Answer to Question #100560 in Classical Mechanics for Aaliyah Hope

Question

A box of books weighing 304 N moves with
a constant velocity across the floor when it is
pushed with a force of 373 N exerted downward at an angle of 39.4◦ below the horizontal.
Find µk between the box and the floor.

Answer 1

The FBD is shown below

The Newton's second law in projections on the axes

$$F_f=F\cos\theta$$ $$N=mg+F\sin\theta$$

The friction force

$$F_f=\mu_kN$$

Hence

$$\mu_k=\frac{F\cos\theta}{mg+F\sin\theta}$$ $$\mu_k=\frac{373\cos 39.4^{\circ}}{304+373\sin 39.4^{\circ}}=0.533$$