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?

a. 0.4
b. 0.5
c. 0.7
d. 0.9

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:

                        ∑

                              ------(1)

Resolving into y component:

                        ∑

                               ------(2)

Static frictional force, μ       ------(3)

substituting from equation (1) and from equation (2) into equation (3)

                          μ

                          μ

                         μ

                         μ

The angle the vehicles make with the horizontal α = 42°

                         μ ≥ tan 42°

                         μ ≥ 0.9

two charges are fixed in place on the x-axis as shown. the charge at x = 0 is negative and has magnitude q = 2 μcoulombs (1 μcoulomb = 10-6 coulombs). the charge at x = d, (d = +12 cm), is positive and has magnitude q = 4 μcoulombs. find a point x = xo along the x-axis at which the electric field is zero.

that would be because of both gravity and friction. so     c