Physics midterm question: extended boom crane torques, forces

Physics 205A Midterm 2, fall semester 2016
Cuesta College, San Luis Obispo, CA

A telescoping boom crane extends its length (while keeping the mass of the boom constant), supported by a vertical piston. (Calculate all torques with respect to the pivot, located at the base of the boom, approximated here as a uniform beam.) Discuss why the force exerted by the piston increases as the boom is extended. 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 (short boom or long boom), the cw piston torque = ℓ_piston⋅F_piston and ccw weight torque = ℓ_w⋅w; and
  2. since Newton's first law applies to both cases (short boom and long boom), 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_w⋅w; then
  3. for the long boom case compared to the short boom case, the perpendicular lever arm ℓ_w is longer (while w remains the same), and since ℓ_piston remains the same, then F_piston must increase.
• r:
  As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes.
• t:
  Nearly correct, but argument has conceptual errors, or is incomplete.
• 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.
• 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: midterm02oPt0
p: 17 students
r: 10 students
t: 11 students
v: 17 students
x: 1 student
y: 0 students
z: 0 students

A sample "p" response (from student):