20181012

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 µs = 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 µsN = (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):

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