Cuesta College, San Luis Obispo, CA
Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 8.59, Review & Synthesis 10 (p. 311).
[20 points.] A 0.45 kg solid disk of radius 0.050 m has an initial translational speed of 2.8 m/s as it rolls without slipping across a floor. The disk begins to roll up a ramp with a horizontal level 0.80 m above the floor. Will the disk make it to the horizontal level at the top of the ramp? Neglect drag. Show your work and explain your reasoning.Solution and grading rubric:
- p = 20/20:
Correct. Sets up an energy conservation equation with changes in gravitational potential energy, translational kinetic energy, and rotational kinetic energy summing to zero (applying v = R*ω for rolling without slipping, and I = (1/2)*m*R2 for a solid cylinder), and solves for yi = 0.60 m, which is interpreted to mean that it will not reach the top of the ramp. Arithmetical
errors (± signs, cancellation, decimal point) okay. - 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. - v = 8/20:
Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Neglects rotational kinetic energy, thus solving for the translational speed of a sliding (point) mass. Or neglects translational kinetic energy, thus solving for the rotational speed of a cylinder given the gravitational potential energy of an equivalent point mass. - x = 4/20:
Implementation of ideas, but credit given for effort rather than merit. Garbled attempt at calculating energy terms, or may involve kinematics. - y = 2/20:
Irrelevant discussion/effectively blank. - z = 0/20:
Blank.
Grading distribution:
Sections 70854, 70855
Exam code: finalB0xs
p: 23 students
r: 0 students
t: 11 students
v: 7 students
x: 3 students
y: 0 students
z: 4 students
A sample "p" response (from student 3234):
Another sample "p" response (from student 4224):
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