Physics 205A Midterm 1, fall semester 2013
Cuesta College, San Luis Obispo, CA
Cf. Giambattista/Richardson/Richardson,
Physics, 2/e, Problem 4.63
A force of 10.0 N pushes on 5.0 kg crate that is initially stationary, and as a result it becomes unstuck and begins to slide. When the 2.0 kg book is stacked on top of the crate, a force of 10.0 N pushes on the crate, and both book and crate remain motionless. Determine a plausible numerical value for the coefficient of static friction µ
s for the crate and the floor. Show your work and explain your reasoning using a free-body diagram, the properties of forces, and Newton's laws.
Solution and grading rubric:
- p:
Correct. Draws free-body diagrams and applies Newton's laws and
definitions of maximum static friction forces. For the crate, the applied force
of 10.0 N must be just at or above the maximum static friction force of µs⋅(49
N), which yields a maximum value of 0.20 for µs. For the book stacked on the
crate, the applied force of 10.0 N must be below the maximum static friction
force of µs⋅(68 N), which yields a minimum value of 0.15 for µs. Thus the
static coefficient of friction µs between the crater and floor must have some
specific value between 0.15 and 0.20. May instead have determined that µs =
0.20 for the critical case of the applied force just being able to unstick the
crate, and demonstrates that this µs value would result in a maximum static
friction force of 14 N for the book on crate, such that it would remain
stationary; or determined that µs = 0.15 for the critical case of the applied
force just being able to unstick the book on crate, and demonstrates that this
µs value would result in a maximum static friction force of 7.4 N for the crate,
such that it would become unstuck.
- r:
Nearly correct, but includes minor math errors. Determines bounding
values for µs (0.15, 0.20), but does not explicitly interpret µs must be some
value between 0.15 and 0.20.
- t:
Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. Has free-body diagram and methodical application
of Newton's laws to determine one of the boundary values of µs from one of the
two cases, but does not explicitly demonstrate that it would apply to the other
case.
- v:
Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Free-body diagram identifies most forces and their
directions, with some attempt at applying Newton's laws.
- x:
Implementation of ideas, but credit given for effort rather than merit. Garbled/incomplete free-body diagram with little to no application of
Newton's laws, etc.
- y:
Irrelevant discussion/effectively blank.
- z:
Blank.
Grading distribution:
Sections 70854, 70855, 73320
Exam code: midterm01p0To
p: 18 students
r: 9 students
t: 9 students
v: 33 students
x: 4 students
y: 0 students
z: 0 students
A sample "p" response (from student 0825), finding the range of possible µ
s values:
Another sample "p" response (from student 0494), demonstrating that the lowest possible µ
s value would work in both cases:
A force of 10.0 N pushes on 5.0 kg crate that is initially stationary, and as a result it becomes unstuck and begins to slide. When the 2.0 kg book is stacked on top of the crate, a force of 10.0 N pushes on the crate, and both book and crate remain motionless. Determine a plausible numerical value for the coefficient of static friction µs for the crate and the floor. Show your work and explain your reasoning using a free-body diagram, the properties of forces, and Newton's laws. 
