Physics midterm question: comparing Young's moduli of fishing lines

Physics 205A Midterm 2, fall semester 2018
Cuesta College, San Luis Obispo, CA

A long 1.00 m fishing line and a short 0.50 m fishing line (same cross-sectional area) are each strung horizontally over a pulley, and are attached to a 100 g mass and a 50 g mass, respectively. As a result both fishing lines stretch the same amount from their original lengths. It is not known if these fishing lines are made of the same material. Discuss which material has the greater Young's modulus value (or if there is a tie), and why. 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 they stretch the same amount ΔL and have the same cross-sectional area A; and
  2. the longer L fishing line has a greater tension force F applied to it than the shorter L fishing line with a lesser tension force F; and
  3. since Young's modulus Y = (F⋅L)/(A⋅ΔL), the longer L fishing line with the greater tension force F will have a larger Young's modulus (specifically four times larger) than the shorter fishing line with the lesser tension force.
• r:
  As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes. Typically has clerical errors (mislabeling "long" versus "short" labels), and so concludes that Young's modulus must be the same for both fishing lines.
• t:
  Nearly correct, but argument has conceptual errors, or is incomplete. Typically only recognizes length L or tension force F has having an affect on Young's modulus Y; or has recognizes both quantities as having an affect on Y, but someone argues that these cancel each other out, such that the fishing lines have the same Y value.
• 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.
• 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: midterm02r3iN
p: 37 students
r: 6 students
t: 11 students
v: 2 students
x: 0 students
y: 0 students
z: 1 student

A sample "p" response (from student 5683):
A sample "p" response (from student 8812):
A sample "p" response (from student 1113):