Chapter 4, Problem 70AP

Measuring coefficients of friction A coin is placed near one edge of a book lying on a table, and that edge of the book is lifted until the coin just slips down the incline as shown in Figure P4.82. The angle of the incline, θ_C, called the critical angle, is measured. (a) Draw a free-body diagram for the coin when it is on the verge of slipping and identify all forces acting on it. Your free-body diagram should include a force of static friction acting up the incline. (b) Is the magnitude of the friction force equal to μ_sn for angles less than θ_C? Explain. What can you definitely say about the magnitude of the friction force for any angle θ ≤ θ_c? (c) Show that the coefficient of static friction is given by μ_s = tan θ_c. (d) Once the coin starts to slide down the incline, the angle can be adjusted to a new value θ_c’ ≤ θ_c such that the coin moves down the incline with constant speed. How does observation enable you to obtain the coefficient of kinetic friction?

Figure P4.82