Physics midterm question: strain in lengthening loaded cable

Physics 205A Midterm 2, fall semester 2016
Cuesta College, San Luis Obispo, CA

A boom crane suspends a load from a 2.0 m long vertical cable. The load is lowered and held at a lower height by lengthening the cable to 4.0 m long. The weight of the cable is negligible compared to the weight of the load. Discuss why the strain in the cable does not change for this process. 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 load (F) applied to the cable does not change, as well as the Young's modulus (Y) and cross-sectional area (A) of the cable; and
  2. since strain is the (unitless) ratio (ΔL/L), then since (F/A) = Y⋅(ΔL/L), then from (ΔL/L) = F/(Y⋅A) it can be seen that both cables must experience the same strain.
• 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.
• 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, 73320
Exam code: midterm02oPt0
p: 25 students
r: 4 students
t: 8 students
v: 12 students
x: 6 students
y: 1 student
z: 0 students

A sample "p" response (from student 2217):