Physics midterm problem: Cooper's Hill Cheese-Rolling and Wake event

Physics 205A Midterm 2, fall semester 2012
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problems 8.59, 8.60

"Gloucester Cheese Rolling 2012 OFFICIAL - World's Stupidest Competition"
Maximilien Czech (maxdreamcreator)
youtu.be/dtvG9XDtjv4

The annual Cooper's Hill Cheese-Rolling and Wake event in Gloucester, England is held on the last Monday in May.

From the top of the hill a round of...cheese is rolled, and competitors race down the hill after it. The first person over the finish line at the bottom of the hill wins the cheese. In theory, competitors are aiming to catch the cheese, however it has around a one second head start, and can reach speeds up to 70 mph [31 m/s]...[*]

Determine whether it is plausible or not for the cheese to attain this translational speed at the bottom of the hill. Neglect kinetic friction and drag. Approximate the cheese wheel as a solid cylinder of radius 0.25 m[**] and mass 3.6 kg[***], which rolls without slipping after it is released from rest at the top of a hill 90 m in elevation, which makes an angle of 45° with respect to the horizontal[***]. 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.)

[*] wiki.pe/Cooper's_Hill_Cheese-Rolling_and_Wake.
[**] "20 inches wide," britishcheese.com/doublegloucester.
[***] "The cheeses used today are Double Gloucester cheeses weighing 7-8 lb," "distance from start to finish is approximately 90 meters as measured on the map," "slope has a gradient that is in places 1-in-2 and in others 
1-in-1," cheese-rolling.co.uk/where.htm.

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 (no non-conservative work) for a solid cylinder (disk) rolling without slipping, solves for the final translational speed at the bottom of the hill, and notes the plausibility of attaining the stated speed.
• r:
  Nearly correct, but includes minor math errors. As (p), but has misplaced or missing factors in algebra, or uses hypotenuse instead of height. Plausibility argument consistent with results.
• t:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. Garbles rolling without slipping condition, but considers changes in translational kinetic energy, rotational kinetic energy, and gravitational potential energy in the energy balance equation.
• v:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. As (t), but does not systematically take into account changes in all three energy forms in an energy balance equation.
• x:
  Implementation of ideas, but credit given for effort rather than merit. Some attempt at calculating only one energy term, or an attempt to apply translational kinematics.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Grading distribution:
Sections 70854, 70855
Exam code: midterm02gL0u
p: 19 students
r: 14 students
t: 13 students
v: 5 students
x: 2 students
y: 1 student
z: 0 students

A sample "p" response (from student 1970)
Another sample "p" response (from student 9187), with participants, spectators, and a very large wheel of cheese: