Physics midterm question: different mass boxes attached to comparable springs

Physics 205A Midterm 2, fall semester 2015
Cuesta College, San Luis Obispo, CA

Two horizontal springs are attached to boxes of different masses. The springs have the same strength, and the oscillation amplitudes are the same. Discuss why the boxes will have the same amount of translational kinetic energy at x = 0. Ignore friction/drag. Explain your reasoning using the properties of translational kinetic energy, elastic potential energy, energy conservation and mass-spring systems.

Solution and grading rubric:

• p:
  Correct. Discusses/demonstrates the application of energy conservation:
  1. at x = +A, both boxes have the same amount of elastic potential energy (same-strength springs, same amplitudes);
  2. since there is zero translational kinetic energy at x = +A, then both boxes have the same amount of total energy (equal to the elastic potential energy at x = +A);
  3. at x = 0, both boxes have zero elastic potential energy, such that all of their (same) total energy is in the form of translational kinetic energy at that location, which must then be the same.
  May have also discussed how box 1 (with presumably less mass) will have a shorter period, higher frequency, or faster maximum speed than box 2.
• r:
  As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes. May confuse changes in energy forms with amounts of energy (e.g., 0 = KE_tr + PE_elas, E = ∆KE_tr + ∆PE_elas, etc.), and/or not explicitly noting that maximum elastic potential energy and maximum translational kinetic energy values occur at different locations, etc.
• 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.
• x:
  Implementation of ideas, but credit given for effort rather than merit. Approach other than that of applying energy conservation.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Grading distribution:
Sections 70854, 70855, 73320
Exam code: midterm02h4W6
p: 15 students
r: 31 students
t: 12 students
v: 10 students
x: 2 students
y: 0 students
z: 0 students

A sample "p" response (from student 1337):