Cuesta College, San Luis Obispo, CA
Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 5.79
[20 points.] A 0.0023 kg coin is to be placed on a horizontal turntable that will rotate at 4.7 rad/s. The coefficient of static friction between the coin and the turntable is 0.25, and the coin is at a distance of 0.087 m from the center of the turntable. Will the coin stay on the turntable, or begin to slide off? Show your work and explain your reasoning.
Solution and grading rubric:
- p = 20/20:
Correct. Compares the maximum static friction force with the required net force for uniform circular motion, or the maximum radial acceleration that the static friction force can provide with the radial acceleration at 4.7 rad/s, and interprets relative values correctly to state whether coin would slide off or not. - r = 16/20:
Nearly correct, but includes minor math errors. - t = 12/20:
Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. Mixes (correctly calculated magnitudes of) forces and accelerations, or problematic calculation to compare forces or to compare accelerations, but rational comparison of relative values to reach a conclusion. - v = 8/20:
Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Use of energy conservation or kinematics to calculate quantities to compare. - x = 4/20:
Implementation of ideas, but credit given for effort rather than merit. - y = 2/20:
Irrelevant discussion/effectively blank. - z = 0/20:
Blank.
Grading distribution:
Section 72177
p: 2 students
r: 0 students
t: 4 students
v: 6 students
x: 0 students
y: 1 student
z: 0 students
Sections 70854, 70855
p: 3 students
r: 2 students
t: 8 students
v: 21 students
x: 11 students
y: 1 student
z: 2 students
A sample "p" response (from student 5555):
Another sample "p" response (from student 9626):
A sample "r" response (from student 2889), using a = w*r^2 instead of a = r*w^2:
A sample "v" response (from student 7895), who appears to be a gambler:
Another sample "v" response (from student 1230), ensuring that the coin will stay on by other means:
A sample "x" response (from student 2022):
Another sample "x" response (from student 1052):
I would not score student 9626 with P since it is not in fact correct. The correct outcome is deduced but a common conceptual error is asserted. There is no outward force trying to push the coin off. Instead an inward force of 0.0044N is required to prevent it from traveling in a straight line (slide off) and as friction is capable of roughly 25% more than this, friction is capable of keeping the coin on the record. Asserting an outward force is conceptually incorrect. Since the student gives no hint of non-inertial frames, we need not debate a potential reply invoking this perspective.
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