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?

The minimum static friction between the vehicle’s tires and the road is 0.9.

The given parameters;

angle of inclination of the slope, θ = 42⁰

The net horizontal force on the car is calculated as follows;

Thus, the minimum static friction between the vehicle’s tires and the road is 0.9.

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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

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