Question

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 1

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

Answer 2

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

• Let the mass of the car = m
• Let acceleration due to gravity = g

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

$mgsin(\theta) - \mu_s F_n = 0\\\\\mu_sF_n = mgsin(\theta)\\\\\mu_s mgcos(\theta) = mgsin(\theta)\\\\\mu_s cos(\theta) = sin(\theta)\\\\\mu_s = \frac{sin(\theta)}{cos(\theta)} = tan(\theta)\\\\\mu_s = tan(42)\\\\\mu_s = 0.9$

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

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