Physics midterm question: comparing the stretching of fishing lines

Physics 205A Midterm 2, fall semester 2017
Cuesta College, San Luis Obispo, CA

A long, thin fishing line and a short, thick fishing line (both made of the same material) are strung horizontally over a pulley, and attached to a 100 g mass and a 50 g mass, respectively. Discuss why the thin fishing line will stretch a greater amount than the thick fishing line. 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 systematic manner by:
  1. recognizing that the Young's modulus (Y) is the same for both fishing lines ("made of the same material"); and
  2. applying Hooke's law to show that the long, thin fishing line will stretch a greater amount ΔL = (F⋅L)/(A⋅Y) due to the combined contribution of three separate factors:
     1. a greater force F applied to it (which increases ΔL); and
     2. a smaller cross-sectional area A (which increases ΔL); and
     3. a longer, original unstretched length L (which increases ΔL).
• r:
  As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes. Typically missing one of the three factors (a)-(c) above, but correctly discusses the effect of the two remaining factors.
• t:
  Nearly correct, but argument has conceptual errors, or is incomplete. Typically missing or misinterprets one of the three factors (a)-(c) above, but does not explicitly discuss how these factors affect ΔL in Hooke's law.
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. At least some systematic attempt at using Hooke's law quantities. Typically missing two of three factors (a)-(c) above, and does not explicitly discuss how these factors affect ΔL in Hooke's law.
• x:
  Implementation/application of ideas, but credit given for effort rather than merit. Approach other than that of relating strain (force per unit area), Young's modulus, and strain using Hooke's law.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.
  

Grading distribution:
Sections 70854, 70855
Exam code: midterm02bu2Z
p: 15 students
r: 12 students
t: 2 students
v: 3 students
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 4532):