Physics midterm problem: box on box

Physics 8A Midterm 1, Spring Semester 2007
Cuesta College, San Luis Obispo, CA

Physics 8A learning goal M1.5

[20 points.] Two boxes are stacked upon each other. A horizontal force of 40.0 N is applied as shown to the top box. The magnitude of the friction force between the surfaces of the upper and lower boxes is 23.0 N. Both boxes accelerate to the right with a constant magnitude of 2.00 m/s^2, as they move together across a frictionless floor. Determine the mass of the upper box, and the mass of the lower box. Show your work and explain your reasoning.

(Cf. Young and Freeman, University Physics, 11/e, Exercise 4.24, Problem 4.39.)

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 is equal to the vector sum of the given applied force (right) and friction force (left), and set equal to the mass of the top box times the given acceleration; m_top = 8.50 kg. Then Newton's second law is applied to the bottom box, where the net force only consists of the friction force (right, which is the third law pair to the friction force of the bottom box on the top box), and set equal to the mass of the bottom box times the given acceleration (which must be the same as the top box); m_bottom = 11.5 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 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:
p: 7 students
r: 14 students
t: 9 students
v: 3 students
x: 3 students
y: 0 students
z: 2 students