Question

The 14000 N car is at rest on the plane surface. The unit vector en = 0.456i + 0.570j + 0.684k is perpendicular to the surface. Determine the magnitudes of the total normal force N and the total friction force f exerted on the surface by the car’s wheels.

Answer 1

The forces on the car are its weight, the normal force, and the friction force.

The normal force is in the direction of the unit vector, so it can be written

N = Ne_n = N(0.456i + 0.570j + 0.684k)

The equilibrium equation is 

Ne_n + f - (14000 N)j =0

The friction force f is perpendicular to N, so we can eliminate the friction force from the equilibrium equation by taking the dot product of the equation with en.