Cuesta College, San Luis Obispo, CA
Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 6.28, Problem 8.60
[10 points.] A block and a cylinder of the same mass both start from rest and respectively slide or roll without slipping down identical ramps. Which object (if any) has a faster speed at the bottom of the ramp, 0.50 m below their starting points? Neglect drag and friction. Explain your answer using energy conservation and properties of rotating/rolling objects. Solution and grading rubric:
- p = 10/10:
Correct. Both objects undergo the same decrease in potential energy, which all goes into translational kinetic energy for the block, but this potential energy must go into both translational kinetic energy and rotational kinetic energy for the cylinder, and thus the cylinder will have slower translational speed. - r = 8/10:
As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes. Accounts for rotational kinetic energy for the cylinder, but concludes that will be moving faster. - t = 6/10:
Nearly correct, but argument has conceptual errors, or is incomplete. Neglects to include rotational kinetic energy for the cylinder, but at least uses energy conservation. - v = 4/10:
Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Uses methods other than a systematic application of energy conservation. - x = 2/10:
Implementation/application of ideas, but credit given for effort rather than merit. - y = 1/10:
Irrelevant discussion/effectively blank. - z = 0/10:
Blank.
Grading distribution:
Section 72177
p: 2 students
r: 5 students
t: 6 students
v: 0 students
x: 0 students
y: 0 students
z: 0 students
A sample "p" response (from student 4747):
A sample "t" response (from student 1445):
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