Two curves on a highway have the same radii R = 1 ….

Two curves on a highway have the same radii R = 1 . 20 × 10 2   m . However, one is unbanked (Fig. 3.1) and the other is banked at an angle θ (Fig. 3.2). A car of mass 2 . 00 × 10 2   k g  can safely travel along the unbanked curve at a maximum speed v 0 = 25 . 0   m s , (a) what is the coefficient of static friction between the tires and the road? (b) If the banked curve is frictionless and the car can negotiate it at the same maximum speed v 0 = 25 . 0   m s , what is the angle θ  of the banked curve? If the coefficient of static friction between the tires and the road is half the μ s found in (a) and the angle θ is the same as the banked angle found in (b), (c) what is the maximum speed of the car for it to travel on the banked curve safely (d) what is the minimum speed of the car so that it would travel on the banked curve without sliding down? If the minimum speed of the car on a banked road with the coefficient of static friction half the μ s found in (a) is  v 0 = 25 . 0   m s , (e) what is the angle θ  of the banked curve? (Hint: sin 90 ° + θ = cos θ , cos 90 ° + θ = – sin θ , sin 180 ° + θ = – sin θ , cos 180 ° + θ = – cos θ ) fig3_q19.jpg
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