Physics final exam problem: tow truck vs. tugboat tug-of-war

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

"Chevron Delo's Ultimate Tug Of War"
DeloPerformance
youtu.be/a6HUFm6FKD4

A tow truck[*] (mass 2.5×10⁴ kg) and a tugboat pull on each other in a tug-of-war.[**] It is claimed[***] that the tugboat requires more tension to pull the truck when the cable is diagonal (10° below the horizontal), and less tension to pull the truck when the cable is horizontal. Discuss whether this claim is plausible or implausible, and how you know this. Assume that the truck's wheels are locked, and the truck is sliding to the right across the horizontal dock at constant speed. The kinetic friction coefficient for tires on concrete[****] is 0.8. Show your work and explain your reasoning using free-body diagrams, the properties of forces, and Newton's laws.

[*] rechtieninternationaltrucks.com/listings/2015-kenworth-t838-heavy-duty-wrecker-with-vulcan-v703/.
[**] youtu.be/a6HUFm6FKD4.
[***] throt-l.com/autos/surf-turf-tug-of-war-test-pits-a-kenworth-tow-truck-vs-a-900hp-tug-boat/.
[****] Raymond A. Serway, Robert J. Beichner, Physics for Scientists and Engineers with Modern Physics (5th ed.), Saunders (1999), p. 133.

Solution and grading rubric:

• p:
  Correct. Draws free-body diagrams for both diagonal and horizontal cable cases, where:
  1. from Newton's first law is applied along the vertical direction for both cases, such that it is clear that the diagonal cable case will result in a greater (upwards) normal force being exerted by the dock on the truck in the diagonal case;
  2. from the dependence of kinetic (sliding) friction on the normal force, there will result a greater amount of kinetic friction force of the dock on the truck in that case;
  3. from Newton's first law is applied along the horizontal direction for both cases, such that it is clear that the horizontal component of the cable tension on the truck will be greater for the diagonal cable case, such that the claim is plausible.
  (It is not necessary to use both vertical and horizontal components of the cable tension force in the diagonal case to show that it would have a greater magnitude than for the horizontal case in order to prove that the claim is plausible. Also may have numerically solved for the cable tension for each case.)
• r:
  Nearly correct, but includes minor math errors. As (p), but application of Newton's laws and/or properties of forces is slightly problematic.
• t:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. May have horizontal components of the cable tensions as equal for both cases, etc.
• v:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Some substantive attempt at applying properties of forces and Newton's laws to free-body diagrams.
• x:
  Implementation of ideas, but credit given for effort rather than merit. No systematic application of properties of forces and Newton's laws to the forces on free-body diagrams.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Grading distribution:
Sections 70854, 70855
Exam code: final7rUk
p: 9 students
r: 12 students
t: 9 students
v: 17 students
x: 21 students
y: 2 students
z: 0 students

A sample "p" response (from student 0217):
Another sample "p" response (from student 2681):