Physics quiz question: pulling on still-stuck crate

Physics 205A Quiz 3, fall semester 2013
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 4.53

A rope exerts a tension force of 4.0 N on a 5.0 kg crate, which remains motionless on a non-frictionless floor. The magnitude of the static friction force on the crate is __________ 4.0 N.
(A) less than.
(B) more than.
(C) exactly equal to.
(D) (Not enough information is given.)

Correct answer (highlight to unhide): (C)

The crate has two vertical forces acting on it:

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

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

The crate has two horizontal forces acting on it (as it moves to the right):

Static friction force of floor on crate (to the left).
Tension force on crate (to the right, magnitude T = 4.0 N).

Since the crate remains stationary, Newton's first law is applicable here, and thus the static friction force and applied tension force are equal in magnitude and opposite in direction. (Note that the maximum amount of static friction force that must be overcome in order for the crate to become unstuck should be some value greater than 4.0 N.)

Sections 70854, 70855, 73320
Exam code: quiz03eL3v
(A) : 9 students
(B) : 43 students
(C) : 17 students
(D) : 1 student

Success level: 24%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.11