FIGURE 5-5
-A box is sliding down an incline tilted at an angle 14.0° above horizontal. The box is sliding down the incline at a speed of 1.70 m/s. The coefficient of kinetic friction between the box and the incline is 0.380. How far does the box slide down the incline before coming to rest?
A)1.16 m
B)2.33 m
C)1.78 m
D)0.720 m
E)The box does not stop. It accelerates down the plane.

Question

FIGURE 5-5 
-A box is sliding down an incline tilted at an angle 14.0° above horizontal. The box is sliding down the incline at a speed of 1.70 m/s. The coefficient of kinetic friction between the box and the incline is 0.380. How far does the box slide down the incline before coming to rest?
A)1.16 m 
B)2.33 m 
C)1.78 m 
D)0.720 m 
E)The box does not stop. It accelerates down the plane.

Quizplus · Accepted Answer

Explanation:The force of kinetic friction is:$$f_k=\mu_kn$$$$f_k=(0.380)(mg\cos14.0\degree)$$The work done by the force of kinetic friction is:$$W_f=-f_kd$$The change in kinetic energy of the box is:$$\Delta K=\frac{1}{2}mv_f^2-\frac{1}{2}mv_i^2$$The work-energy theorem states that the net work done on an object is equal to the change in its kinetic energy. Therefore, we have:$$W_f=\Delta K$$$$-f_kd=\frac{1}{2}mv_f^2-\frac{1}{2}mv_i^2$$$$-(0.380)(mg\cos14.0\degree)d=\frac{1}{2}m(0)^2-\frac{1}{2}m(1.70	ext{ m/s})^2$$$$d=\frac{(1.70	ext{ m/s})^2}{2(0.380)(g\cos14.0\degree)}$$$$d=1.16	ext{ m}$$

FIGURE 5-5 -A Box Is Sliding Down an Incline Tilted at an Tilted