Answer:
D. 0.9
Explanation:
Calculating minimum coefficient of static friction, we first resolve the forces (normal and frictional) acting on the vehicle at an angle to the horizontal into their x and y components. After this, we can now substitute the values of x and y components into equation of static friction. Diagrammatic illustration is attached.
Resolving into x component:
∑[tex]F_{x} = F_{s} - mgsin\alpha =0[/tex]
[tex]F_{s} = mgsin\alpha[/tex] ------(1)
Resolving into y component:
∑[tex]F_{y} = F_{n} - mgcos\alpha =0[/tex]
[tex]F_{n} = mgcos\alpha[/tex] ------(2)
Static frictional force, [tex]F_{s} \leq[/tex] μ [tex]F_{n}[/tex] ------(3)
substituting [tex]F_{s}[/tex] from equation (1) and [tex]F_{n}[/tex] from equation (2) into equation (3)
[tex]mgsin\alpha \leq[/tex] μ [tex]mgcos\alpha[/tex]
[tex]sin\alpha \leq[/tex] μ [tex]cos\alpha[/tex]
μ [tex]\geq \frac {sin\alpha}{cos\alpha} [/tex]
μ [tex]\geq tan\alpha [/tex]
The angle the vehicles make with the horizontal α = 42°
μ ≥ tan 42°
μ ≥ 0.9
