The coefficients of static and kinetic friction between a 3.0-kg box and a horizontal desktop are 0.40 and 0.30,respectively.What is the force of friction that the desktop exerts on the box when a 15-N horizontal push is exerted on the box?
A)12 N
B)8.8 N
C)15 N
D)6.0 N
E)4.5 N

Question

Quizplus · Accepted Answer

The force of friction can be calculated as follows:
If the box is at rest, the force of friction will be equal and opposite to the applied force, 15 N. Therefore, frictional force = 15 N.
However, if the box is moving, we need to use the coefficients of friction to calculate the force of friction. The maximum frictional force will be equal to the product of the coefficient of static friction and the normal force, i.e., F_friction,max = μ_static x (m x g) = 0.40 x (3.0 kg x 9.8 m/s^2) = 11.76 N. Since the applied force of 15 N is greater than the maximum static frictional force, the box will start moving and the force of friction will be equal to the product of the coefficient of kinetic friction and the normal force, i.e., F_friction = μ_kinetic x (m x g) = 0.30 x (3.0 kg x 9.8 m/s^2) = 8.82 N. Therefore, the force of friction that the desktop exerts on the box is 8.82 N, which is closest to option B) 8.8 N.

The Coefficients of Static and Kinetic Friction Between a 3