Physics midterm problem: crane-suspended caboose

Physics 205A Midterm 2, fall semester 2013
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 8.30

"_DSC8438.JPG"
Northwest Railway Museum
http://trainmuseum.blogspot.com/2010/11/x101-caboose-caper.html

At the Northwest Railway Museum in 2011, a train caboose was lifted and transported using two cranes[*][**]. Assume that when the caboose is suspended such that it is horizontal, the tension in each crane's cable is 73,000 N. If the caboose is instead tilted at an angle such that the center of mass is slightly closer to one cable than the other, determine the magnitude of the left cable tension force, and magnitude of the right cable tension force. Assume all forces on the caboose are vertical. Show your work and explain your reasoning.

[*] "X101 caboose caper," November 7, 2010, http://trainmuseum.blogspot.com/2010/11/x101-caboose-caper.html.

[**] Image source: "Terex RT 345 loading chart," http://www.bigge.com/crane-charts/how-to-read-load-charts.html.

Solution and grading rubric:

• p = 20/20:
  Correct. Applies Newton's first laws for (a) translational equilibrium (the two upwards tension forces balancing the downward weight force) and (b) rotational equilibrium (the clockwise torques balancing the counterclockwise torques, about any selected pivot point). Then solves for the two tension forces.
• r = 16/20:
  Nearly correct, but includes minor math errors. May have instead solved for the (correct) tension values by appealing to a "lever arm proportions" without explicitly demonstrating how Newton's first law for rotational equilibrium would result in this.
• t = 12/20:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. At least identifies forces that exert torques on the caboose, and attempts to apply Newton's first laws for translational and rotational equilibrium.
• v = 8/20:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Some attempt at applying Newton's first laws for translational or rotational equilibrium.
• x = 4/20:
  Implementation of ideas, but credit given for effort rather than merit. May involve periods of simple harmonic motion systems, and Young's law.
• y = 2/20:
  Irrelevant discussion/effectively blank.
• z = 0/20:
  Blank.

Grading distribution:
Sections 70854, 70855, 73320
Exam code: midterm02j0R6
p: 5 students
r: 13 students
t: 9 students
v: 19 students
x: 18 students
y: 2 students
z: 1 student

A sample "p" response (from student 1983):