car. Assume rolling friction and air drag are negligible (and that no propulsion force is required to maintain a constant speed). Include your coordinate axes in your drawing.
(B) Use Newton's second law to write an equation for the resulting centripetal force. Then solve the equation for the normal force of road on the tires in terms of: the mass of the car m, the radius of the curve r, time to make the curve t, banked angle θ , and any needed constants of proportionality. Simplify as possible.
(C) A race-car has a mass of 750kg and needs to take the 90o turn of radius 160m in 10.0 seconds regardless of the coefficient of static friction between the tires and the track. What should the minimum banking angle θ be?