Chapter 6, Problem 92P

Airport luggage. In an airport, luggage is transported from one location to another by a conveyor belt. At a certain location, the belt moves down an incline that makes an angle of 2.5° with the horizontal. Assume that with such a slight angle there is no slipping of the luggage and that an $x$ axis extends up the incline. Determine the frictional force from the belt on a box with weight 69 N when the box is on that incline for the following situations: (a) The belt is stationary. (b) The belt has a constant speed of 0.65 m/s. (c) The belt has a speed of 0.65 m/s that is increasing at a rate of $0.20\text{m}/{\text{s}}^2$. (d) The belt has a speed of 0.65 m/s that is decreasing at a rate of $0.20\text{m}/{\text{s}}^2$. (e) The belt has a speed of 0.65 m/s that is increasing at a rate of $0.57\text{m}/{\text{s}}^2$.