Answer to Question #296727 in Physics for Ica

Question

A box with a weight of 1260 N was dragged across the horizontal floor by a man by pulling a rope that is tied on the box. The man exerts a force of F= 485N on the rope, which is inclined at an angle of = 25o and the floor exerts a friction force of 98N on the box.

Find the following:

a. Draw the free-body diagram of the box.

b. The magnitude of the acceleration of the box.

c. Find the coefficient of friction

d. Find the normal force by the floor to the box.

Answer 1

a. Draw the free-body diagram of the box.

b. The magnitude of the acceleration of the box.

$$a=\frac{F\cos25^\circ-F_f}{m}=\frac{485\cos 25^\circ-98}{1260/9.8}=2.7\:\rm m/s^2$$

c. Find the coefficient of friction.

$$\mu_k=\frac{F_f}{N}=\frac{F_f}{W-F\sin25^\circ}$$

$$\mu_k=\frac{98}{1260-485\sin25^\circ}=0.09$$

d. Find the normal force by the floor to the box.

$$N=W-f\sin25^\circ=1260-485\sin25^\circ=1055\:\rm N$$