The coefficient of friction (static and kinetic) between anobject and a surface can be measured by putting the object on anadjustable inclined plane. (a) Draw a free-body diagram for theobject, assuming static friction holds it in place on the incline.(b) Find an equation that can be used to solve for µs, in terms ofthe angle θmax which is the largest angle that the object can sitwithout sliding. (Hint: You can reduce the problem to twounknowns—the magnitude of ~n and the coefficient µs—so you willneed two equations to solve for them both. Newton’s 2nd Law canprovide both equations, since there are forces in both the x and ydirections.) (c) Find the angle θconst where the object will movewith a constant velocity down the incline if it is given an initialpush. (d) Which is bigger, θconst or θmax? Describe the motion ofthe object (e.g., is it speeding up, slowing down, etc.) for eachrange of θ: between 0 and the smaller special angle, between thetwo special angles, and between the larger special angle and 90◦ .(Hint: You can check your answer with an experiment; a textbookcover provides a decent adjustable incline.)
