Question

Certain suv ads claim that their vehicles can climb a slope of 45?. what is the minimum coefficient of static friction between the tires and the road for this to be possible?

Answer 1

First, you make a force body diagram to illustrate the problem. Then, apply Newton's laws of motion.

Summation of forces along the y-direction:

F = 0 (bodies at equilibrium) = Normal force - weight*cos45 = 0
Normal force = wcos45

Summation of forcesalong the x-direction:

F = 0 (bodies at equilibrium) = Frictional force - weight*sin45 = 0
x*Normal force - weight*sin45 = 0   (let x be the min coeff of static friction)
x*weight*cos45 = weight*sin 45
x = sin45/cos45 = 1

Therefore, the minimum coefficient of static friction must be 1.