Answer to Question #239479 in Physics for rshiii

Question

3. A 6.0 lb box is pulled along the horizontal floor by a rope that makes an angle of 30o above the horizontal. The coefficient of kinetic friction between the box and the floor is 0.10. If the tension in the rope is 1.0 lb, find the acceleration of the box.

Answer 1

Given:

$F=1.0\:\rm lb=4.45\: N$

$\theta=30^{\circ}$

$\mu=0.10$

$m=6\:\rm lb=2.72\: kg$

The Newton's second law says

$$ma_x=F_x, \quad ma_y=F_y$$

$$ma_x=F\cos\theta-F_f,\quad 0=F\sin\theta+N-mg$$

$$F_f=\mu N=\mu(mg-F\sin\theta)$$

$$a_x=\frac{F\cos\theta-F_f}{m}=\frac{F\cos\theta-\mu(mg-F\sin\theta)}{m}$$

$$a_x=\frac{4.45\cos30^{\circ}-0.1(2.72*9.8-4.45\sin30^{\circ})}{2.72}=0.52\:\rm m/s^2$$