Physics midterm question: tilting up a plywood board

Physics 205A Midterm 2, fall semester 2014
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Multiple-Choice Question 8.10, Problem 8.19

A Physics 205A student lifts a plywood board and keeps it stationary, while it is just off of the floor, or when it is nearly vertical. In both cases the student exerts a force perpendicular to the top edge of the board, which can be approximated as a uniform beam pivoted at the bottom edge. Discuss why more force must be exerted to hold it just off the floor, compared to when it is nearly vertical. 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. Newton's first law applies to each case, such that the cw torque of the student equals the ccw torque of the weight;
  2. the weight force is the same in either case, as is the perpendicular lever arm for the student's force;
  3. since the perpendicular lever arm for weight is less for the second case, then the magnitude of the student's force will be less.
• r:
  Nearly correct, but includes minor math errors. As (p), but typically does not explicitly note that the perpendicular lever arm for the student's force is the same in either case (board length L).
• t:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. Typically has a different perpendicular lever arm for the student's force in either case.
• v:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Some garbled attempt at applying Newton's first law to torques, forces, and perpendicular lever arms. May apply Newton's first law to equate weight or student torque in one case to the weight or student torque in the other case.
• 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: midterm02veR1
p: 22 students
r: 9 students
t: 13 students
v: 14 students
x: 8 students
y: 0 students
z: 0 students

A sample "p" response (from student 9950):
A sample "t" response (from student 1991), with the student's lever arm being different for either case, while the torque produced by the weight force remains the same: