Online reading assignment: Milky Way history, big bang clues (SLO campus)

Astronomy 210, fall semester 2018
Cuesta College, San Luis Obispo, CA

Students have a weekly online reading assignment (hosted by SurveyMonkey.com), where they answer questions based on reading their textbook, material covered in previous lectures, opinion questions, and/or asking (anonymous) questions or making (anonymous) comments. Full credit is given for completing the online reading assignment before next week's lecture, regardless if whether their answers are correct/incorrect. Selected results/questions/comments are addressed by the instructor at the start of the following lecture.

The following questions were asked on reading textbook chapters and previewing presentations on the history of the Milky Way and big bang clues, a comic strip adaptation of Neil deGrasse Tyson's "The Most Astounding Fact" 2008 interview for TIME magazine, and Minute Physics' video explanation of Olbers' paradox.


Selected/edited responses are given below.

Describe something you found interesting from the assigned textbook reading or presentation preview, and explain why this was personally interesting for you.

"This suggests a simple 'monolithic collapse' model of Milky Way evolution, where hydrogen for star formation gradually migrated from a spherical shape to its current flattened disk shape. This model is perhaps too simple."

"I think it is mindblowing that we are able to see (with the naked eye) light that is over 2.5 million years old. Literally like a time machine that see things we can't touch, but just admire. It makes me feel really small and insignificant in the expanse of our universe."

"One light year is crazy to me, let alone how far away everything is based on light years. It's mind-blowing."

"The thought that telescopes are technically time machines is really abstract."

"That at the start of the universe was primarily hydrogen interesting because that is how the all of the stars started to form."

"Learning about how the universe is expanding. Also how scientists used this information to look into the past to find out how old the universe is."

"I found the 'edge of time' to be interesting. The thought of the universe having a finite age isn't something I thought of before. We always want to think of something having an end, but the universe is expanding."

"That all galaxies are fleeing away from the Milky Way."

"That the big bang occurred everywhere; before I assumed it happened in a specific location."

"The part concerning the infinity of space really interests me it always has. Is there and end to it all? If there is whats beyond the end of space? It really gets me."

Describe something you found confusing from the assigned textbook reading or presentation preview, and explain why this was personally confusing for you.

"Lookback time was confusing at first, but having the concept of light years explained cleared this up."

"Understanding which stars have more or less metals then others."

"Metal-rich versus metal-poor stars and how this relates to their location in the galaxy."

"Need some review over what produces a specific kind of element. I couldn't find it within the blog lecture, but I'm sure it's there. Just need some further review."

"How the stars and later type II supernovas created metals in its core if it didn't have any metals to start out with."

"The difference between population I stars and population II stars? What confuses me is how the ages of population I stars can be older than population II stars?"

"I find it confusing to understand how the universe is expanding everywhere. What is causing this?"

"Metallicities."

"Wow is there an 'edge of time.' and what is beyond that?"

"I am confused if we can only see 14 billion light years away as that is what they predict how old our universe is."

"How can astronomers and other scientist say the Universe and all of the things within it are a certain age? The textbook states, the ages of particular parts of the universe are 'somewhat uncertain,' but scientist still claim their theories are correct without any real, provable evidence."

Indicate how the amount of these elements in the universe have changed over time.
(Only correct responses shown.)

Hydrogen: decreased [47%]
Metals (elements heavier than hydrogen and helium): increased [95%]

The outermost layers of __________ are more abundant in metals (elements heavier than hydrogen and helium).

extremely old stars that formed a long time ago.	*********** [11]
young stars that formed very recently.	******** [8]
(There is a tie.)	[0]
(Neither, as stars cannot have metals.)	[0]
(Unsure/guessing/lost/help!)	[0]

Indicate what produced these elements.
(Only correct responses shown.)

Hydrogen in the sun's core: the very early universe [64%]
Helium in the sun's core: the sun [32%]
Carbon in your body: another star, in the past [58%]
Calcium in your bones: another star, in the past [47%]
Iron in your blood: another star, in the past [47%]
Gold and silver from mines: another star, in the past [32%]

Ask the instructor an anonymous question, or make a comment. Selected questions/comments may be discussed in class.

"Is time travel really real?" (No, but looking back in time is real.)

"Look-back time is absolutely insane. How are we seeing Deneb as it was 1,400 if we are looking in the present? Or Andromeda, how are we seeing the stars from millions of years ago? I'm so confused? HELP P-DOG!"

"How far away is the most distance star or galaxy we can see and if it is more that 13.8 billion light years away how can we see it?" (Since as we look further and further out, we see things further and further back in time, so if we far out enough, we'll eventually be looking so far back in time that we will see what the universe was like before the first stars were even born; this is about 14 billion light years away, as it was 14 billion years ago.)

"I was a little confused with where the elements were produced."

"Please explain the relationship between population I and II type stars."

"Why is the universe expanding?"

Online reading assignment: heat transfers

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

Students have a bi-weekly online reading assignment (hosted by SurveyMonkey.com), where they answer questions based on reading their textbook, material covered in previous lectures, opinion questions, and/or asking (anonymous) questions or making (anonymous) comments. Full credit is given for completing the online reading assignment before next week's lecture, regardless if whether their answers are correct/incorrect. Selected results/questions/comments are addressed by the instructor at the start of the following lecture.

The following questions were asked on reading textbook chapters and previewing a presentation on heat transfers.


Selected/edited responses are given below.

Describe what you understand from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically demonstrate your level of understanding.

"This reading covers transfers of heat. Convection, where heat is transferred by the movement of a fluid. Conduction, where heat is transferred through a material directly. Radiation, where heat is traveled through electromagnetic waves and a look into their applications."

"I learned that conduction is heat transferred through solid objects, convection through fluids, and radiation in the form of light. I also learned that power is measured as the amount of energy transferred per time."

"Fourier's law of conduction seems sort of alright. Power is proportional to the temperature difference ∆T and inversely proportional to thermal resistance R, which itself is proportional to thickness of the material, and inversely proportional to its resistivity and area."

"By increasing the thickness or decreasing the Area of an a wall (material), you decrease heat flow. Heat is conducted based on the modules bouncing around (molecular energy). Metals have more free electrons, which increases this bobbling around (increasing heat conduction). I get that Q is inversely proportional to thickness/length. Also, radiation doesn't require a material medium."

"How different colors (or materials) like the blackbody and the silverbody both absorb and radiate heat differently."

"I understand how to apply Fourier's and Stefan's law to real life scenarios, but not mathematically."

"I wouldn't say I understand this chapter completely. I'm hoping class will resolve this feeling."

Describe what you found confusing from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically identify the concept(s) that you do not understand.

"I have never been exposed to the equations that are involved with the different heat exchanges, so of course they will begin to make more sense once I start using them more."

"In particular I don't fully understand thermal resistance."

"I think some of the equations used for each concept might be a bit confusing for me. Other than that I think learning it in class will reinforce the idea."

"Blackbody, silverbody, and radiation were confusing, but now I am fine."

"Kind of confused by radiation. I thought black things heated up fast...but I didn't know they loose heat fast too? Also I think it would be good to see a Stefan's law problem worked out, there's a lot of symbols in there."

"I didn't quite understand Stefan's law and would greatly benefit from an overview of it in lecture."

"The calculations."

"I understood all of the concepts in this section."

In order to maximize the thermal resistance of these exterior walls, should the following parameters be minimized, maximized (or has no effect)?
(Only correct responses shown.)

insulation thickness d: maximize [88%]
insulation conductivity κ: minimize [69%]
Total surface area A exposed to the outdoors: minimize [79%]

In order to minimize the amount of heat flowing per time through these exterior walls, should the following parameters be minimized, maximized (or has no effect)?
(Only correct responses shown.)

temperature difference ∆T between indoors and outdoors: minimize [74%]
thermal resistance R of the walls: maximize [77%]

For these two Leica M cameras, if they are both cooler than the surrounding environment, both will begin to heat up by absorbing radiative heat (say, from the sun). The __________ model have a faster rate of heat absorbed per time.

black.	********************************** [34]
silver.	** [2]
(There is a tie.)	* [1]
(Unsure/guessing/lost/help!)	** [2]

For these snowboarders, if they are warmer than the surrounding environment, they will begin to cool down by emitting radiative heat (say, to the overcast sky and the snowy landscape). The snowboarder wearing the __________ jacket will have a faster rate of heat radiated per time.

black.	******************** [20]
silver.	**************** [16]
(There is a tie.)	* [1]
(Unsure/guessing/lost/help!)	** [2]

Ask the instructor an anonymous question, or make a comment. Selected questions/comments may be discussed in class.

"How about more examples of blackbody and silverbody applicable to global warming and the similarities and differences to the albedo effect?"

"Interesting presentation today, I enjoyed it!"

"Heat transfers are 'cool!' If I'm snowboarding in white I will reflect more light but since silverbodies are bad at emitting heat, could I then stay warmer than the dude in all black since blackbodies emit heat better?" (Yes, for a cloudy day, or at night, or in a cave, or whenever absorbing heat from the sun or other sources (like a fireplace) is not a factor.)

Online reading assignment: Milky Way history, big bang clues (NC campus)

Astronomy 210, fall semester 2018
Cuesta College, San Luis Obispo, CA

Students have a weekly online reading assignment (hosted by SurveyMonkey.com), where they answer questions based on reading their textbook, material covered in previous lectures, opinion questions, and/or asking (anonymous) questions or making (anonymous) comments. Full credit is given for completing the online reading assignment before next week's lecture, regardless if whether their answers are correct/incorrect. Selected results/questions/comments are addressed by the instructor at the start of the following lecture.

The following questions were asked on reading textbook chapters and previewing presentations on the history of the Milky Way and big bang clues, a comic strip adaptation of Neil deGrasse Tyson's "The Most Astounding Fact" 2008 interview for TIME magazine, and Minute Physics' video explanation of Olbers' paradox.


Selected/edited responses are given below.

Describe something you found interesting from the assigned textbook reading or presentation preview, and explain why this was personally interesting for you.

"I found the topic of when the universe and how it began very interesting; I like reading about the theories and wonder if they are 100% accurate."

"How we can look back into time in a certain manner of speaking by observing the stars light that is coming from light years away. The fact that we are not seeing the object as it is but as it was from the amount of light years it takes to get here."

"Light is like time travel but not. Light from other areas may not currently exist today but it did years ago."

"How old our galaxy is, and how they could determine this was interesting because it's such a large span of time that is really hard to imagine."

"The early universe started out with basically just only hydrogen, and the first-generation massive stars then gathered this hydrogen and promptly got to work."

"That elements humans are made out of came from stars. I never realized were that closely connected to space."

"The iron, carbon, and calcium in us is as old as like everything."

"What I found cool was that the universe keeps expanding; I thought it was interesting because it makes me question about other life forms."

Describe something you found confusing from the assigned textbook reading or presentation preview, and explain why this was personally confusing for you.

"How metals have formed over time."

"The origins of elements in the universe."

"Olbers' question about the edge of the universe."

"How from the big bang planets and suns and galaxies formed."

"'Big bang'--I'm unclear as to what is being referred to exactly: if it's a process, or how it works overall."

"The Hubble law--I did not quite understand it and would like further explanation on it."

"Most of this reading I found confusing, didn't really understand or knew where to find the answers :("

Indicate how the amount of these elements in the universe have changed over time.
(Only correct responses shown.)

Hydrogen: decreased [31%]
Metals (elements heavier than hydrogen and helium): increased [54%]

The outermost layers of __________ are more abundant in metals (elements heavier than hydrogen and helium).

extremely old stars that formed a long time ago.	***** [5]
young stars that formed very recently.	****** [6]
(There is a tie.)	[0]
(Neither, as stars cannot have metals.)	* [1]
(Unsure/guessing/lost/help!)	* [1]

Indicate what produced these elements.
(Only correct responses shown.)

Hydrogen in the sun's core: the very early universe [54%]
Helium in the sun's core: the sun [38%]
Carbon in your body: another star, in the past [38%]
Calcium in your bones: another star, in the past [45%]
Iron in your blood: another star, in the past [38%]
Gold and silver from mines: another star, in the past [38%]

Ask the instructor an anonymous question, or make a comment. Selected questions/comments may be discussed in class.

"Can we learn about black holes?" (We already did; but now we're going to learn about the big bang.)

"Do you think we'll one day actually be able use this concept of look-back time to make time travel (the science fiction kind) actually possible?" (The light that travels to us from distant objects is "old," and allows us to see what was going on at the moment that light started out from its source. The distant source of that light is living in the present, though, and there (conventionally) is no way to travel to that distant source and wind up in its past, even though we can see how it was in the past.)

"As I have always heard that the universe is ever expanding. Could there be galaxies forming in between those spaces and the light just hasn't reached us yet?" (The space between galaxies is empty (otherwise we wouldn't be able to see other galaxies), so no gas or dust is there for new stars and planets (and galaxies) to form. That stuff only happens within galaxies.)

"How was your Thanksgiving? (Eh, it was okay. I'm fine with okay; for me okay is pretty awesome. How was your Thanksgiving?)

Online reading assignment: internal energy conservation

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

Students have a bi-weekly online reading assignment (hosted by SurveyMonkey.com), where they answer questions based on reading their textbook, material covered in previous lectures, opinion questions, and/or asking (anonymous) questions or making (anonymous) comments. Full credit is given for completing the online reading assignment before next week's lecture, regardless if whether their answers are correct/incorrect. Selected results/questions/comments are addressed by the instructor at the start of the following lecture.

The following questions were asked on reading textbook chapters and previewing a presentation on internal energy conservation.


Selected/edited responses are given below.

Describe what you understand from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically demonstrate your level of understanding.

"I understand heat and internal energy and that heat tends to flow from a hotter temperature object to a lower temperature object."

"If something's thermal energy increases, the temperature increases. If the thermal energy decreases, the temperature decreases."

"I understood a lot because I learned this in chemistry. Heat always flows from high to low, if the environment has no effect then each energy term must directly mirror the other..."

"If the thermal energy of a system is increasing (heating), that means external heat is positive and is adding into the system. If it's decreasing (cooling), external heat is negative and it's removing from the system. Zero means no energy is being transferred in or out of the thermal internal energy system."

"Thermal internal energy depends on temperature. It makes sense that a low temperature object has low thermal internal energy, and a higher temperature indicates higher thermal internal energy. Energy not transferred in/out of the thermal internal energy of a system is isolated from the environment and heat exchange between the system and the external environment is zero."

"Thermal energy is transmittable between objects in the form of heat. Temperature changes are a direct result transferences of proportionate amounts of thermal energy. It is also worth noting that different materials are able to retain and transfer thermal energy very differently."

"I understand that when we look at thermal internal energy we are more focused on the change in temperature of an object or objects. Everything has its own specific heat capacity similar to last chapter when we were talking about the Young's modulus. Heat is added to a system or taken away from a system and that energy is conserved in thermally isolated areas. However, perfect thermally isolated areas do not appear often in the natural environment but we can create those in things like a thermos (still not perfect)."

Describe what you found confusing from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically identify the concept(s) that you do not understand.

"I don't understand how internal energy and temperature relate to each other."

"I understand the heat and energy concepts. I am confused about using the equations. I will pay attention in class and keep on visiting the tutors."

"New symbols/terms for these things are going to take some getting used to."

"Simple concepts in this reading. Not too much that is confusing."

"Nothing too confusing from this reading thus far."

Two objects that are brought into contact with each other will reach thermal equilibrium when they have the same:

internal energy.	******** [8]
temperature.	*************** [15]
(Both of the above choices.)	************* [13]
(Neither of the above choices.)	[0]
(Unsure/lost/guessing/help!)	*** [3]

Raw seafood is placed on a block of salt that has already been heated up. The energy contained in the high-temperature block of salt is then transferred to the seafood, cooking it. While it is being cooked, the internal thermal energy of the seafood __________, while the thermal internal energy of the salt block __________.

increases; decreases.	************************************ [36]
decreases; increases.	* [1]
does not change; does not change.	* [1]
(Unsure/lost/guessing/help!)	* [1]

For the seafood cooking on the salt block (ignoring heat transfers with the environment), the object that experienced the greatest amount of change (increase or decrease) in thermal internal energy was the:

seafood.	************* [13]
salt block.	* [1]
(There is a tie.)	*************************** [22]
(Unsure/lost/guessing/help!)	*** [3]

Frozen meat is placed in a water bath, in order to defrost it. At the very start of this defrosting process (where the frozen meat just begins to warm up from its below-freezing temperature, and the ice crystals inside have not yet reached the melting point), the internal thermal energy of the meat __________, while the thermal internal energy of the water __________.

increases; decreases.	******************************* [31]
decreases; increases.	** [2]
does not change; does not change.	**** [4]
(Unsure/lost/guessing/help!)	** [2]

For the frozen meat in the water bath (ignoring heat transfers with the environment), the object that experienced the greatest amount of change (increase or decrease) in thermal internal energy was the:

frozen meat.	******** [8]
water bath.	******* [7]
(There is a tie.)	********************* [21]
(Unsure/lost/guessing/help!)	*** [3]

A shot of whiskey is mixed with a pint of beer to make a boilermaker. Assuming that the whiskey and beer have approximately the same temperature before they are mixed together, the internal thermal energy of the whiskey __________, while the thermal internal energy of the beer __________.

increases; decreases.	[0]
decreases; increases.	* [1]
does not change; does not change.	************************************ [36]
(Unsure/lost/guessing/help!)	** [2]

For the shot of whiskey being mixed with the pint of beer (ignoring heat transfers with the environment), the object that experienced the greatest amount of change (increase or decrease) in thermal internal energy was the:

shot of whiskey.	* [1]
pint of beer.	** [2]
(There is a tie.)	********************************* [33]
(Unsure/lost/guessing/help!)	*** [3]

Ask the instructor an anonymous question, or make a comment. Selected questions/comments may be discussed in class.

"I'm pretty sure that the salt block and seafood experience the same amount of change in internal energy, but if the salt block is bigger in size than the seafood that is being placed on it or if the difference in temperature is extreme (the salt block is fresh out of the oven and the seafood is frozen), wouldn't the seafood experience a greater change in internal thermal energy than the seafood? Also wouldn't the salt block have the least amount of change due to the fact that it is has more mass than the seafood?" (Yes, both the salt block and the seafood would experience the same amount of change--if the seafood gains 10,000 J, then the salt block must have lost 10,000 J (if we can neglect heat exchanged with the environment). Even if the salt block and seafood temperatures are very different, they will still undergo the same decrease/increase in internal energy. However, due to their different masses and different heat capacities, they will experience different temperature changes; typically the salt block will only "cool down a little" (experience a small temperature decrease) while the seafood will "heat up a lot" (experience a large temperature increase) despite experiencing the same amount of change (decrease/increase) in internal energy.)

"I am not exactly sure about whiskey-beer questions. If both have the same temperature prior to mixing, then there should not be a change in their thermal internal energies?" (Yes.)

"I understand that the change in thermal energies is equal for two objects interacting (only with each other, and not with the environment) and have reached thermal equilibrium. But does that mean they should have the same final temperature?" (Yes, the definition of thermal equilibrium means that the two objects have the same final temperature. Since heat flows from a hotter object to a cooler object, once the two objects have reached the same final temperature, then the exchange of heat stops.)

"Thermal energy transfers happen all around us everyday!"

"I never thought I'd see Q = m·c·ΔT outside of chemistry :/" (We're going over it here in physics, because I don't think chemistry truly covers the nuances of that equation.)

"Hope you had a great Thanksgiving?" (Eh, it was okay. I'm fine with okay; for me okay is pretty awesome. How was your Thanksgiving?)

Astronomy midterm question: possible IAU classification of "rounded" 2006 RH120?

Astronomy 210 Midterm 2, fall semester 2018
Cuesta College, San Luis Obispo, CA

2006 RH₁₂₀ (previously known as "6R10DB9") is an object that orbits the sun most of the time, but periodically is caught by Earth's gravity to make several loops around Earth, before returning back to its normal orbit around the sun:

Is 2006 RH₁₂₀ a "second moon?" I'd call it a chunk of rock that orbits the sun almost all the time, spending only a few months orbiting Earth in 2006. It will make passes by us in 2028 and 2044 (at safe distances), and every twenty years or so after that. Eventually, it'll get caught for a few orbits around Earth again, and will almost certainly be ejected again, just as happened this time. 2006 RH₁₂₀ quite likely got where it is as a result of being blasted off the surface of the moon by an impact.[*][**]

In the (unlikely) event that 2006 RH₁₂₀ is found to have a rounded shape, discuss how it should be classified when it is in its usual orbit around the sun. Explain using the International Astronomical Union classification scheme.

[*] projectpluto.com/pluto/mpecs/6r1.htm.
[**] Illustration credit: Gregg Dinderman, skyandtelescope.com/astronomy-news/earths-other-moon/.

Solution and grading rubric:

• p:
  Correct. Discusses IAU classification scheme to argue that 2006 RH₁₂₀ when in its usual orbit around the sun would pass qualification I (orbits the sun directly), and with a presumably (however unlikely) rounded shape would pass qualification II (rounded shape), but as it is periodically captured by Earth's gravity 2006 RH₁₂₀ does not dominate its orbit, and thus would presumably be classified as a dwarf planet.
• 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. Explicitly lists IAU requirements, but does not apply them correctly/consistently.
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Discussion only tangentially related to the IAU classification scheme.
• x:
  Implementation/application of ideas, but credit given for effort rather than merit. Discussion unrelated to the IAU classification scheme.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Grading distribution:
Section 70158
Exam code: midterm02SYnR
p: 29 students
r: 0 students
t: 0 students
v: 4 students
x: 0 students
y: 1 student
z: 1 student

Section 70160
Exam code: midterm02NdI0
p: 6 students
r: 2 students
t: 6 students
v: 3 students
x: 1 student
y: 0 students
z: 0 students

A sample "p" response (from student 4073):

Physics midterm question: rotational kinetic energies of basketball vs. tennis ball

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

A basketball (mass 0.43 kg, radius 0.11 m) and a tennis ball (mass 0.058 kg, radius 0.033 m) 
both roll without slipping across a horizontal floor with the same constant speed of 0.50 m/s. Discuss why the basketball will have more rotational kinetic energy than the tennis ball.



Both objects are hollow spheres (I = (2/3)·M·R²).

Solution and grading rubric:

• p:
  Correct. Numerically calculates for each ball the angular speed from the v = R⋅ω condition for rolling without slipping, and moment of inertia I = (2/3)·M·R², and then includes both these factors to compare the rotational kinetic energy KE_rot = (1/2)⋅M⋅ω^2 of both objects, such that the basketball has a larger numerical value for the rotational kinetic energy than the tennis ball.
• 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. At least shows that the basketball has a higher moment of inertia than the tennis ball, but claims that they have the same angular speed, or does not explicitly show that difference in angular speeds is much smaller than the difference in moments of inertia in determining that the basketball has a greater rotational kinetic energy.
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner.
• 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: midterm02r3iN
p: 17 students
r: 2 students
t: 37 students
v: 1 student
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student):

Physics midterm question: comparing horizontal forces supporting tilted beams

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

A horizontal force is applied to hold a uniform beam stationary at an angle of 80° above the horizontal, and another horizontal force is applied to hold it stationary at an angle of 10° above the horizontal. (Calculate all torques with respect to the pivot, located at the base of the beam.) Discuss why less force required to hold the beam when it is at the higher 80° angle. 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:
  Complete free-body diagrams with forces and perpendicular lever arms, and discusses/demonstrates:
  1. the magnitude of the weight force w is the same for both higher and lower beams; but
  2. the lever arms ℓ_F are not the same, where ℓ_F is longer for the higher beam, and shorter for the lower beam; and
  3. the lever arms ℓ_w are not the same, where ℓ_w is shorter for the higher beam, and longer for the lower beam; and
  4. Newton's first law for rotations applies to both higher and lower beams, where the ccw force τ = F⋅ℓ_F and cw weight τ = w⋅ℓ_w must balance each other out, and so:

     F⋅ℓ_F = w⋅ℓ_w,
     
     F = w⋅(ℓ_w/ℓ_F);

     such that
  5. for the higher beam, the shorter ℓ_w in the numerator and longer ℓ_F in the denominator means that the applied force F is smaller than for the lower beam (where it has a longer ℓ_w in the numerator and a shorter ℓ_F in the denominator).
• r:
  As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes. At least demonstrates that for the higher beam ℓ_w is shorter and ℓ_F is longer, but typically discusses only how one of these contributes to making the applied force smaller.
• t:
  Nearly correct, but argument has conceptual errors, or is incomplete. Typically argues that F is smaller for the higher beam because ℓ_F is larger (while claiming ℓ_w is the same for both beams); or F is smaller for the higher beam because ℓ_w is smaller (while claiming ℓ_F is the same for both beams).
• 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 first law to torques, forces, and perpendicular lever arms.
• 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
Exam code: midterm02r3iN
p: 17 students
r: 4 students
t: 21 students
v: 10 students
x: 5 students
y: 0 students
z: 0 students

A sample "p" response (from student 5250):

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 midterm question: comparing Young's moduli of fishing lines

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

A long 1.00 m fishing line and a short 0.50 m fishing line (same cross-sectional area) are each strung horizontally over a pulley, and are attached to a 100 g mass and a 50 g mass, respectively. As a result both fishing lines stretch the same amount from their original lengths. It is not known if these fishing lines are made of the same material. Discuss which material has the greater Young's modulus value (or if there is a tie), and why. Explain your reasoning using the properties of stress, strain, and Hooke's law.

Solution and grading rubric:

• p:
  Correct. Applies Hooke's law in a systematic manner by:
  1. recognizing that they stretch the same amount ΔL and have the same cross-sectional area A; and
  2. the longer L fishing line has a greater tension force F applied to it than the shorter L fishing line with a lesser tension force F; and
  3. since Young's modulus Y = (F⋅L)/(A⋅ΔL), the longer L fishing line with the greater tension force F will have a larger Young's modulus (specifically four times larger) than the shorter fishing line with the lesser tension force.
• r:
  As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes. Typically has clerical errors (mislabeling "long" versus "short" labels), and so concludes that Young's modulus must be the same for both fishing lines.
• t:
  Nearly correct, but argument has conceptual errors, or is incomplete. Typically only recognizes length L or tension force F has having an affect on Young's modulus Y; or has recognizes both quantities as having an affect on Y, but someone argues that these cancel each other out, such that the fishing lines have the same Y value.
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. At least some systematic attempt at using Hooke's law quantities.
• x:
  Implementation/application of ideas, but credit given for effort rather than merit. Approach other than that of relating strain (force per unit area), Young's modulus, and strain using Hooke's law.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.
  

Grading distribution:
Sections 70854, 70855
Exam code: midterm02r3iN
p: 37 students
r: 6 students
t: 11 students
v: 2 students
x: 0 students
y: 0 students
z: 1 student

A sample "p" response (from student 5683):
A sample "p" response (from student 8812):
A sample "p" response (from student 1113):

Physics midterm problem: categorizing a cart collision

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

A 0.90 kg cart traveling in the +x direction at 0.45 m/s collides with a 0.15 kg cart that is initially at rest. The carts are not stuck together after the collision. After the collision, the 0.90 kg cart continues traveling in the +x direction at 0.35 m/s. Ignore friction, drag and other external forces during this brief collision. Find (a) the final velocity of the 0.15 kg cart, and (b) classify this collision as elastic, inelastic, or completely inelastic. Show your work and explain your reasoning using properties of collisions, energy (non-)conservation, and momentum conservation.


Solution and grading rubric:

• p:
  Correct. Finds final speed v_f2 = +0.60 m/s of the 0.15 kg cart, using conservation of momentum (as there is negligible drag/friction for this brief collision). It is not known whether the carts are permanently deformed and/or energy was lost to thermal/sound systems, so collision could be either inelastic or elastic (but cannot be completely inelastic because the carts are not stuck together after the collision). Explicitly tests for whether or not translational kinetic energy is conserved, and finds that since it is not conserved, this collision must be inelastic.
  
• r:
  Nearly correct, but includes minor math errors.
  
• t:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. Has correct v_f2 from momentum conservation, and at least some attempt at testing for translational kinetic energy conservation.
  
• v:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Application of momentum conservation, but v_f2 is incorrect, with little or no test of kinetic energy conservation.
  
• x:
  Implementation of ideas, but credit given for effort rather than merit.
  
• y:
  Irrelevant discussion/effectively blank.
  
• z:
  Blank.
  

Grading distribution:
Sections 70854, 70855
Exam code: midterm02r3iN
p: 28 students
r: 7 students
t: 13 students
v: 4 students
x: 5 students
y: 0 students
z: 0 students

A sample "p" response (from student 1408):

Physics quiz question: marshmallow compression

Physics 205A Quiz 6, fall semester 2018
Cuesta College, San Luis Obispo, CA

A marshmallow has a height of 3.8×10^–2 m, a circular cross-sectional area of 5.1×10^–4 m², and a Young's modulus of 2.9×10⁴ N/m².[*][**] A downwards force of 10 N is applied evenly onto the top of the marshmallow. As a result, the marshmallow is compressed by:
(A) 6.7×10^–9 m.
(B) 1.3×10^–5 m.
(C) 2.6×10^–2 m.
(D) 2.0×10⁴ m.

[*] amazon.com/ask/questions/Tx21SLNIPLG0WI4.
[**] physics.info/elasticity/.

Correct answer (highlight to unhide): (C)

Hooke's law is given by:

(F/A) = Y·(∆L/L),

such that the amount that the marshmallow would be compressed is:

∆L = (F·L)/(A·Y),

∆L = ((10 N)·(3.8×10^–2 m))/((5.1×10^–4 m²)·(2.9×10⁴ N/m²)),

∆L = 0.02569303584... m,

or to two significant figures, the marshmallow would compress by 2.6×10^–2 m.

(Response (A) is (F·L·A)/Y; response (B) is F·L/Y; response (D) is the stress F/A.)

Sections 70854, 70855
Exam code: quiz06POr7
(A) : 4 students
(B) : 3 students
(C) : 43 students
(D) : 2 students

Success level: 83%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.50

Physics quiz question: mass-spring strength constant

Physics 205A Quiz 6, fall semester 2018
Cuesta College, San Luis Obispo, CA

A 0.75 kg mass attached to a horizontal spring has a 2.0 s period of oscillation. Neglect friction and drag. The spring strength constant of this spring is:
(A) 7.6×10^–2 N/m.
(B) 5.6 N/m.
(C) 7.4 N/m.
(D) 9.9 N/m.

Correct answer (highlight to unhide): (C)

The period T of a mass m attached to a spring with spring strength constant k is given by:

T = 2·π·√(m/k),

such that the spring strength constant k will be:

k = m·(2·π/T)² = (0.75 kg)·(2·π/(2.0 s))² = 7.4022033008... kg/s²,

or as expressed in more conventional units to two significant figures, the spring constant is 7.4 (kg·m/s²)·(1/m) = 7.4 N/m.

(Response (A) is m·(T/(2·π))²; response (B) is (m·2·π/T)²; and response (D) is m·2·π/T.)

Sections 70854, 70855
Exam code: quiz06POr7
(A) : 6 students
(B) : 5 students
(C) : 40 students
(D) : 1 student

Success level: 77%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.58

Physics quiz question: mass-spring translational kinetic energy

Physics 205A Quiz 6, fall semester 2018
Cuesta College, San Luis Obispo, CA

A 0.75 kg mass attached to a horizontal spring has a 2.0 s period of oscillation. Neglect friction and drag. The velocity versus time graph for this mass-spring system is shown at right. The earliest time that the mass will have its maximum translational kinetic energy is:
(A) 0 s.
(B) 0.5 s.
(C) 1.0 s.
(D) 1.5 s.

Correct answer (highlight to unhide): (B)

The translational kinetic energy of the mass-spring system will be at a maximum when the velocity v has its greatest magnitude (regardless of direction), which occurs at t = 0.5 s and t = 1.5 s.

Sections 70854, 70855
Exam code: quiz06POr7
(A) : 5 students
(B) : 38 students
(C) : 6 students
(D) : 3 students

Success level: 73%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.67

Physics quiz question: Oregon Convention Center pendulum cable length

Physics 205A Quiz 6, fall semester 2018
Cuesta College, San Luis Obispo, CA

the longest pendulum currently in existence is at the Oregon Convention Center in Portland, OR, a 40 kg mass swinging on a cable with a period of 9.25 seconds.[*] At that location the magnitude of the acceleration due to gravity g is 9.82611 m/s².[**] The length of the cable for this pendulum is:
(A) 4.53 m.
(B) 14.5 m.
(C) 21.3 m.
(D) 209 m.

[*] Martin Beech, The Pendulum Paradigm: Variations on a Theme and the Measure of Heaven and Earth, BrownWalker Press (2014), p. 42.
[**] wolframalpha.com/input/?i=gravitational+acceleration+portland,+or.

Correct answer (highlight to unhide): (C)

The period of a pendulum is given by:

T = 2·π·√(L/g),

which does not depend on the mass. Since the period T = 9.25 s and gravitational constant g = 9.82611 m/s² are known, the length L can then be solved for:

L = g·(T/(2·π))²,

L = (9.82611 m/s²)·((9.25 s)/(2·π))² = 21.2963585648... m,

or to three significant figures, the length of the pendulum cable is 21.3 m.

(Response (A) is g·((2·π)/T)²; response (B) is g·T/(2·π); response (C) is ((g·T)/(2·π))².)

Sections 70854, 70855
Exam code: quiz06POr7
(A) : 1 student
(B) : 3 students
(C) : 46 students
(D) : 2 students

Success level: 88%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.42

Physics quiz question: San Luis Obispo, CA pendulum period

Physics 205A Quiz 6, fall semester 2018
Cuesta College, San Luis Obispo, CA

the longest pendulum currently in existence is at the Oregon Convention Center in Portland, OR, a 40 kg mass swinging on a cable with a period of 9.25 seconds.[*] At that location the magnitude of the acceleration due to gravity g is 9.82611 m/s².[**]

In San Luis Obispo, CA, the magnitude of the acceleration due to gravity g is 9.80844 m/s².[***]

If a similar pendulum were constructed in San Luis Obispo, CA, and set into the motion with the same amplitude, it would have a period __________ the period of the pendulum in Portland, OR.
(A) less than.
(B) equal to.
(C) greater than.
(D) (Not enough information is given.)

[*] Martin Beech, The Pendulum Paradigm: Variations on a Theme and the Measure of Heaven and Earth, BrownWalker Press (2014), p. 42.
[**] wolframalpha.com/input/?i=gravitational+acceleration+portland,+or.
[***] wolframalpha.com/input/?i=gravitational+acceleration+san+luis+obispo,+ca.

Correct answer (highlight to unhide): (C)

The period of a pendulum is given by:

T = 2·π·√(L/g),

which does not depend on the mass, and only on the length L of the cable (which is the same for both locations), and the gravitational acceleration constant g (which is different for these locations).

Since San Luis Obispo, CA has a slightly smaller gravitational acceleration constant (9.80844 m/s²) compared to Portland, OR (9.82611 m/s²), then the pendulum in San Luis Obispo, CA will have a slightly longer period compared to Portland, OR.

This can be shown quantitatively by writing out the pendulum period equations for both locations:

T_Portland = 2·π·√(L_Portland/g_Portland),

T_SLO = 2·π·√(L_SLO/g_SLO).

Since the cable length would be the same for both locations, then:

L_SLO = L_Portland,

and solving for the period for the pendulum in San Luis Obispo, CA:

g_SLO·(T_SLO/(2⋅π)² = g_Portland·(T_Portland/(2⋅π)²,

g_SLO·(T_SLO/(2⋅π)² = g_Portland·(T_Portland/(2⋅π)²,

(T_SLO)² = (T_Portland)²⋅(g_Portland/g_SLO) ,

T_SLO = T_Portland√(g_Portland/g_SLO),

T_SLO = (9.25 s)·√((9.82611 m/s²)/(9.80844 m/s²)) = 9.2583282333... s,

which to three significant figures is 9.26 s, and thus longer than the period of the pendulum in Portland, OR.

Sections 70854, 70855
Exam code: quiz06POr7
(A) : 10 students
(B) : 10 students
(C) : 32 students
(D) : 0 students

Success level: 61%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.58

Physics quiz question: comparing piano string wave speeds

Physics 205A Quiz 6, fall semester 2018
Cuesta College, San Luis Obispo, CA

A D₃ piano string[*] has linear mass density of 7.8 g/m, and is stretched with a tension of 626 N. A thicker A₀ piano string has a linear mass density of 291 g/m, and is stretched with a greater tension of 1,350 N. The __________ has a faster transverse wave speed.
(A) D₃ piano string.
(B) A₀ piano string.
(C) (There is a tie.)
(D) (Not enough information is given.)

[*] A. Stulov, "Physical Modelling of the Piano String Scale," Applied Acoustics, vol. 69 (2008) pp. 977–984, cs.ioc.ee/~stulov/appl08.pdf.

Correct answer (highlight to unhide): (A)

The speed v of transverse waves along the piano string depends on the tension F and the linear mass density (mass per unit length) (m/L):

v = √(F/(m/L)).

For the D₃ piano string (linear mass density is 7.8 g/m = 7.8×10^–3 kg/m) the wave speed is:

v = √((626 N)/(7.8×10^–3 kg/m)) = 283.2956234332... m/s,

or to two significant figures, 2.8×10² m/s.

The A₀ piano string (linear mass density is 291 g/m = 0.291 kg/m) the wave speed is:

v = √((1,350 N)/(0.291 kg/m)) = 68.111491378... m/s,

or to two significant figures, 68 m/s.

Thus the D₃ piano string has a faster transverse wave speed than the A₀ piano string.

Sections 70854, 70855
Exam code: quiz06POr7
(A) : 44 students
(B) : 6 students
(C) : 2 students
(D) : 0 students

Success level: 85%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.42

Physics quiz archive: simple harmonic motion, waves

Physics 205A Quiz 6, fall semester 2018
Cuesta College, San Luis Obispo, CA
Sections 70854, 70855 version 1
Exam code: quiz06POr7



Sections 70854, 70855 results

0- 6 :
7-12 :	**** [low = 9]
13-18 :	********
19-24 :	********************* [mean = 23.3 +/- 5.6]
25-30 :	******************** [high = 30]