Physics final exam problem: bobsleigh non-conservative energy losses

Physics 205A Final Exam, fall semester 2014
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 6.9, Comprehensive Problems 6.87, 6.79

"Bobsleigh - Four-Man Heats 3 & 4 - Russia Win Gold | Sochi 2014 Winter Olympics"
Olympics
youtu.be/KK77jDwfd1M

The Sanki Sliding Center bobsleigh track used for the 2014 Sochi Winter Olympics is 1,365 m long (as measured along the track), and the drop in height from start-to-finish is 131.9 m[*]. The four-man Russian Federation Team 1 won the gold medal for this competition with their last run starting with an initial speed of 14.1 m/s, and ending with a final speed of 38.1 m/s[**]. Assume that the total mass of the bobsleigh and riders was the maximum allowed value of 6.30×10² kg[***], and the kinetic friction force between the bobsleigh and ice has a constant value of 60 N[****].

Find (a) the total amount of non-conservative work done on the bobsleigh (due to friction, air drag, bumping against the track walls, etc.), and (b) determine whether the energy lost due to kinetic friction during this bobsleigh run was negligible or substantive. Show your work and explain your reasoning using the properties of energy forms and (non-)conservation of energy.

[*] "Sliding Center Sanki: Track," wki.pe/Sliding_Center_Sanki#Track.
[**] youtu.be/KK77jDwfd1M.
[***] olympic.org/bobsleigh-equipment-and-history.
[****] M. Scherge, R. Böttcher, M. Richter, and U. Gurgel, "High-Speed Ice Friction Experiments under Lab Conditions: On the Influence of Speed and Normal Force," Tribology, International Scholarly Research Notices (2013), article 703202, dx.doi.org/10.5402/2013/703202.

Solution and grading rubric:

• p:
  Correct. Determines:
  1. the total work done by non-conservative forces against the motion of the bobsleigh, by setting up an energy/transfer equation, and solving for the net change in the (increasing) translational kinetic energy and (decreasing) gravitational potential energy of the bobsleigh;
  2. the non-conservative work done by the kinetic friction force against the motion of the bobsleigh;
  3. compares the two values, and finds that while the kinetic friction force does a substantive amount of non-conservative work against the bobsleigh, it is not the prevalent source of energy loss for the bobsleigh's mechanical energy systems.
• r:
  Nearly correct, but includes minor math errors. Two of the three points (1)-(3) correct, the third is problematic/incomplete.
• t:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. Only one of the three points (1)-(3) correct, other two are problematic/incomplete. 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 energy terms, but does not tie them together in an 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: finalm34T
p: 3 students
r: 15 students
t: 24 students
v: 12 students
x: 1 student
y: 3 students
z: 4 students

A sample "p" response (from student 1107):