Physics quiz question: unsticking a book from rest

Physics 205A Quiz 3, spring semester 2009
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Comprehensive Problem 4.124

A 5.0 kg book on a horizontal table is initially at rest. The coefficient of static friction is 0.33. The coefficient of kinetic friction is 0.27. What is the magnitude of the minimum horizontal applied force required to make the book start to slide?
(A) 3 N.
(B) 13 N.
(C) 16 N.
(D) 49 N.

Correct answer (highlight to unhide): (C)

The box has two vertical forces acting on it:

Weight force of Earth on book (downwards, magnitude w = m·g = 49 N).
Normal force of floor on book (upwards, magnitude N = 49 N).

Because the suitcase is stationary in the vertical direction, these two forces are equal in magnitude and opposite in direction, due to Newton's first law.

The book has two horizontal forces acting on it:

Friction (static or kinetic) force of floor on book (to the left).
External applied force on book (to the right).

In order to "unstick" the book, the horizontally applied force must overcome the maximum possible static friction force magnitude:

f_s,max = µ_s·N = µ_s·m·g = (0.33)(5.0 kg)(9.80 N/kg) = 16 N,

such that the applied force F_applied magnitude must exceed 16 N in order to unstick the book.

(Response (D) is the magnitude of the weight force: w = m·g; response (B) is the magnitude of the kinetic friction force on the book after it has been unstuck and sliding: f_k = µ_k·N = µ_k·m·g; while response (A) is the result of the difference f_s,max – f_k.)

Student responses
Sections 30880, 30881
(A) : 3 students
(B) : 5 students
(C) : 32 students
(D) : 6 students

Success level: 66%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.62