## 20161103

### Physics final exam problem: rolling spool non-conservative energy losses

Physics 205A Final Exam, fall semester 2015
Cuesta College, San Luis Obispo, CA

"Hilarious moving company accident!"
ME5723
youtu.be/jo3ohNxEGkM

A spool of cable (approximated as a disk of 0.90 m radius and 80 kg mass) is rolled up a ramp built on a flight of stairs. It is (accidentally) released from rest, rolls down the ramp, and has a final speed of 12 m/s as it reaches the bottom of the ramp[*]. If the spool was released from a vertical height of 14 m above the bottom of the ramp, determine how much energy (if any) was lost to drag/friction. Show your work and explain your reasoning using the properties of rotational inertia, energy forms, and (non-)conservation of energy.

(Given: Idisk = (1/2)·M·R2.)

[*] youtu.be/jo3ohNxEGkM.

Solution and grading rubric:
• p:
Correct. Sets up a transfer-balance energy conservation equation with changes in translational kinetic energy, rotational kinetic energy (with the rolling without slipping condition), and gravitational potential energy, and finds the amount of energy lost to drag/friction, which is the sum of all these changes in total mechanical energy forms.
• r:
Nearly correct, but includes minor math errors.
• t:
Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. At least enough steps are shown that would theoretically result in a complete answer, multiple errors notwithstanding.
• 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.
• 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, 73320
Exam code: final7rUk
p: 13 students
r: 14 students
t: 23 students
v: 11 students
x: 5 students
y: 2 students
z: 2 students

A sample "p" response (from student 1114):