Question

The car has a mass of 1.6 Mg and center of mass at G. If the coefficient of static friction between the shoulder of the road and the tires is μs = 0.41, determine the greatest slope θ the shoulder can have without causing the car to slip or tip over if the car travels along the shoulder at constant velocity.

Answer 1

Answer:

$\theta = 22.29$

Explanation:

Taking summation of force at perpendicular  to the plane

$\sum F_p = 0$

$2N_A +2N_B -mgcos\theta = 0$

$N_A +N_B - mgcos\theta = 0$

$N_A +N_B = mgcos\theta$

Taking summation along the plane, therefore we have

$\sum Fa = 0$

$f_A +f_B -mgsin\theta = 0$  

$\mu N_A+\mu N_B - mgsin\theta = 0$

$\mu(N_A +N_B) = mgcos\theta$

from equation 1 and 2 we have

$\mu =\frac{sin\theta}{cos\theta}$

$\mu = 0.41$

$\mu = tan\theta$

$\theta = tan^{-}\mu$

$\theta = 22.29$