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):

Physics quiz question: partially submerged block resting on bottom

Physics 205A Quiz 5, fall semester 2019
Cuesta College, San Luis Obispo, CA

A solid block has 75% of its volume below water, while resting on the bottom of a water tank. The force with the largest magnitude is the:
(A) weight force of Earth on the block.
(B) buoyant force of water on the block.
(C) normal force of tank bottom on the block.
(D) (There is a tie.)
(E) (Not enough information is given.)

Correct answer (highlight to unhide): (A)

The block has three vertical forces acting on it:

Weight force of Earth on block (downwards, magnitude w = m·g).
Buoyant force of water on block (upwards, magnitude F_B = ρ_fluid·g·(Volume submerged)).
Normal force of tank bottom on block (upwards, magnitude N).

Because the block is stationary in the vertical direction, from Newton's first law all of the up and down forces must sum to zero. This means that the two upwards forces (buoyant force and normal force) are together equal to the one downwards force (weight), such that the weight force has the largest magnitude of these three forces.

Sections 70854, 70855
Exam code: quiz05Gu1L
(A) : 30 students
(B) : 2 students
(C) : 5 students
(D) : 14 students
(E) : 0 students

Success level: 58%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.67

Physics quiz archive: rotations, torque, pressure, buoyancy, fluid flow

Physics 205A Quiz 5, fall semester 2019
Cuesta College, San Luis Obispo, CA
Sections 70854, 70855, version 1
Exam code: quiz05Gu1L



Sections 70854, 70855 results

0- 6 :	** [low = 6]
7-12 :	*********
13-18 :	***********
19-24 :	***************** [mean = 19.8 +/- 6.3]
25-30 :	************* [high = 27]

Physics midterm question: floating ebony-balsa wood cubes

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

A wooden cube is made by gluing ebony (denser) and balsa (less dense) pieces together. Both pieces have the same volume. The total density of the cube is less than that of water. The cube is carefully placed into water such that it floats "top-heavy" (ebony on top of balsa). The cube is then turned over such that it floats "bottom-heavy" (balsa on top of ebony). Discuss which orientation will float higher (or if there is tie), and why. (Ignore any water that may soak into the wood pieces, and the thin layer of glue between the two wood pieces.) Explain your reasoning using the properties of densities, volumes, forces, Newton's laws, Archimedes' principle (buoyant forces), and free-body diagrams.

Solution and grading rubric:

• p:
  Correct. Recognizes that:
  1. each block ("bottom-heavy" or "top-heavy") has two vertical forces acting on it:

     Weight force of Earth on block (downwards, magnitude w = m⋅g),
     Buoyant force of water on block (upwards, magnitude F_B = ρ_water⋅g⋅V_sub);

     and
  2. because each block ("bottom-heavy" or "top-heavy") is stationary in the vertical direction, then its downwards weight force must have the same magnitude as its upwards buoyant force, due to Newton's first law; and
  3. since the mass of each block ("bottom-heavy" or "top-heavy") does not matter which type of wood is stacked above the other, the magnitude of the weight is the same, making the magnitudes of the buoyant forces the same; such that
  4. the amount submerged volume underwater for both blocks must be the same.
  
  Thus the buoyant forces on each block ("bottom-heavy" or "top-heavy") are equal, and thus the amount of volume submerged for either block must be the same.
• r:
  As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes. May somehow claim that the cube will float differently when "bottom-heavy" or "top-heavy," or does not explicitly conclude that the cube will float at the same water level whether "bottom-heavy" or "top-heavy."
• t:
  Nearly correct, but argument has conceptual errors, or is incomplete. At least recognizes that the weight force on the block is unchanged whether "bottom-heavy" or "top-heavy," but somehow has different buoyant forces acting (thus Newton's first law would not apply to at least one of the blocks); or has different weights and different buoyant forces acting on the blocks, but for each block these forces are balanced via Newton's first law.
• 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
p: 21 students
r: 17 students
t: 13 students
v: 6 students
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 0921):

Physics quiz archive: rotations, torque, pressure, buoyancy, fluid flow

Physics 205A Quiz 5, fall semester 2018
Cuesta College, San Luis Obispo, CA
Sections 70854, 70855, version 1
Exam code: quiz05Ro74



Sections 70854, 70855 results

0- 6 :
7-12 :	******** [low = 9]
13-18 :	**************
19-24 :	************************* [mean = 19.6 +/- 5.2]
25-30 :	***** [high = 30]

Physics midterm question: anchored foam block with rising water level

Physics 205A Midterm 2, fall semester 2017
Cuesta College, San Luis Obispo, CA

A foam block is anchored by a string to the bottom of a container of water. As more water is poured into this container, discuss why the tension in the string increases. (Ignore any stretching of the length of the string, such that the block remains at the same level while the water level rises.) Explain your reasoning using the properties of densities, volumes, forces, Newton's laws, Archimedes' principle (buoyant forces), and free-body diagrams.

Solution and grading rubric:

• p:
  Correct. Recognizes that:
  1. the block has three vertical forces acting on it:

     Weight force of Earth on block (downwards, magnitude w = m⋅g),
     Tension force of container on block (downwards, magnitude T),
     Buoyant force of water on block (upwards, magnitude F_B = ρ_water⋅g⋅V_sub = ρ_water⋅g⋅(0.50⋅V_block); and

  2. because the block is stationary in the vertical direction, the sum of the two downwards forces is equal and opposite in direction to the upwards force due to Newton's first law; and
  3. as more water is poured into the container, the volume of the block that is submerged increases, increasing the amount of upwards buoyant force of water on the block from F_B = ρ_water⋅g⋅(0.50⋅V_block) to ρ_water⋅g⋅(0.75⋅V_block); such that
  4. the downwards tension force of the container on the block must also increase (as the weight force remains constant), in order for the two downwards forces to still balance out the increase in the upwards force on the block.
  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. Excludes weight force, or adds extraneous normal force, but still recognizes why buoyant force increases, thus increasing the tension force.
• t:
  Nearly correct, but argument has conceptual errors, or is incomplete. Excludes weight force and adds extraneous normal force.
• 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: midterm02bu2Z
p: 30 students
r: 16 students
t: 4 students
v: 0 students
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 1902):
Another sample "p" response (from student 7164):

Physics quiz question: weights of comparable floaters

Physics 205A Quiz 5, fall semester 2017
Cuesta College, San Luis Obispo, CA

Two solid objects of different sizes both float with 75% of their volumes below water. It is 
not known whether these objects are made of the same material. The __________ object has a greater weight.
(A) smaller.
(B) larger.
(C) (There is a tie.)
(D) (Not enough information is given.)

Correct answer (highlight to unhide): (A)

The magnitude of the buoyant force is given by:

F_B = ρ_fluid·g·(Volume submerged),

where the density ρ is of the surrounding fluid (water) and the gravitational constant g = 9.80 m/s². Since the volume of water displaced by the smaller object is less than the volume of water displaced by the larger object, then the smaller object has a smaller magnitude buoyant force exerted on it.

Newton's first law applies to both objects, as they are stationary, and thus the forces acting on either object must sum to zero.
Since the smaller object has a small upwards buoyant force acting on it, then it must have a correspondingly small downwards weight force acting on it. Similarly, the larger object has a larger buoyant force and a larger weight force acting on it. Thus the larger object has a greater weight than the smaller object.

Sections 70854, 70855
Exam code: quiz05nWaW
(A) : 1 student
(B) : 32 students
(C) : 4 students
(D) : 12 students

Success level: 65%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.17

Physics quiz archive: rotations, torque, pressure, buoyancy, fluid flow

Physics 205A Quiz 5, fall semester 2017
Cuesta College, San Luis Obispo, CA
Sections 70854, 70855, version 1
Exam code: quiz05nWaW



Sections 70854, 70855 results

0- 6 :
7-12 :	***** [low = 9]
13-18 :	***************
19-24 :	********************* [mean = 19.7 +/- 4.8]
25-30 :	***** [high = 27]

Physics quiz question: buoyant force on inflating pufferfish

Physics 205A Quiz 5, fall semester 2016
Cuesta College, San Luis Obispo, CA

"The Puffer Fish"
Uploader1977
commons.wikimedia.org/wiki/File:The_Puffer_Fish.jpg

A long-spined pufferfish (Diodon holocanthus) swimming underwater expands its volume three-fold by gulping water into its stomach.[*] As a result, the magnitude of the buoyant force on the pufferfish:
(A) decreases.
(B) remains constant.
(C) increases.
(D) (Not enough information is given.)

[*] divingintaganga.blogspot.com/2010/09/how-and-why-pufferfish-inflate.html .

Correct answer (highlight to unhide): (C)

The magnitude of the buoyant force is given by:

F_B = ρ_fluid·g·(Volume submerged),

where the density ρ is of the surrounding fluid (seawater) and the gravitational constant g = 9.80 m/s². The volume of sea water displaced by the pufferfish increases, and thus the upwards buoyant force on it while increase in magnitude while it is filling with water. (However, since the fish is filling with water, the downwards weight force of gravity on increases as well.)

Sections 70854, 70855, 73320
Exam code: quiz05b0oM
(A) : 3 students
(B) : 11 students
(C) : 40 students
(D) : 1 student

Success level: 75%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.24

Physics quiz archive: rotations, torque, pressure, buoyancy, fluid flow

Physics 205A Quiz 5, fall semester 2016
Cuesta College, San Luis Obispo, CA
Sections 70854, 70855, 73320, version 1
Exam code: quiz05b0oM



Sections 70854, 70855, 73320 results

0- 6 :	*** [low = 6]
7-12 :	***********
13-18 :	************************* [mean = 16.6 +/- 6.0]
19-24 :	************
25-30 :	* [high = 30]

Physics midterm question: rising water level in dry dock

Physics 205A Midterm 2, fall semester 2015
Cuesta College, San Luis Obispo, CA

“Cruise Ship timelapse - Extension of Braemar at Blohm+Voss”
MK timelapse GmbH
youtu.be/QirVr-pEVU4

A cruise ship rests on the floor of a dry dock with a small amount of water. As the water level rises (but not enough water to "float" the ship yet, so it is still resting on the bottom of the dry dock), discuss why the normal force of the floor on the ship decreases. Explain your reasoning using the properties of densities, volumes, forces, Newton's laws, Archimedes' principle (buoyant forces), and free-body diagrams.

Solution and grading rubric:

• p:
  Correct. Recognizes that:
  1. from Newton's first law the downwards weight force (which has a constant magnitude, as its mass remains constant) on the ship is equal to the two upwards buoyant and normal forces on the ship;
  2. as the water level rises, the amount of the ship's submerged volume increases, increasing the amount of buoyant force on the ship (Archimedes' principle);
  such that the normal force must decrease in magnitude in order for the two upwards forces to still balance the downwards weight force.
• 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 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 of ideas, but credit given for effort rather than merit. Appeal 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, 73320
Exam code: midterm02h4W6
p: 47 students
r: 10 students
t: 4 students
v: 9 students
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 3158):

Physics quiz question: hanging vs. anchored submerged objects

Physics 205A Quiz 5, fall semester 2015
Cuesta College, San Luis Obispo, CA

Two objects of different volumes and different densities are in a tank of water. One object hangs down from a string, while the other object is anchored to the bottom with a string. The amount of tension in each string is the same. The __________ object has a greater magnitude buoyant force exerted on it.
(A) hanging.
(B) anchored.
(C) (Not enough information is given.)
(D) (There is a tie.)

Correct answer (highlight to unhide): (A)

The magnitude of the buoyant force is given by:

F_B = ρ_fluid·g·(Volume submerged),

where the density ρ is of the surrounding fluid (water) and the gravitational constant g = 9.80 m/s². Both objects are fully submerged, and since the volume of water displaced by the hanging object is greater than the volume of water displaced by the anchored object, then the hanging object has a greater magnitude buoyant force exerted on it.

(The list of the forces acting on the hanging object are:

Buoyant force of water F_B = ρ_fluid·g·(Volume submerged) (upwards),
Tension force of string T (upwards),
Weight force of Earth w = m·g (downwards).

The list of the forces acting on the hanging object are:

Buoyant force of water F_B = ρ_fluid·g·(Volume submerged) (upwards),
Tension force of string T (downwards),
Weight force of Earth w = m·g (downwards).

Newton's first law applies to both objects, as they are stationary, and thus the forces acting on either object must sum to zero.

For the hanging object, the magnitude of the downward weight force w must equal the sum of the magnitudes of the upwards tension force T and (larger) upwards buoyant force F_B, and thus the hanging object will have a larger magnitude weight force than the anchored object (which has a downward weight force w equal to the (smaller) upwards buoyant force F_B minus the tension force T.)

Sections 70854, 70855, 73320
Exam code: quiz05bL8D
(A) : 18 students
(B) : 29 students
(C) : 17 students
(D) : 1 student

Success level: 27%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.80

Physics quiz archive: rotations, torque, pressure, buoyancy, fluid flow

Physics 205A Quiz 5, fall semester 2015
Cuesta College, San Luis Obispo, CA
Sections 70854, 70855, 73320, version 1
Exam code: quiz05bL8D



Sections 70854, 70855, 73320 results

0- 6 :	** [low = 0]
7-12 :	****************
13-18 :	************************** [mean = 17.2 +/- 6.1]
19-24 :	**************
25-30 :	******** [high = 30]

Physics final exam question: submerged metal sample resting at bottom

Physics 205A Final Exam, fall semester 2014
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problems 9.29(a), 9.31

A physics question on an online discussion board[*] was asked:

You're told the volume of a metal sample that is sitting fully submerged at the bottom of a tank filled with water. You're given the density of the water and the density of the metal. Why is the buoyant force equal to ρ·g·V, but not equal to the weight of the sample?

Discuss (a) why the buoyant force of the water on the sample is equal to ρ·g·V (specify which substances ρ and V refer to), and (b) why the buoyant force is not equal to the weight of the sample. Explain your reasoning using the properties of densities, volumes, forces, Newton's laws, Archimedes' principle (buoyant forces), and a free-body diagram.

[*] answers.yahoo.com/question/index?qid=20080722184533AA69bUO.

Solution and grading rubric:

• p:
  Correct. Discusses:
  1. that the density ρ and the volume V in the buoyant force equation refer to the density of water and of the entire sample, respectively;
  2. the buoyant force is not equal to the weight of the sample, as the weight of the sample equals the two upwards forces on the sample: the buoyant force and the normal force, from discussion of Newton's first law and/or shown on a free-body diagram.
• r:
  Nearly correct, but includes minor math errors. One of the two points (1)-(2) correct, other is problematic/incomplete.
• t:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. Only one of the two points (1)-(2) correct, other is missing, or both are problematic.
• v:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Some garbled attempt at applying Archimedes' principle and Newton's laws.
• x:
  Implementation of ideas, but credit given for effort rather than merit.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Grading distribution:
Sections 70854, 70855, 73320
Exam code: finalm34T
p: 15 students
r: 14 students
t: 19 students
v: 10 students
x: 2 students
y: 1 student
z: 1 student

A sample "p" response (from student 9950):

Physics quiz archive: rotations, torque, pressure, buoyancy, fluid flow

Physics 205A Quiz 5, fall semester 2014
Cuesta College, San Luis Obispo, CA
Sections 70854, 70855, 73320, version 1
Exam code: quiz05mRp4



Sections 70854, 70855, 73320 results

0- 6 :	*** [low = 6]
7-12 :	*****************
13-18 :	************************* [mean = 16.5 +/- 5.7]
19-24 :	**************
25-30 :	***** [high = 30]

Physics quiz question: raising the sunken Mighty Servant 3

Physics 205A Quiz 5, fall semester 2013
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problems 9.27, 9.31

"Mighty Servant 3 carrying her last cargo, the semi-submersible drilling rig GSF Aleutian Key"
(Anonymous)
wki.pe/File:20061204_MightyServant3_JUSTbefore.JPG

In December 6, 2006 the ship Mighty Servant 3 accidentally sank, resting fully submerged on the ocean floor.[*] (No lives were lost in this incident.) The Mighty Servant 3 was later raised by filling its water-filled compartments with air. Up until the point where it just began to rise off of the ocean floor, its weight __________, while the buoyant force on it __________ in magnitude.
(A) decreased; decreased.
(B) decreased, remained constant.
(C) decreased; increased.
(D) increased; decreased.
(E) increased; remained constant.
(F) increased; increased.

[*] cargolaw.com/2006nightmare_mightyserve3.html.

Correct answer (highlight to unhide): (B)

The magnitude of the buoyant force is given by:

F_B = ρ_fluid·g·(Volume submerged),

where the density ρ is of the surrounding fluid (seawater) and the gravitational constant g = 9.80 m/s². The volume of sea water displaced by the ship, while still completely submerged, does not change, and thus the buoyant force on it still has the same magnitude while it is filling with air. However, since air is replacing the seawater in its compartments, the weight of the ship decreases.

Sections 70854, 70855, 73320
Exam code: quiz05LuF7
(A) : 5 students
(B) : 31 students
(C) : 23 students
(D) : 1 student
(E) : 1 student
(F) : 0 students

Success level: 51%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.50

Physics quiz archive: rotations, torque, pressure, buoyancy, fluid flow

Physics 205A Quiz 5, fall semester 2013
Cuesta College, San Luis Obispo, CA
Sections 70854, 70855, 73320, version 1
Exam code: quiz05LuF7



Sections 70854, 70855, 73320 results

0- 6 :
7-12 :	************ [low = 12]
13-18 :	*********************** [mean = 18.4 +/- 4.9]
19-24 :	**********************
25-30 :	**** [high = 30]

Physics midterm question: partially vs. fully submerged buoys

Physics 205A Midterm 2, fall semester 2012
Cuesta College, San Luis Obispo, CA

Two buoys (same volumes, same densities) used for generating electrical power from wave motion[*] are each anchored to the ocean floor with cables, and are either partially or fully submerged in sea water. Discuss why the tension in the cable attached to the partially submerged buoy is less than the tension in the cable attached to the fully submerged buoy. Ignore the mass of the cables. Explain your reasoning using the properties of densities, volumes, forces, Newton's laws, and Archimedes' principle.

[*] www2.teknat.uu.se/forskning/uu/beskrivning.php?id=31&vetenskapsid=31&lang=en.

Solution and grading rubric:

• p:
  Correct. Identifies three forces acting on each buoy (tension downwards, weight downwards, and buoyant force upwards). Each buoy is stationary (in translational equilibrium), such that by Newton's first law, the buoyant force is equal in magnitude to the sum of the tension and weight forces. The two buoys have the same weight, due to their same volumes and densities (thus same masses). The partially submerged buoy has a smaller upwards bouyant force acting on it, as it displaces less volume underwater. Thus the downwards tension force on the partially submerged buoy (which is the difference between the buoyant force and weight) must be less than the downwards tension force on the fully submerged buoy.
• r:
  As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes. Identifies weight forces acting on both buoys, but does not explicitly discuss how/why these weights are identical.
• t:
  Nearly correct, but argument has conceptual errors, or is incomplete. Omits weight forces, effectively discussing a case where the buoys are extremely lightweight compared to the magnitude of the tension and buoyant forces. Still (a) applies Newton's first law to those two forces, and (b) understands how buoyant force depends on submerged volume.
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. As (t), but does not explicitly explain how bouyant force depends on submerged volume.
• x:
  Implementation/application of ideas, but credit given for effort rather than merit.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.
  

Grading distribution:
Sections 70854, 70855
Exam code: midterm02gL0u
p: 14 students
r: 5 students
t: 22 students
v: 13 students
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 9494):

Physics quiz question: partially, fully submerged submarines

Physics 205A Quiz 5, fall semester 2012
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problems 9.27, 9.31

Two submarines[*] (same volumes) are either partially or fully submerged in sea water. The __________ submerged submarine experiences a greater buoyant force.
(A) partially.
(B) fully.
(C) (There is a tie.)
(D) (Not enough information is given.)

[*] Diagram adapted from "SSBN Typhoon Class (Type 941), Russian Federation," naval-technology.com/projects/ssbn-typhoon-class/ssbn-typhoon-class8.html.

Correct answer (highlight to unhide): (B)

The magnitude of the buoyant force is given by:

F_B = ρ_fluid·g·(Volume submerged),

where the water density ρ and the gravitational constant g are identical for both submarines. Since the fully submerged submarine displaces more water (has a greater submerged volume) than the partially submerged submarine, the fully submerged submarine will have a greater buoyant force exerted upwards on it. (Subsequently, due to Newton's first law, the upwards buoyant force on each submarine must be balanced by their respective downwards weight forces, such that the fully submerged submarine will also have a greater weight force than the partially submerged submarine.)

Sections 70854, 70855
Exam code: quiz05L4mN
(A) : 11 students
(B) : 34 students
(C) : 7 students
(D) : 0 students

Success level: 65%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.42

Physics quiz archive: rotations, torque, pressure, buoyancy, fluid flow

Physics 205A Quiz 5, fall semester 2012
Cuesta College, San Luis Obispo, CA
Sections 70854, 70855, version 1
Exam code: quiz05L4mN



Sections 70854, 70855 results

0- 6 :	***** [low = 6]
7-12 :	*************
13-18 :	****************** [mean = 16.0 +/- 5.7]
19-24 :	***************
25-30 :	* [high = 30]