20161015

Physics midterm question: horizontally-pulled, diagonally-suspended box

Physics 205A Midterm 1, fall semester 2016
Cuesta College, San Luis Obispo, CA

A box is suspended by an ideal pulley and cable, which is attached at its other end to a wall. A force is applied to the box, pulling it horizontally to the right, such that the lower part of the cable is diagonal instead of vertical. Discuss why the magnitude of the tension in the cable is greater than the magnitude of the applied force. Explain your reasoning using free-body diagram(s), the properties of forces, and Newton's laws.

Solution and grading rubric:
  • p:
    Correct. Complete free-body diagram, and discusses/demonstrates:
    1. Newton's first law applies along the horizontal direction, as there is no horizontal motion, such that the magnitude of the horizontal component of the tension force on the box to the left must equal the magnitude of the applied force on the box to the right:

      Tx = Fapplied;

    2. since the magnitude of the tension force T = √(Tx2 + Ty2), then:

      T > Tx,

      and since Tx = Fapplied from before, thus:

      T > Fapplied.

    (Additional discussion may include Newton's first law applying along the vertical direction, as there is no vertical motion, such that the magnitude of the upwards vertical component of the tension force on the box must equal the magnitude of the downwards weight force of Earth on the box: Ty = w.)
  • 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 laws to free-body diagram(s).
  • x:
    Implementation of ideas, but credit given for effort rather than merit. No systematic application of Newton's laws to the forces on free-body diagram(s).
  • y:
    Irrelevant discussion/effectively blank.
  • z:
    Blank.
Grading distribution:
Sections 70854, 70855, 73320
Exam code: midterm01br1Q
p: 9 students
r: 3 students
t: 13 students
v: 15 students
x: 17 students
y: 0 students
z: 0 students

A sample "p" response (from student 8108):

Another sample "p" response (from student 2127):

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