   Chapter 4, Problem 82AP

Chapter
Section
Textbook Problem

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, θC, 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 μsn for angles less than θC? Explain. What can you definitely say about the magnitude of the friction force for any angle θ ≤ θc? (c) Show that the coefficient of static friction is given by μs = tan θc. (d) Once the coin starts to slide down the incline, the angle can be adjusted to a new value θc’ ≤ θc 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

(a)

To determine
The free body diagram.

Explanation

The free body diagram is given below.

• N is the normal force.
• m is the mass of the coin.
• g is the acceleration due to gravity...

(b)

To determine
The friction force.

(c)

To determine
The co-efficient of static friction.

(d)

To determine
The co-efficient of static friction.

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