Question

on an icy day, you worry about parking your car in your driveway, which has an incline of 12°.Your neighbor's driveway has an incline of 9.0°,and the driveway across the street is at 6.0°.the coefficient of static friction between tire rubber and ice is 0.15. which driveway(s) will be safe to park in? note : i need a complete solution​

Answer 1

Answer:

The answer is 6°

Explanation:

As we know that if we resolve the force into components the maximum force will be acting on the y component of force in the vertical Fy direction.

0 = N - mgCosθ = Fy (max)

N = mgCosθ

Now the force of friction will be equal to.

Ffs = μ sN

Ffs = μs mgCosθ

Now Fx (max)

Fx (max) = mgSinθ - Ffs = 0

Ffs = mgSinθ = μs mgCosθ

After cancellation:

μs  = tanθ

θ  = tan^-1 (μs )

θ  = tan^-1 (0.15) = 8.5°

We need θ  < 8.5°. For no sliding Fg < Ffs to be safe.

Thus the the safe drive away across the street should be 6°.