Physics midterm question: stuck or unstuck crate?

Physics 205A Midterm 1, fall semester 2018
Cuesta College, San Luis Obispo, CA

A force is applied to the right on a 5.0 kg crate on a horizontal floor that has a static friction coefficient µ_s = 0.35. Initially the crate is stationary. Discuss whether or not the crate will remain stationary if the magnitude of the applied force is slowly increased from zero up to a value just below the magnitude of the normal force of the floor on the crate. 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 diagram, and discusses/demonstrates:
  1. the crate has two vertical forces acting on it:

     Weight force of Earth on crate (m·g = 49 N, downwards),
     Normal force of table on crate (49 N, upwards),

     and since there is no vertical motion, these two vertical forces must be equal in magnitude due to Newton's first law;
  2. the maximum amount of static friction force that must be overcome in order to unstick the crate is µ_s⋅N = (0.35)·(49 N) = 17 N; and
  3. since the applied force is slowly increased is "slowly increased from zero up to a value just below the magnitude of the normal force of the floor on the crate" (from 0 N up to 49 N), then the applied force will eventually be greater than maximum static friction force, such that the crate will unstick (and begin 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.
• t:
  Nearly correct, but argument has conceptual errors, or is incomplete. Some substantive attempt at analyzing how/if the maximum static friction force is overcome using Newton's laws and a free-body diagram.
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Some garbled attempt at analyzing how/if the maximum static friction force is overcome using Newton's laws and a free-body diagram.
• x:
  Implementation of ideas, but credit given for effort rather than merit. No systematic attempt at using Newton's laws and a free-body diagram.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Grading distribution:
Sections 70854, 70855
Exam code: midterm01g4iN
p: 20 students
r: 7 students
t: 7 students
v: 12 students
x: 11 students
y: 0 students
z: 0 students

A sample "p" response (from student 6577):