Cuesta College, San Luis Obispo, CA
A 0.40 m long copper rod with a square profile (0.10 m × 0.10 m) can be oriented standing up, or laid down on its side on a floor. If the same amount of downwards force is applied to the top surface in each case, discuss whether the standing-up rod or the laid-down rod will compress a greater ∆L amount (or if there will be a tie). Explain your reasoning using the properties of stress, strain, and Hooke's law.
Solution and grading rubric:
Correct. Applies Hooke's law in a systematic manner by:
- recognizing that the applied force F and Young's modulus Y are the same for both rods; and
- as a result ΔL depends only on the original length L divided by cross-sectional area A; and
- since the standing-up rod has a longer original length (L = 0.40 m) and a smaller cross-sectional area (A = 0.010 m2), it will compress more than the laid-down rod with a shorter original length (L = 0.10 m) and a greater cross-sectional area (A = 0.040 m2).
As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes.
Nearly correct, but argument has conceptual errors, or is incomplete. Considers only difference in cross-sectional areas (neglecting the difference in original lengths), or vice versa; or recognizes both differences but somehow argues that the rods will still compress by the same amount.
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.
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.
Irrelevant discussion/effectively blank.
Sections 70854, 70855
Exam code: midterm02sQm5
p: 18 students
r: 1 student
t: 28 students
v: 3 students
x: 2 students
y: 0 students
z: 0 students
A sample "p" response (from student 2586):
A sample "t" response (from student 6672), recognizing that the original length L changes with different orientation, but claims the cross-sectional area A is the same:
A sample "t" response (from student 2875), recognizing that the cross-sectional area A changes with different orientation, but claims the original length L is the same: