Physics quiz question: lever arm of applied force

Physics 205A Quiz 5, fall semester 2013
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problems 8.19, 8.35

A horizontal force is applied to the middle of a square uniform object to keep it stationary. 
The square object is 0.50 m on each side, mounted on a 
pivot at one corner. (Calculate all torques with respect to 
the pivot.) The r_⊥ lever arm for the applied force is:
(A) 0.25 m.
(B) 0.35 m.
(C) 0.50 m.
(D) 0.56 m.

Correct answer (highlight to unhide): (A)

First, a line of force is extended along the force vector. The perpendicular lever arm for this force is drawn such that it starts at the pivot point, and must end intersecting the line of force perpendicularly. Here, the line of force extends through the midpoint of the square object. The perpendicular lever arm then starts from the pivot point, along the side of the square, and ends at the line of force, halfway along the side of the square. Thus the perpendicular lever arm is one-half of the side of the square, or 0.25 m.

(Response (B) is the diagonal distance from a corner to the center of the square; response (C) is the side of the square; and response (D) is the diagonal distance from one corner of the square to the opposite corner.)

Sections 70854, 70855, 73320
Exam code: quiz05LuF7
(A) : 35 students
(B) : 5 students
(C) : 14 students
(D) : 7 students

Success level: 57%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.18