Physics midterm question: longer single cable vs. doubled-up shorter cables

Physics 205A Midterm 2, fall semester 2012
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Conceptual Questions 10.4, 10.13

A 10 kg mass is suspended from a 1.0 m cable attached to the ceiling. Another 10 kg mass is suspended from two 0.50 m cables. All of these cables are made of the same material, have the same diameter, and all lengths are measured before the cables are stretched. Discuss why the single cable will stretch more than either of the double cables. Explain your reasoning using the properties of stress, strain, and Hooke's law.

Solution and grading rubric:
  • p:
    Correct. Applies Hooke's law in a quantitative manner to argue that the single long cable will stretch more than the two shorter cables due to (a) the longer length, and (b) smaller cross-sectional area (may also say that there is twice as much force applied to the single long cable compared to one of the two shorter cables).
  • 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. Describes only one of the two contributions (a)-(b) that makes the single long cable stretch more than the two shorter cables.
  • v:
    Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner.
  • x:
    Implementation/application of ideas, but credit given for effort rather than merit.
  • y:
    Irrelevant discussion/effectively blank.
  • z:
Grading distribution:
Sections 70854, 70855
Exam code: midterm02gL0u
p: 11 students
r: 8 students
t: 29 students
v: 6 students
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 7582), using a "plug-and-chug" approach:

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