Halliday, Resnick & Walker — Force and Motion–II: Problem 92

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 \(2.5^\circ\) 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 \(69\text{ N}\) when the box is on that incline for the following situations: (a) The belt is stationary. (b) The belt has a constant speed of \(0.65\text{ m/s}\). (c) The belt has a speed of \(0.65\text{ m/s}\) that is increasing at a rate of \(0.20\text{ m/s}^2\). (d) The belt has a speed of \(0.65\text{ m/s}\) that is decreasing at a rate of \(0.20\text{ m/s}^2\). (e) The belt has a speed of \(0.65\text{ m/s}\) that is increasing at a rate of \(0.57\text{ m/s}^2\).