Answer to Question #100560 in Classical Mechanics for Aaliyah Hope

Question #100560
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.
1
Expert's answer
2019-12-17T09:54:24-0500

The FBD is shown below



The Newton's second law in projections on the axes


Ff=FcosθF_f=F\cos\thetaN=mg+FsinθN=mg+F\sin\theta

The friction force


Ff=μkNF_f=\mu_kN

Hence


μk=Fcosθmg+Fsinθ\mu_k=\frac{F\cos\theta}{mg+F\sin\theta}μk=373cos39.4304+373sin39.4=0.533\mu_k=\frac{373\cos 39.4^{\circ}}{304+373\sin 39.4^{\circ}}=0.533


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