Physics midterm question: horizontally and diagonally-pulled suitcases

Physics 205A Midterm 1, fall semester 2011
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Example 4.13

A suitcase is dragged across a floor either using a horizontal rope, or using a diagonal upwards rope. The floor is not frictionless. Discuss why there is less kinetic friction force on the diagonally upwards pulled suitcase. Explain your reasoning by using free-body diagram(s), the properties of friction, forces, and Newton's laws.

Solution and grading rubric:

• p:
  Correct. Discusses how (kinetic) friction force is proportional to the normal force exerted by the floor, and from Newton's first law, the vertical component of the applied force decreases the normal force (as they must together be equal to the weight) and thus the friction force is less than the first case, when then normal force is equal to the weight.
  
• 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. May state that the vertical component of the applied force decreases the weight, such that the normal force (equal to the weight) is decreased, thus decreasing the kinetic friction force (proportional to the normal force).
  
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. At least some application of Newton's laws to compare kinetic friction forces using a free body diagram, with applied force decomposed into horizontal and vertical components.
  
• x:
  Implementation/application of ideas, but credit given for effort rather than merit. Appeals to less surface area as causing less friction.
  
• y:
  Irrelevant discussion/effectively blank.
  
• z:
  Blank.
  

Grading distribution:
Sections 70854, 70855
Exam code: midterm01w4Sh
p: 16 students
r: 0 students
t: 15 students
v: 19 students
x: 3 students
y: 0 students
z: 0 students

A sample "p" response (from student 3389), correctly applying Newton's first law along the vertical direction for both suitcases, but inadvertently labeling it "Newton's second law" for the second suitcase: