Physics midterm problem: basketball rolling up ramp

Physics 205A Midterm 2, fall semester 2019
Cuesta College, San Luis Obispo, CA

A basketball (mass 0.43 kg, radius 0.11 m) rolls without slipping with a constant initial velocity of 2.4 m/s across a horizontal floor. The basketball begins to roll up a ramp. Determine the highest vertical height that the basketball will reach before rolling back down the ramp. Ignore friction and drag. Show your work and explain your reasoning using the properties of rotational inertia, energy forms, and conservation of energy.

The basketball is a hollow sphere (I_{hollow sphere} = (2/3)·M·R².)


Solution and grading rubric:

• p:
  Correct. Sets up a transfer-balance energy conservation equation with the sum of the changes in translational kinetic energy of the basketball, rotational kinetic energy of the basketball, and gravitational potential energy of the basketball set to zero (as no energy is lost to non-conservative work), fills in all known/given values, and solves for the unknown. (May have ± sign errors for final terms subtracting initial terms, but in a somewhat consistent manner that still results in correct final height of basketball).
• r:
  Nearly correct, but includes minor math errors. Or multiple arithmetic errors.
• t:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. Typically omits one of the energy terms, but attempts to apply energy conservation to the remaining two terms.
• v:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Calculations of some energy terms, but does not sufficiently tie them together in a transfer-balance energy conservation equation. Typically has only one energy term, or relates an energy term with a non-energy quantity (such as weight, momentum, moment of inertia, etc.).
• x:
  Implementation of ideas, but credit given for effort rather than merit. Approach involving methods other than energy conservation.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Grading distribution:
Sections 70854, 70855
Exam code: midterm02sQm5
p: 26 students
r: 16 students
t: 7 students
v: 3 students
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 8520):
Another sample "p" response (from student 1203):