20181123

Physics midterm question: comparing horizontal forces supporting tilted beams

Physics 205A Midterm 2, fall semester 2018
Cuesta College, San Luis Obispo, CA

A horizontal force is applied to hold a uniform beam stationary at an angle of 80° above the horizontal, and another horizontal force is applied to hold it stationary at an angle of 10° above the horizontal. (Calculate all torques with respect to the pivot, located at the base of the beam.) Discuss why less force required to hold the beam when it is at the higher 80° angle. 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:
    Complete free-body diagrams with forces and perpendicular lever arms, and discusses/demonstrates:
    1. the magnitude of the weight force w is the same for both higher and lower beams; but
    2. the lever arms ℓF are not the same, where ℓF is longer for the higher beam, and shorter for the lower beam; and
    3. the lever arms ℓw are not the same, where ℓw is shorter for the higher beam, and longer for the lower beam; and
    4. Newton's first law for rotations applies to both higher and lower beams, where the ccw force τ = F⋅ℓF and cw weight τ = w⋅ℓw must balance each other out, and so:
      F⋅ℓF = w⋅ℓw,

      F = w⋅(ℓw/ℓF);
      such that
    5. for the higher beam, the shorter ℓw in the numerator and longer ℓF in the denominator means that the applied force F is smaller than for the lower beam (where it has a longer ℓw in the numerator and a shorter ℓF in the denominator).
  • r:
    As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes. At least demonstrates that for the higher beam ℓw is shorter and ℓF is longer, but typically discusses only how one of these contributes to making the applied force smaller.
  • t:
    Nearly correct, but argument has conceptual errors, or is incomplete. Typically argues that F is smaller for the higher beam because ℓF is larger (while claiming ℓw is the same for both beams); or F is smaller for the higher beam because ℓw is smaller (while claiming ℓF is the same for both beams).
  • 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
Exam code: midterm02r3iN
p: 17 students
r: 4 students
t: 21 students
v: 10 students
x: 5 students
y: 0 students
z: 0 students

A sample "p" response (from student 5250):

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