Question

A small box has a mass of 5.0kg. The coefficients of static and kinetic friction between the box and a horizontal desktop are 0.42 and 0.32, respectively. What is the frictional force on the box when a 18-N horizontal push is applied to the box

Answer 1

The net force acting on the box perpendicular to the surface is

∑ F[perp] = F[normal] - mg = 0

where mg is the weight of the box. Then

F[normal] = (5.0 kg) g = 49 N

so that the maximum static friction felt by the box is

F[s. friction] = 0.42 F[normal] = 20.58 N

Since the applied force of 18 N has a smaller magnitude than the max static friction, the block will not move, so the applied force and static friction cancel. In other words, the net force parallel to the surface is

∑ F[para] = F[push] - F[s. friction] = 0

so that

F[s. friction] = 18 N