Physics midterm question: comparing net force for afloat vs. submerged sinking block

Physics 205A Midterm 2, fall semester 2019
Cuesta College, San Luis Obispo, CA

A solid object is (a) partially submerged in water as it sinks with increasing speed, then while (b) completely underwater it still sinks with increasing speed. Discuss why the magnitude of the net force on the object is greater for case (a) than for case (b). Ignore friction and drag. Explain your reasoning using the properties of Newton's laws, Archimedes' principle (buoyant forces), and free-body diagrams.

Solution and grading rubric:

• p:
  Correct. Recognizes that:
  1. each block (a) or (b) has two vertical forces acting on it:

     Weight force of Earth on block (downwards, magnitude w = m⋅g, same for both (a) and (b)),
     Buoyant force of water on block (upwards, magnitude F_B = ρ_water⋅g⋅V_sub, less for (a)); and

  2. block (a) has a downwards weight force, and an upwards buoyant force much less than the magnitude of the weight force; and
  3. block (b) has the same downwards weight force as (a), also with an upwards buoyant force less than the magnitude of the weight force, but with a magnitude greater than the magnitude of the buoyant force in (a) (as more volume is submerged); and
  4. from Newton's second law, the downwards net force for (a) has a greater magnitude than the downwards net force for (b), as demonstrated by either explicit comparison of vector lengths and/or comparing terms in ΣF = +F_B − w equations for each case.
  May either draw a free-body diagram, and/or discuss these forces and Newton's laws in words.
• r:
  As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes. Typically does not explicitly demonstrate Newton's second law via vector addition (different up vectors drawn much less than, or a little less than the same down vector for each case; and/or comparing same/different quantities in ΣF = +F_B − w equations for each case).
• t:
  Nearly correct, but argument has conceptual errors, or is incomplete. At least recognizes that the object has a greater buoyant force once it is fully submerged.
• v:
  imited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Some constructive attempt at relating the buoyant force to the density of the fluid and volume displaced (Archimedes' principle) and/or Newton's first law.
• x:
  Implementation/application of ideas, but credit given for effort rather than merit. Appeals to some other properties of fluids and densities other than Archimedes' principle and Newton's laws.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.
  

Grading distribution:
Sections 70854, 70855
Exam code: midterm02sQm5
p: 13 students
r: 12 students
t: 8 students
v: 15 students
x: 4 students
y: 0 students
z: 0 students

A sample "p" response (from student 3372):