Physics final exam problem: weights added to boxes about to slide

Physics 205A Final Exam, fall semester 2012
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problems 4.74, 4.85

A 3.0 kg box on a horizontal table is attached by a string to a hanging 1.2 kg mass. The string and pulley are ideal, but the table is not frictionless. A Physics 205A student observes that the 1.2 kg hanging mass is just sufficient enough to overcome static friction between the 3.0 kg box and the table. The student resets this experiment, adding 0.1 kg to the box, and 0.1 kg to the hanging mass. Determine whether static friction between the box (now 3.1 kg) and the table would be overcome by the hanging mass (now 1.3 kg). Show your work and explain your reasoning using a free-body diagram, the properties of forces, and Newton's laws.

Solution and grading rubric:

• p:
  Correct. Draws free-body diagrams, and applies properties of forces and Newton's laws to determine the static friction coefficient between the box and table for the first case; then for the second case determines that static friction would be overcome for the box either by discussing how (a) the hanging mass will exert a tension force on the box greater than the maximum static friction force on the box, or (b) the required static friction coefficient between the box and table to remain stationary is greater than the static friction coefficient in the first case, and since the static friction coefficient remains constant, the static friction on the box will again be overcome.
• r:
  Nearly correct, but includes minor math errors.
• t:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors.
• v:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. At least some attempt at applying properties of forces and Newton's laws.
• x:
  Implementation of ideas, but credit given for effort rather than merit. Approach does not substantively use properties of forces and Newton's laws.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Grading distribution:
Sections 70854, 70855
Exam code: finalPr0p
p: 16 students
r: 3 students
t: 8 students
v: 11 students
x: 9 students
y: 2 students
z: 2 students

A sample "p" response (from student 4585):
Another sample "p" response (from student 7582):