Physics midterm problem: Russky Bridge scale model

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

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problems 8.35(a), 8.37

[20 points.] A Physics 205A student makes a scale model of the Russky Bridge in Vladivostok, Russia(*), during its construction. A meter stick(**) of uniform density and mass 0.178 kg is attached to a pivot point, and is suspended by two parallel strings that each have the same magnitude tension force. A 0.080 kg mass is attached to the far end of the meter stick. Determine the magnitude of the tension force in either of the strings. Show your work and explain your reasoning.

Image source: Vitaliy Ankov, "Lifting a double bridge bay section during the construction," http://russiaprofile.org/photos/52678_6.html

(*) "The world's largest cable-stayed bridge," http://en.wikipedia.org/wiki/Russky_Bridge.
(**) http://flic.kr/p/duoug.

Solution and grading rubric:

• p = 20/20:
  Correct. Applies Newton's first law (rotational equilibrium) by balancing out the sum of the two clockwise torques (of meter stick's weight, and of the mass hanging at end) with the sum of the two counterclockwise torques (of the middle and end strings, which have the same magnitude tension, but different lever arms), and solves for their tensions, which is 1.2 N. (May have used masses instead of weights for the meter stick and hanging mass in calculating torques.)
• r = 16/20:
  Nearly correct, but includes minor math errors. Effectively solves for tension in a system supported by only one string (either attached to the middle, or the end). Still has correct sum of clockwise torques, and identifies correct lever arm for the relevant string.
• t = 12/20:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. May have either (a) separately set the inner string's torque equal to the torque of the meter stick's weight, and the outer string's torque equal to the torque of the hanging mass' weight, and separately solved for the two different string tensions. Or (b) may have claimed that the two strings exert equal amounts of (counterclockwise) torque, and then solved for at least one of the string tensions. At least identifies four different torques acting on the meter stick, calculates each torque with the proper lever arms, and attempts to apply the rotational equilibrium condition.
• v = 8/20:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Some attempt at finding lever arms and applying rotational equilibrium condition to torques.
• x = 4/20:
  Implementation of ideas, but credit given for effort rather than merit. May involve periods of simple harmonic motion systems.
• y = 2/20:
  Irrelevant discussion/effectively blank.
• z = 0/20:
  Blank.

Grading distribution:
Sections 70854, 70855
Exam code: midterm02gL0u
p: 9 students
r: 6 students
t: 5 students
v: 25 students
x: 9 students
y: 0 students
z: 0 students

A sample "p" response (from student 1223):