Physics midterm question: comparing inversion of stacked two-object systems

Physics 205A Midterm 1, fall semester 2015
Cuesta College, San Luis Obispo, CA

In case (A), a 5.0 kg crate rests on a 2.0 kg book. In case (B), the 2.0 kg book rests on the 5.0 kg crate. (Everything is stationary in both cases (A) and (B).) Discuss why the magnitude of the normal force of the book on the crate is greater for case (A) than in case (B). 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 diagrams for the crate and the book for either case (or just shows the essential forces necessary for applying Newton's first law and Newton's third law) to discuss/demonstrate:
  1. Case (A):
     Crate has two forces acting on it, which must be equal in magnitude and opposite in direction due to Newton's first law:

     w_{Earth on crate} = m_crate⋅g = 49 N downwards;
     N_{book on crate} = 49 N upwards.

  2. Case (B):
     Book has two forces acting on it, which must be equal in magnitude and opposite in direction due to Newton's first law:

     w_{Earth on book} = m_book⋅g = 20 N downwards;
     N_{crate on book} = 20 N upwards.

  3. From Newton's third law in case (B), the upwards N_{crate on book} force must be equal in magnitude and opposite in direction to the downwards N_{book on crate} force, and thus N_{book on crate} (downwards) = 20 N.
  
  Therefore for case (A), N_{book on crate} = 49 N (upwards) has a greater magnitude than in case (B), where N_{book on crate} = 20 N (downwards).
• 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. Typically only compares N_{book on crate} from case (A) with N_{crate on book} from case (B) (missing Newton's third law discussion). At least has complete free-body diagrams for the crate in case (A) and the book in case (B), with discussion of applying Newton's first law to the forces acting on each object in each case.
• 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 a free-body diagram. May discuss how upwards N_{floor on book} in case (A) has a greater magnitude (69 N) than the 20 N magnitude of the various forces in case (B) (w_{Earth on book}, N_{book on crate}, N_{crate on book}).
• x:
  Implementation of ideas, but credit given for effort rather than merit. No systematic application of Newton's laws to the forces on a free-body diagram.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Grading distribution:
Sections 70854, 70855, 73320
Exam code: midterm01j0r6
p: 7 students
r: 12 students
t: 31 students
v: 23 students
x: 3 students
y: 2 students
z: 0 students

A sample "p" response (from student 4815):
A sample "t" response (from student 0801), omitting Newton's third law and only comparing N_{book on crate} from case (A) with N_{crate on book} from case (B):