Cuesta College, San Luis Obispo, CA
Cf. Giambattista/Richardson/Richardson, Physics, 1/e, Comprehensive Problem 4.146
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Solution and grading rubric:
- p = 20/20:
Correct. At the angle where static friction is (about to be) overwhelmed, it is equal to the x-component of weight, and Newton's first law is used to determine that the angle theta = 24.2 degrees. At this angle, kinetic friction acts on box, and Newton's second law is used to find that the acceleration of the box is 1.52 m/s^2 down along the ramp. - r = 16/20:
Nearly correct, but includes minor math errors. Correct angle for ramp, but acceleration has minor problems, such as kinetic friction being the only force acting along the x-direction in Newton's second law, or divides by g instead of by mass on both sides of Newton's second law. - t = 12/20:
Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. Angle of board is wrong, but accounts for both kinetic friction and the x-component of weight acting on the box in Newton's second law. Or determines correct angle of board, but nothing much further than that. - v = 8/20:
Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Some systematic attempt at both the (limiting) static and accelerating case. - 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:
p: 3 students
r: 4 students
t: 9 students
v: 9 students
x: 7 students
y: 1 student
z: 0 students
A sample of a "p" response (from student 6154) is shown below:
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An "r" response (from student 2012), where the sine and cosine components were inadvertently switched, but following results were essentially correct:
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Another "r" response (from student 5711), where at the last step, g is divided from both sides of Newton's second law, instead of m:
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A "t" response (from student 2880), where only the angle of the board is found:
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