Some car manufacturers claim that their vehicles could climb a slope of 42 ∘. For this to be possible, what must be the minimum coefficient of static friction between the vehicle's tires and the road?

Answer: 0.9

Explanation:

For an inclined surface the coefficient of friction (n) is the ratio of the moving force (Fm) to the normal reaction (R) acting on the body.

n = Fm/R

Fm = WSintheta = mgsintheta

R = Wcostheta = mgcostheta

n = Wsintheta/Wcostheta

n = sintheta/costheta

n = tan theta

n = tan 42°

n = 0.9

Therefore, minimum coefficient of static friction between the vehicle's tires and the road is 0.9