Physics final exam question: thermal expansion of pendulum string

Physics 205A Final Exam, fall semester 2015
Cuesta College, San Luis Obispo, CA

A Physics 205A student builds a simple pendulum using a string and a mass, and at a certain temperature it has a period of 1.50 s. As the temperature increases, determine whether the period will increase, decrease, or remain the same. Ignore friction/drag, and only consider the thermal expansion of the string. Explain your reasoning using the properties of simple harmonic motion and thermal expansion.

Solution and grading rubric:
  • p:
    Correct. Discusses how the period of a simple pendulum depends on the gravitational acceleration constant (which does not change) and the string length (which expands due to the increase in temperature), such that the period will increase.
  • 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. Some garbled attempt at applying thermal expansion to the simple pendulum parameters.
  • x:
    Implementation/application of ideas, but credit given for effort rather than merit. Approach other than applying thermal expansion to the simple pendulum parameters.
  • y:
    Irrelevant discussion/effectively blank.
  • z:
Grading distribution:
Sections 70854, 70855, 73320
Exam code: final7rUk
p: 47 students
r: 1 students
t: 15 students
v: 6 students
x: 2 students
y: 0 students
z: 0 students

A sample "p" response (from student 5612):

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