Physics midterm question: removing top object to lessen static friction

Physics 205A Midterm 1, fall semester 2014
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 4.63

A book is placed on a crate. An applied force of 13 N pushes horizontally on the crate, which remains stationary. (The floor is not frictionless.) The book is then removed from off the top of the crate, with the same applied force of 13 N pushing horizontally on the crate. Discuss why the crate will begin to speed up after the book is lifted from off the top. Explain your reasoning using free-body diagram(s), the properties of forces, and Newton's laws.

Solution and grading rubric:

• p:
  Correct. Complete free-body diagrams, and discusses/demonstrates:
  1. the maximum static friction force that must be overcome in order to unstick an object is equal to µ_s⋅N; if a force is applied against the static friction force that is less than µ_s⋅N, the object will remain stuck;
  2. the normal force of the floor on the crate/book system is greater than the normal force of the floor on just the crate system (either using Newton's first and third laws on separate stacked crate, stacked book, and lone crate diagrams, or on combined crate/book versus lone crate diagrams); such that the maximum static friction force to be overcome is greater for the stacked crate/book system than for the lone crate system;
  3. the applied force of 13 N is less than the maximum static friction force of the floor on the stacked/crate system, such that it remains stationary; while the applied force of 13 N must have been greater than the slightly less maximum static friction force of the floor on the lone crate system, such that it unsticks and begins to accelerate to the right.
• r:
  As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes. Minor problem/omission with either free-body diagram, Newton's laws, or properties of static friction.
• t:
  Nearly correct, but argument has conceptual errors, or is incomplete. Two of free-body diagram, Newton's laws, or properties of static friction have minor problems/omissions, or one of those is incomplete/omitted.
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Some garbled attempt at applying Newton's laws to a free-body diagram.
• x:
  Implementation of ideas, but credit given for effort rather than merit. Approach other than that of applying Newton's laws to a free-body diagram.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Grading distribution:
Sections 70854, 70855, 73320
Exam code: midterm01m0oU
p: 17 students
r: 10 students
t: 29 students
v: 17 students
x: 0 students
y: 0 students
z: 1 student

A sample "p" response (from student 2072), treating the book and crate as separate objects for the first case:
Another sample "p" response (from student 5323):