Physics final exam problem: accelerating stacked boxes

Physics 205A Final Exam, fall semester 2011
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problems 4.142, 4.144

Two boxes are stacked upon each other. 
A rope with a tension force of 18 N is applied as shown to the bottom box. The magnitude of the static friction force between the surfaces of the top and bottom boxes is 4.5 N. Both boxes accelerate to the right with a constant magnitude of 1.5 m/s², as they move together across a frictionless floor. Determine (a) the mass of the top box, and the (b) mass of the bottom box. Show your work and explain your reasoning.

Solution and grading rubric:

• p = 20/20:
  Correct. Only horizontal motion is of interest here, such that a complete free-body diagram involving vertical forces is not necessary. Newton's second law is applied to the top box, where the net force only consists of the friction force, and set equal to the mass of the top box times the given acceleration (which must be the same as the bottom box); m_top = 3.0 kg. Then Newton's second law is applied to the bottom box, where the net force is equal to the vector sum of the given applied force (right) and friction force (left, equal to the friction force of the bottom fox on the top box, due to Newton's third law), and set equal to the mass of the bottom box times the given acceleration; m_bottom = 9.0 kg. There may be minor round-off discrepancies, and skipped steps as long as the relevant application of Newton's laws and force vector directions and summations are clearly indicated.
  
• r = 16/20:
  Nearly correct, but includes minor math errors. Successful at correctly finding mass of one box only, or of both boxes combined only.
  
• t = 12/20:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. At least some attempt at applying Newton's second law to part of or the whole system, but free-body diagram is problematic or fragmented; or attempt at free-body diagram with problematic application of Newton's second law, and Newton's third law.
  
• v = 8/20:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Serious attempt at a free-body diagram, or some attempt at applying Newton's laws.
  
• x = 4/20:
  Implementation of ideas, but credit given for effort rather than merit.
  
• y = 2/20:
  Irrelevant discussion/effectively blank.
  
• z = 0/20:
  Blank.
  

Grading distribution:
Sections 70854, 70855
Exam code: finalB0xs
p: 21 students
r: 13 students
t: 5 students
v: 7 students
x: 1 student
y: 0 students
z: 1 student

A sample "p" response (from student 3389), but applying Newton's laws correctly, but confounding N1, N2, and N3 labels: