Physics final exam question: comparing boom crane piston forces

Physics 205A Final Exam, fall semester 2016
Cuesta College, San Luis Obispo, CA

A telescoping boom crane can either be supported by two types of diagonal pistons, attached to the same point along the boom. (Calculate all torques with respect to the pivot, located at the base of the boom, approximated here as a uniform beam.) Determine which piston is exerting a greater magnitude force on the boom, or if there is a tie. Explain your reasoning using diagram(s) with locations of forces and perpendicular lever arms, the properties of torques, and Newton's laws.

Solution and grading rubric:

• p:
  Correct. Complete free-body diagrams with forces and perpendicular lever arms, and discusses/demonstrates:
  1. for either case (piston (A) or piston (B)), the cw piston torque = l_piston⋅F_piston and ccw weight torque = l_weight⋅w; and
  2. since Newton's first law applies to both cases (piston (A) or piston (B)), the ccw torque of the piston on the boom equals the cw torque of the weight on the boom such that l_piston⋅F_piston = l_weight⋅w; then
  3. for piston (A) and piston (B), the ccw torque of the piston on the boom l_piston⋅F_piston has the same value;
  4. the perpendicular lever arm l_piston is smaller for piston (A) and larger for piston (B), and since l_piston⋅F_piston remains constant, then F_piston must be larger for piston (A) and smaller for piston (B).
• r:
  As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes. May have only implied Newton's first law in order to compare (equal) piston torques.
• t:
  Nearly correct, but argument has conceptual errors, or is incomplete. May not have recognized difference in l_piston lever arms (claiming that they are the same, and thus F_piston forces are the same); or recognizes difference in l_piston, but claims that piston (B) has the greater F_piston force.
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Some garbled attempt at applying Newton's first law to torques, forces, and perpendicular lever arms. May have pistons exerting different amounts of torques.
• x:
  Implementation of ideas, but credit given for effort rather than merit. Approach other than that of applying Newton's first law to torques, forces, and perpendicular lever arms.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Grading distribution:
Sections 70854, 70855, 73320
Exam code: finali0w4
p: 22 students
r: 3 students
t: 19 students
v: 5 students
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 6436):