Physics quiz question: cable-supported beam

Physics 205A Quiz 5, fall semester 2012
Cuesta College, San Luis Obispo, CA

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

A 12 kg uniform beam of length 0.80 m is mounted on a pivot at one end, and supported by a cable attached to the other end. With respect to the pivot, the perpendicular lever arm ℓ for the tension force of the cable on the beam is:
(A) 0.40 m.
(B) 0.46 m.
(C) 0.56 m.
(D) 0.66 m.

Correct answer (highlight to unhide): (B)

The tension force of the cable acts on the beam at the left end, along the cable. The ℓ lever arm for the cable tension force must extend from the pivot to perpendicularly intercept the tension force line of action (which is along the cable itself), such that this will be a diagonal line of length:

ℓ = L·sin35°.

(Response (A) is L/2; response (C) is L·tan35°; response (D) is L·cos35°.)

Sections 70854, 70855
Exam code: quiz05L4mN
(A) : 3 students
(B) : 28 students
(C) : 10 students
(D) : 11 students

Success level: 54%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.42