Solve This Physics Problem

Question

Three diagrams (one with variable F, the other two with variables F and the angle 𝜃) show a block of mass m being pulled or pushed at constant acceleration along a table with a force F. The coefficient of kinetic friction is 𝜇k. What is the magnitude of the friction force in each case? Give your answer in terms of the pushing force F, m, 𝜇k, and the angle 𝜃.

Answer 1

The magnitude of the friction force is given by fₖ = μₖF_N

The normal force depends on the angle between the applied force (F) and the horizontal direction of motion.

Since F_N – mg + F sinθ = 0, this means that F_N = mg – F sinθ.

So fₖ = μₖ(mg – F sinθ)

There are 3 basic scenarios (depicted in the figure above where F_N is the blue vector arrow):

θ < 0: fₖ > μₖmg

θ = 0: fₖ = μₖmg

θ > 0: fₖ < μₖmg