Forces problem - Please Help ASAP

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 0.170. 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

Looks like sliding -- both up & down -- will happen with 10 degree hills

Issue seems similar to block on inclined plane -- at what angle of tilt will it lose its grip and start sliding?

If sliding begins, no constant speed traction uphill, and decent speed will be altered by the same sliding.

gravity downhill force = mg sin @; no inclined angle, sine is zero & no gravity downhill.

static gripping friction = 0.170 mg cos @; no inclined angle, cosine is 1 & entire weight is normal contact force to apply the friction.

gravity overcomes friction when mg sin @ = 0.170 cos @ ............  or tan @ = 0.170

for very thin triangles or shallow hills, tan @ = sin @ = angle @ in radians

0.17 radians x 60 degrees per radian = 10 degrees