Physics midterm question: cable-supported beam

Physics 205A Midterm 2, fall semester 2011
Cuesta College, San Luis Obispo, CA

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

A uniform beam is mounted on a pivot at one end, and supported at its center by a cable perpendicular to the beam. Discuss why the magnitude of the tension in the cable is less than the weight of the beam. Explain your reasoning using diagram(s) with locations of forces and perpendicular lever arms, the properties of torques, and Newton's laws.

Solution and grading rubric:
  • p:
    Correct. The counterclockwise torque from cable equals the clockwise torque from weight, but the cable has a larger lever arm (L/2) than weight (L·cos(25°)/2), such that the cable tension force must be smaller than the weight force.
  • r:
    As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes.
  • t:
    Nearly correct, but argument has conceptual errors, or is incomplete. Applies Newton's first law for rotations, but r discussion is garbled or missing.
  • v:
    Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. At least attempts to discuss torques, forces, lever arms, but Newton's first law for rotations is not clearly used. May instead use Newton's first law for vertical forces and involve the force of the pivot point, but does not clearly break up tension into vertical and horizontal components.
  • x:
    Implementation of ideas, but credit given for effort rather than merit. Does not discuss torques, forces, lever arms.
  • y:
    Irrelevant discussion/effectively blank.
  • z:

Grading distribution:
Sections 70854, 70855
Exam code: midterm02fR3q
p: 16 students
r: 3 students
t: 10 students
v: 24 students
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 4816):

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