Physics- Forces/Free Body Diagram Questions

Question

A horizontal force of 76N is required to slide a 23kg box across a tile floor at constant velocity. What is the coefficient of sliding friction between the box and the floor?

PLEASE I AM STRUGGLING!

Answer 1

The required force to slide the box at constant velocity is the amount of force which will equal the force of kinetic friction, so that the net force F_net = F_k + F_push = 0. Therefore, the force of kinetic friction is equal to 76 N because a 76 N force will cancel it out. The magnitude of the force of kinetic friction is given by F_k = µ_k * F_N where F_N is the normal force and µ_k is the coefficient of kinetic friction. The normal force is the force which prevents the box from falling through the floor. Assuming the box is on a flat surface, the normal force will have equal magnitude and opposite direction as the force of gravity, so that those two forces cancel out and the net force in the vertical direction is zero. Therefore, the magnitude of the normal force is given by F_N = m*g. Plugging this into our first equation and using the fact that F_k = 76 N and m = 23 kg, we can solve for µ_k: F_k = µ_k * F_N => F_k = µ_k * m * g => 76 = µ_k * 23 * 9.8 => µ_k = 76 / (23 * 9.8) = 0.34.

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