Physics final exam problem: sliding and falling string-connected boxes

Physics 205A Final Exam, spring semester 2009
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 4.87

Consider a 5.0 kg box on a horizontal table, which is not frictionless. A second box of mass 2.0 kg hangs from an ideal cord of negligible mass that runs over an ideal pulley and then is connected to the 5.0 kg box. The boxes are released from rest, and accelerate at a rate of 1.6 m/s². What is the magnitude of the kinetic friction force on the 5.0 kg box? Show your work and explain your reasoning using free-body diagram(s), the properties of forces, and Newton's laws.

Solution and grading rubric:

• p:
  Correct. Isolates 5.0 kg and 2.0 kg boxes by drawing free-body diagrams for each, and applies Newton's second law to each box. Finds that the upwards tension force on the 2.0 kg box is 16.4 N (which is equal in magnitude to the rightwards tension force on the 5.0 kg box, from Newton's third law). Thus the leftwards kinetic friction force on the 5.0 kg box must be 8.4 N. (May also use a combined 7.0 kg box with only weight and kinetic friction acting on opposite directions on it.)
  
• r:
  Nearly correct, but includes minor math errors.
  
• t:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. Applies Newton's first law instead of Newton's second law to the 2.0 kg box, effectively making the tension force 19.6 N.
  
• v:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Some application of Newton's laws to forces shown on free-body diagrams.
  
• x:
  Implementation of ideas, but credit given for effort rather than merit. Approach involving methods other than application of Newton's laws.
  
• y:
  Irrelevant discussion/effectively blank.
  
• z:
  Blank.
  

Grading distribution:
Sections 30880, 30881
Exam code: finalDe4f
p: 3 students
r: 2 students
t: 17 students
v: 10 students
x: 6 students
y: 1 student
z: 0 students

A sample "p" response (from student 0915), treating the 5.0 kg box and 2.0 kg box as separate objects:
Another sample "p" response (from student 2679), treating the 5.0 kg box and the 2.0 kg box as a single object:
A sample "r" response (from student 2411), which has the 2.0 kg box accelerating upwards, due to a sign error on a vector direction:
A sample "t" response (from student 1830), with Newton's first law applied to the 2.0 kg box, but Newton's second law correctly applied to the 5.0 kg box. Note that additional step of finding coefficient of kinetic friction: