Forces Physics problem

A 5.90-kg box is sliding across the horizontal floor of an elevator. The coefficient of kinetic friction between the box and the floor is 0.420. Determine the kinetic frictional force that acts on the box when the elevator is

(a) accelerating upward with an acceleration whose magnitude is 1.50 m/s2, and

(b) accelerating downward with an acceleration whose magnitude is 1.50 m/s2.

the frictional force = u N where u is the coefficient of friction and N is the normal force

the acceleration of the elevator effects the normal force; to see this, write newton's second law for the box;

sum of forces = ma

the forces are the normal force (up) and mg (down), so we have

N - m g = ma or N = m(g+a)

in the first case, N=5.9kg(9.8m/s/s+1.5m/s/s) and f = 0.42N

in the second case, N=5.9kg(9.8m/s/s - 1.5m/s/s) and f = 0.42N

calculate N and f