Physics quiz question: vertical cable on diagonal beam

Physics 8A Quiz 6, Spring Semester 2007
Cuesta College, San Luis Obispo, CA

Physics 8A learning goal Q6.5

[3.0 points.] A uniform, 150 kg beam is supported using a cable connected to the ceiling, as shown at right. The lower end of the beam rests on the floor, which is not frictionless.

Which one of the choices below best corresponds to the static friction force (magnitude and direction) of the floor on the beam?

(A) 735 N, to the left.
(B) 735 N, to the right.
(C) (There is zero static friction force exerted by the floor on the beam.)
(D) (There is not enough information given to determine the static friction force of the floor on the beam.)

(Cf. Young and Freeman, University Physics, 11/e, Problem 11.59.)

Correct answer: (C)
The forces acting on the beam are the tension force (up), normal force of the floor (up), weight (down), and the static friction force (direction unknown). The beam is in equilibrium, so by Newton's first law these forces must sum to zero (along the x- and y-directions), and their torques must sum to zero (about any arbitrary origin). Note that the static friction force, if it exists, is the only x-direction force, and would not be able to be canceled out. Therefore it cannot exist.

Student responses:
(A) : 10 students
(B) : 10 students
(C) : 9 students
(D) : 5 students