Question

The coefficient of friction (static and kinetic) between an object and a surface can be measured by putting the object on an adjustable inclined plane. (a) Draw a free-body diagram for the object, assuming static friction holds it in place on the incline. (b) Find an equation that can be used to solve for µs, in terms of the angle θmax which is the largest angle that the object can sit without sliding. (Hint: You can reduce the problem to two unknowns—the magnitude of ~n and the coefficient µs—so you will need two equations to solve for them both. Newton’s 2nd Law can provide both equations, since there are forces in both the x and y directions.) (c) Find the angle θconst where the object will move with a constant velocity down the incline if it is given an initial push. (d) Which is bigger, θconst or θmax? Describe the motion of the object (e.g., is it speeding up, slowing down, etc.) for each range of θ: between 0 and the smaller special angle, between the two special angles, and between the larger special angle and 90◦ . (Hint: You can check your answer with an experiment; a textbook cover provides a decent adjustable incline.)

Answer 1