Question

You are racing in a rally on a snowy day when the temperature is near the freezing point. The coefficient of static friction between a car's tires and an icy road is 0.104. Your crew boss is concerned about some of the hills on the course and wants you to think about switching to studded tires. To address the issue, he wants to compare the actual hill angles on the course to see which of them your car can negotiate. (a) What is the angle of the steepest incline that a vehicle with four-wheel drive can climb at constant speed? ° (b) Given that the hills are icy, what is the steepest possible hill angle for the same four-wheel drive car to descend at a constant speed?

Answer 1

Gravity down hill force = mg sin theta no inclined angle Therefore theta = 0: no downward force. Static gripping friction = 0.104 mg cos o no inclined angle cos theta = 1: gravity overcomes when mg sin theta = 0.140 mg cos theta Therefore tan theta = 0.104. For smaller angle sin theta = tan theta = theta in radians Rightarrow 0.140 radians times 60 degrees per radians = 6.24 degrees.