Physics midterm question: compressing short and long bars

Physics 5A Midterm 2, fall semester 2007
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 1/e, Conceptual Question 10.4

A cylindrical steel bar is compressed by the application of forces of magnitude F at each end. What magnitude forces would be required to compress by the same amount a steel bar of the same cross-sectional area, but twice the length? 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 less force is required to compress a longer bar by a certain amount than a shorter bar compressed by the same amount.
  
• 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 Hooke's law in a quantitative manner, but argues that more force is required to compress the longer bar.
  
• 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:
  Blank.
  

Grading distribution:
p: 16 students
r: 2 students
t: 13 students
v: 6 students
x: 1 student
y: 0 students
z: 0 students

A sample of a "p" response (from student 4500) is shown below: