Physics final exam problem: disk rolling uphill

Physics 205A Final Exam, fall semester 2011
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 8.59, Review Exercise 10 (p. 311).

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. Determine whether the disk will make it to the horizontal level at the top of the ramp. Neglect drag. Show your work and explain your reasoning using the properties of rotational inertia, energy forms, and conservation of energy.

(Given: I_disk = (1/2)·M·R².)

Solution and grading rubric:

• p:
  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 y_i = 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:
  Nearly correct, but includes minor math errors.
  
• t:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors.
  
• v:
  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:
  Implementation of ideas, but credit given for effort rather than merit. Garbled attempt at calculating energy terms, or may involve kinematics.
  
• y:
  Irrelevant discussion/effectively blank.
  
• z:
  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):