Physics midterm problem: hydrostatic weighing

Physics 205A Midterm 2, fall semester 2011
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problems 9.37, 9.38

[20 points.] The average density of a person can be found by first weighing that person in air and then finding the scale reading for the person completely immersed in water (while suspended from the scale). If a person has a weight 550 N in air and has an average density of 1.05×10³ kg/m³, what would be the scale reading for the person completely immersed in water? The density of water is ρwater = 1.00×10³ kg/m³. Show your work and explain your reasoning.

Solution and grading rubric:

• p = 20/20:
  Correct. Finds volume of person, given density and mass (from weight in air), and calculates bouyant force on person while submerged in water. The scale reading is then the difference between the weight and the bouyant force. Proper use of Newton's first law, definition of bouyant force, and relation between mass and weight.
  
• r = 16/20:
  Nearly correct, but includes minor math errors. May have conflated mass and weight, or density values, but still clearly shows methodical process.
  
• t = 12/20:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors.
  
• v = 8/20:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. At some attempt at using Newton's laws, definition of bouyant force, and relation between mass and weight.
  
• x = 4/20:
  Implementation of ideas, but credit given for effort rather than merit. Discussion not based on methodical application Newton's laws, definition of bouyant force, and relation between mass and weight.
  
• y = 2/20:
  Irrelevant discussion/effectively blank.
  
• z = 0/20:
  Blank.
  

Grading distribution:
Sections 70854, 70855
Exam code: midterm02fR3q
p: 24 students
r: 4 students
t: 5 students
v: 8 students
x: 7 students
y: 0 students
z: 0 students

A sample "p" response (from student 3737), rounding to two significant figures during each step:
Another sample "p" response (from student 3737), rounding to two significant figures only for the very last calculation:

Astronomy midterm question: supergiants larger than same-temperature main-sequence stars?

Astronomy 210 Midterm 2, fall semester 2011
Cuesta College, San Luis Obispo, CA

An astronomy question on an online discussion board[*] was asked and answered:

24gurl: How do astronomers conclude that a supergiant star is larger than a main-sequence star of the same temperature?
Roger: The supergiant star is more luminous than the main sequence star of the same temperature. The only way that a supergiant could be more luminous than the main sequence star is if it is larger, the luminosity is proportional to the star's area...

Discuss whether or not if this answer is correct, and how you know this. Explain using Wien's law, the Stefan-Boltzmann law and/or an H-R diagram.

[*] answers.yahoo.com/question/index?qid=20100217203829AADBeYk.

Solution and grading rubric:

• p:
  Correct. Uses Stefan-Boltzmann law and/or interprets H-R diagram to show that supergiants must be larger than main sequence stars of the same temperature in order to be more luminous than the main sequence stars.
  
• r:
  Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors.
  
• t:
  Contains right ideas, but discussion is unclear/incomplete or contains major errors.
  
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. At least attempts to use Wien's law, H-R diagram and/or the Stefan-Boltzman law.
  
• x:
  Implementation/application of ideas, but credit given for effort rather than merit. Discussion not based on Wien's law, H-R diagram and/or the Stefan-Boltzman law.
  
• y:
  Irrelevant discussion/effectively blank.
  
• z:
  Blank.
  

Grading distribution:Section 70158
Exam code: midterm02s3Ar
p: 16 students
r: 5 students
t: 3 students
v: 9 students
x: 0 students
y: 1 student
z: 0 students

A sample "p" response (from student 1210), with a bonus illustration:

Astronomy midterm question: blue supergiants just as bright as red supergiants?

Astronomy 210 Midterm 2, fall semester 2011
Cuesta College, San Luis Obispo, CA

An astronomy question on an online discussion board(*) was asked and answered:

Pd...: Is it possible that a blue supergiant can be as bright as a red supergiant, (assuming they are the same distance from Earth)?
per..gogy: Technically the blue supergiant would be the brighter one. Blue stars are more luminous than red stars...

Discuss whether or not if this answer is correct, and how you know this. Explain using Wien's law, the Stefan-Boltzmann law and/or an H-R diagram.

*Source: http://answers.yahoo.com/question/index?qid=20110602185220AATh4tm.

Solution and grading rubric:

• p = 20/20:
  Correct. Wien's law: blue stars are hotter, and are located on the left side of an H-R diagram, while red stars are cooler, and are located on the right side. Uses Stefan-Boltzmann law and/or interprets H-R diagram to show that either (a) blue supergiants and red supergiants can have the same size, such that the blue supergiants (being hotter) are more luminous; or (b) blue supergiants and red supergiants can have the same luminosity, but the blue supergiants (being hotter) are smaller in size.
  
• r = 16/20:
  Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors.
  
• t = 12/20:
  Contains right ideas, but discussion is unclear/incomplete or contains major errors.
  
• v = 8/20:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. At least attempts to use Wien's law, H-R diagram and/or the Stefan-Boltzman law.
  
• x = 4/20:
  Implementation/application of ideas, but credit given for effort rather than merit. Discussion not based on Wien's law, H-R diagram and/or the Stefan-Boltzman law.
  
• y = 2/20:
  Irrelevant discussion/effectively blank.
  
• z = 0/20:
  Blank.
  

Grading distribution:Section 70160
Exam code: midterm02n1cT
p: 13 students
r: 6 students
t: 6 students
v: 3 students
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 8386), discussing how the blue supergiant while hotter, would be smaller than the red supergiant in order to have the same luminosity:
Another sample "p" response (from student 1027) instead arguing that a blue supergiant will be brighter than a red supergiant, assuming that they are the same size:

Astronomy midterm question: red dwarf vs. massive main-sequence star metallicity

Astronomy 210 Midterm 2, fall semester 2011
Cuesta College, San Luis Obispo, CA

An astronomy question on an online discussion board[*] was asked and answered:

Pdg: Which star today would have more metals: a red dwarf or a massive main-sequence star?
qp: I'm guessing a massive main-sequence star; because a red dwarf is likely very old...

Discuss whether or not if this answer is correct, and how you know this. Explain using the properties and evolution of stars.

[*] answers.yahoo.com/question/index?qid=20110601124741AA76NMC.

Solution and grading rubric:

• p:
  Correct. Understands that:
  1. older stars are metal-poor having formed from essentially just hydrogen, while newer stars are metal-rich, having formed from hydrogen enriched with metals produced by previous generation stars;
  2. red dwarfs take a long time to become main sequence stars, such that they had to have started forming a long time ago, are thus are metal-poor, while massive stars take a short time to form, such that they formed recently, and thus are metal-rich.
• r:
  Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors. One of the two points (1)-(2) is correct, other is problematic.
• t:
  Contains right ideas, but discussion is unclear/incomplete or contains major errors. Only one of the two points (1)-(2) correct, other is missing, or both are problematic.
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Garbled discussion of properties and evolution of stars, such as breaking down of metals; masses and evolution rates.
• x:
  Implementation/application of ideas, but credit given for effort rather than merit.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Grading distribution:
Section 70158
Exam code: midterm02s3Ar
p: 9 students
r: 3 students
t: 14 students
v: 8 students
x: 0 students
y: 0 students
z: 0 students

Section 70160
Exam code: midterm02n1cT
p: 9 students
r: 3 students
t: 9 students
v: 6 students
x: 1 student
y: 0 students
z: 0 students

A sample "p" response (from student 2541):
Another sample "p" response (from student 1863), using a "House Party" analogy:
Yet another sample "p" response (from student 1985), lavishly illustrated:
A sample "v" response (from student 0628), where older stars would have had more time to absorb metals than recent stars:
Another sample "v" response (from student 1226), where older stars have more time to break down metals:
Yet another sample "v" response (from student 1559), where older stars have more time to fuse metals by breaking them down:

Astronomy midterm question: you at where big bang started?

Astronomy 210 Midterm 2, fall semester 2011
Cuesta College, San Luis Obispo, CA

[20 points.] An astronomy question on an online discussion board[*] was asked and answered:

sai: We know that [the] big bang created everything we know today, but if it formed the universe where did the big bang take place?!
Dude: Right where [you] are standing.

Discuss why this answer is correct, and how you know this. Explain using observations and evidence related to the Hubble law.

[*]Source: http://answers.yahoo.com/question/index?qid=20100926113402AAQcp5I.

Solution and grading rubric:

• p = 20/20:
  Correct. Understands that (a) Hubble's law is that the recession velocity of galaxies is proportional to distance (greater redshift of absorption lines for distant galaxies compared to nearby galaxies), corresponding to the expansion of space between galaxies, and (b) extrapolating time backwards means that the distance between everything was zero, thus any location can be said to be where the big bang took place (or may instead argue for no unique center of expansion for expanding-space-between-galaxies universe).
  
• r = 16/20:
  Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors. One of the two points (a)-(b) is correct, other is problematic.
  
• t = 12/20:
  Contains right ideas, but discussion is unclear/incomplete or contains major errors. Only one of the two points (a)-(b) correct, other is missing, or both are problematic.
  
• v = 8/20:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Discussion based on evidence of the earlier stages in the history of the universe, with little or no substantive discussion of Hubble's law, such as everything was created by the big bang, therefore everything can be said to be where the big bang took place.
  
• x = 4/20:
  Implementation/application of ideas, but credit given for effort rather than merit.
  
• y = 2/20:
  Irrelevant discussion/effectively blank.
  
• z = 0/20:
  Blank.
  

Grading distribution:
Section 70158
Exam code: midterm02s3Ar
p: 4 students
r: 11 students
t: 9 students
v: 7 students
x: 3 students
y: 0 students
z: 0 students

Section 70160
Exam code: midterm02n1cT
p: 7 students
r: 7 students
t: 7 students
v: 4 students
x: 2 students
y: 1 student
z: 0 students

A sample "p" response (from student 1027):
A sample "v" response (from student 1177):
Another sample "v" response (from student 8436), still showing the astronomy love:

Physics quiz archive: simple harmonic motion, waves

Physics 205A Quiz 6, fall semester 2011
Cuesta College, San Luis Obispo, CA
Sections 70854, 70855, version 1


Sections 70854, 70855 results
Exam code: quiz06w4VE

 0- 6 : **  [low = 6]
 7-12 : ********
13-18 : ***************
19-24 : ********************  [mean = 19.2 +/- 5.2]
25-30 : ********  [high = 30]

Overheard: recursive learning about stars

Astronomy 210, fall semester 2011
Cuesta College, San Luis Obispo, CA

(Overheard at a review session just before midterm on the sun/stars/Milky Way/cosmology.)

Instructor: "Just think: you're learning about stars that died...to make the atoms...that made you...so you could learn...about the stars."

Students: (Beat.) "Whoa."

Instructor: "Yeah. Whoa."

Astronomy quiz archive: Milky Way, cosmology

Astronomy 210 Quiz 6, fall semester 2011
Cuesta College, San Luis Obispo, CA

Section 70158, version 1
Exam code: quiz06pOp1

Section 70158

Quiz 6 results (max score = 40):
   0- 8.0 : *  [low = 7.5]
 8.5-16.0 : ****
16.5-24.0 : **************  [mean = 22.8 +/- 6.6]
24.5-32.0 : **********
32.5-40.0 : ***  [high = 36.5]

Astronomy quiz archive: Milky Way, cosmology

Astronomy 210 Quiz 6, fall semester 2011
Cuesta College, San Luis Obispo, CA

Section 70160, version 1
Exam code: quiz06n4Nd

Section 70160

Quiz 6 results (max score = 40):
   0- 8.0 : *  [low = 6.0]
 8.5-16.0 : **
16.5-24.0 : ****
24.5-32.0 : **********  [mean = 27.4 +/- 9.0]
32.5-40.0 : *********  [high = 40.0]

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

Physics 205A Quiz 5, fall semester 2011
Cuesta College, San Luis Obispo, CA
Sections 70854, 70855, version 1


Sections 70854, 70855 results
Exam code: quiz05t0rQ

0- 6 : *  [low = 6]
 7-12 : ***************
13-18 : **********************  [mean = 16.8 +/- 5.2]
19-24 : *********
25-30 : ****  [high = 30]

Presentation: Cuesta College North County campus telescope facility proposal

(Splash screen: waning gibbous moon (less than 24 hours past full), Cuesta College North County campus, Paso Robles, CA.)

This is a proposal presented to the Cuesta College Foundation for a North County campus telescope facility, discussing the current facilities, new location, and potential benefits.

Currently students, staff, guests, and the public are invited to attend star nights at North County campus several times a year.

We'll look at the current equipment, storage facilities, and viewing conditions.

North County campus has three manual, and two automated large-diameter telescopes.

These telescopes share storage space with astronomy, physics, geology, and chemistry lab equipment in room N2409.

Because the telescopes have limited portability, they are moved out of and set up just outside N2409 for star nights. Note that the view of the horizon, already blocked by the N2400 and N2800 buildings, is recently exacerbated by the new Learning Resource Center, along with new exterior lighting and landscaping to follow. (Video link: "111030-1270594.")

So how can we do better?

The proposal before the Cuesta College Foundation is to construct a telescope shelter near the north end of campus, adjacent to the existing gravel parking lot. There will be sufficient storage space and a large concrete pad to roll out all of the existing telescopes for star nights. The construction estimate from Cuesta College Facilities is $18,850.

This particular site has been studied by the North County campus executive dean's office, along with members of the Central Coast Astronomical Society, and has great potential with a clear view of the horizon, and being located sufficiently far away from existing buildings and lighting. (Video link: "111030-1270586.")

Consider the benefits of this proposal.

With all telescopes at North County campus ready to roll out at a clear, dark sky location, students will have greater opportunities to do astronomy in more optimal conditions.

Another potential benefit of this new facility would be an increase in interest from the local astronomy club for hosted events on campus.

And outreach opportunities for local schools, organizations, and the general public on campus.

Questions or comments?

The North County campus of Cuesta College is a location that holds much promise, potential, and possibilities. Thank you for this opportunity to address the Foundation on the proposed telescope facility at North County campus...

...and Cuesta College's students thank you as well!