P-dog's blog: boring but important: 201303

20130330

Presentation: magnetism

Look at these tiny compasses. Just look at them. And look at what happens to them when a bar magnet is brought nearby. Just look at them move around. (Video link: "PH MD SC TUTE 70031A V0541 Nuclear Magnetic Resonance NMR Model.")

In this presentation we discuss the attraction and repulsion of bar magnets in terms of magnetic fields, in parallel with a previous presentation discussing the attraction and repulsion of electric charges in terms of electric fields.

First, a "direct" model of magnetic forces.

By convention we label the two magnets that exert forces on each other as "source" and "test" poles, where the source magnet (with a north N and a south S pole) is said to be exerting a force on the test magnet (with a north n and a south s pole).

Throughout this discussion, don't worry about the magnitude of the forces these magnets exert on each other, as will focus only the direction of these magnetic forces. This force is attractive if the ends of the source magnet and test magnet face each other with opposite poles, and repulsive if the ends of the source magnet and test magnet face each other with like poles.

Note the convention where the source bar magnet (held stationary) has square ends, while the test bar magnet, which would be free to turn about a fixed center, is drawn like a compass with pointy ends.

Second, a more sophisticated "indirect" or two-step model of magnetic forces.

Instead of a source magnet directly exerting a force on a test magnet, in this two-step model, the source magnet is said to create a magnetic B field everywhere around it, and it is this magnetic field that exerts a force on a test magnet.

In order to visualize the magnetic field created by a source magnet, let's imagine filling space with many test magnets, all of them small enough that the only significant force exerted on them is due to the source magnet, and not due to the test magnets on each other. The directions of all of these test magnets shows us how the "influence" of the source magnet at each and every location in space--it is this influence throughout space that is the magnetic field of the source magnet.

Instead of drawing tiny test magnets at each and every location in space to represent the magnetic field of a source magnet, we place a series of test magnets end-to-end, and trace this magnetic field line. We can then replace the line of test magnets with magnetic field lines everywhere, where the direction of these lines denotes the direction of the north ends of the test magnets.

Let's focus on the first step of this two-step model. The source magnet, with a north pole N and a south pole S creates a magnetic field everywhere around it. (Again, don't worry about the magnitude of this magnetic field). The direction of all magnetic fields make closed loops, each coming out of the N pole (which is the "source" of magnetic field lines), and going into the S pole (which is the "sink" of magnetic field lines).

Notice how these magnetic field lines form closed loops, coming out of the N pole of the bar magnet, and coming into the S pole of the bar magnet.

Now what? If there is another magnet anywhere in the presence of this magnetic field, this magnetic field will exert a force on the test bar magnet's north pole n and south pole s. (Again, don't worry about the magnitude of this magnetic force). The direction of the magnetic force on the n pole is along the direction of magnetic field lines, and the force on the s pole is directed against the direction of magnetic field lines. As a result, the test magnet will often twist and move around corresponding to the forces exerted on its n and s poles.

Here, from before, we show the magnetic field lines filling in all space surrounding a source magnet with N and S poles. This magnetic field will cause a magnetic force to be exerted along a field line on the test magnet's n pole, and a magnetic force to be exerted against the field line on the test magnet's s pole. If we hold the middle of these test magnets stationary, but allow them to twist around, they will all align themselves accordingly where n poles "obey" and s poles "disobey" the field lines. (In any case, as a check the direction of the force on any test magnet poles should be attractive or repulsive depending on whether it is the opposite or same end as the source magnet N and S poles.)

Note that all of these magnets have both a north pole and a south pole. While there is speculation on the existence of magnetic monopoles, we will only consider magnetic dipoles, such as these bar magnets.

20130328

Presentation: denser and denser-er (revised)

Before we begin, a recap on the stellar remnants from two previous presentations on the lives and deaths of medium-mass stars and massive stars.

A white dwarf is the remnant of a medium-mass star, but to scale, it is much larger than the two possible remnants of a massive star--a neutron star, and a black hole, which actually has zero size (but is surrounded by an event horizon, which we'll discuss later).

However, while the white dwarf is the largest of these stellar remnants, it is not the most massive--a neutron star is more massive, and a black hole is more massive still.

All of these stellar remnants are incredibly dense, but which stellar remnant is densest? Least dense?

Since we have already discussed the behavior of dense white dwarfs (isolated or in close binary star systems) in a previous presentation, we will look at the other denser and "denser-er" stellar remnants--neutron stars and black holes. ("Dense and 'densibility?'")

First, dense neutron stars.

Imagine being in graduate school in astronomy, if you were Jocelyn Bell in the 1960s. Suppose she was given instructions to show up early on the first day of class with all the other students, in a muddy field behind campus, wearing old clothes. She was given gloves, wire cutters, and a sledgehammer, and was directed to a massive pile of wooden stakes and spools of cable. "Welcome to astronomy graduate school--your research project will be radio astronomy--and you will be building the school's first radio telescope."

After weeks of pounding in wooden stakes and stringing up cables to form a radio telescope mesh, Jocelyn Bell got down to actual radio astronomy, listening to whatever radio signals were detected and noting anything unusual or strange. This is the actual trace of an interesting repeating radio signal she noticed (along with an audio recording of a similar signal). (Video link: "2-10-denseanddenser-discovery.")

These mysterious signals--named "pulsars"--repeat at very precise intervals. The best model we have for explaining these pulsing radio signals is this "lighthouse model," which sends out light beams in certain directions, and the rotation--whether slow or fast--determines the interval between signals. (Video link: "Beacon, San Luis Obispo County Regional Airport, CA.")

Recall that the core of a massive main-sequence star will begin to collapse and implode at the end of its supergiant phase, crushing itself into a neutron star, concentrating its magnetic fields. These strong magnetic fields, with north and south poles, capture stray charged particles, forcing them to emit radio waves in certain directions. No one initially expected that the radio pulse evidence would lead there, but neutron stars turn out to be the answer to the mystery of pulsars. (Video link: "The Oblique Rotator Model for a Pulsar.")

Second, "denser-er" black holes.

This is the main outlet for water in Lake Berryessa water to pass through the Monticello Dam, and is a fair analog for a black hole. If you were swimming far from this dangerous portal, you wouldn't notice its presence, but if you were unfortunate to find yourself near it, you would definitely "feel" its presence. Provided you could swim fast enough, you will can make it back to safety, but there is an imaginary boundary around it at which you could not escape, no matter how fast you can swim--this boundary, or point-of-no-return, can be said to be its "event horizon." (Video link: "The Black Hole—The Glory Hole.")

Now instead of funnels and water, consider stars and black holes and space-time. All objects distort and curve space-time around themselves, and if you're far away from the distorted space-time around massive objects, where space-time is flat (in this crude two-dimensional model), you won't "see" this flatness, but you'll "feel" its flatness because you would not experience any gravitational forces. If you were near a massive object's distorted space-time, again you wouldn't be able to "see" this puckering, but you would "feel" it because your motion would tend to slide down this curved space-time towards the object--which is how gravitational forces work.

Note the space-time depressions around stars, but also the funnel-shaped distortion caused by something that doesn't seem to be there at all--this is the effect of a black hole on space-time. Remember that black holes can't be seen, but its effects on space-time--its gravitational field--can definitely be felt. And like the Lake Berryessa water outlet, you can get near it and get back out to safety provided you can move quickly enough, but there is an imaginary boundary around it at which you could not escape, no matter how fast you can move--this boundary, or point-of-no-return, for everything including light is the black hole's "event horizon." (Video link: "Black hole deforms space.")

So what would it be like to get close to a black hole, in the presence of its distorted space-time, and try to enter it?

Your textbook discusses tidal effects and "spaghettification," and time dilation effects in more detail, but let's try to model how an object would stretch out while circling closer and closer to a black hole, while apparently taking an infinite amount of time (as observed from afar) to circle and enter the event horizon--the point of no return around itself--where not even light can escape.

Here's that same funnel shape representing distorted space-time caused by a black hole. We'll throw in some marbles, taking care to throw them in a tight clump. At first, the clump of marbles will begin slowly spread out, but after circling the "black hole" the marbles will spread out from each other, forming a long line--spaghettification--due to this funnel shaped distortion of space-time!. Although we can't really show the effect of time dilation, there is a crude analog to this from the nature of this funnel-shaped distortion of space-time, as it seems like it takes longer and longer for the marbles to get down further and further into the throat of the funnel. (Video link: " Gravity Well (Reuben H. Fleet Science Center, San Diego, CA).")

So next time you see a charity donation funnel, try this for yourself--don't just roll in one coin, toss in several very closely bunched together, and watch the tidal effects stretch them out, and think about time dilation effects as they seem to take longer and longer to get further and further down the "throat" of curved space-time!

The evidence for black holes, even though we can't "see" them--is to "feel" for them, by looking at the effect of their gravity--their distorted space-time--on nearby companion stars. (Video link: "Black hole and companion star.")

In the subsequent in-class activity you will distinguish between companion stars with compact objects--whether white dwarfs, neutron stars, or black holes.

20130326

Astronomy current events question: nearby star system WISE J104915.57-531906 brown dwarfs

Astronomy 210L, spring semester 2013
Cuesta College, San Luis Obispo, CA

Students are assigned to read online articles on current astronomy events, and take a short current events quiz during the first 10 minutes of lab. (This motivates students to show up promptly to lab, as the time cut-off for the quiz is strictly enforced!)

Barbara K. Kennedy, "'The Closest Star System Found in a Century," March 11, 2013
http://science.psu.edu/news-and-events/2013-news/Luhman3-2013

The brown dwarfs in the newly-discovered nearby WISE J104915.57-531906 system are:
(A) carbon-rich stars.
(B) warm black holes.
(C) white dwarf remnants.
(D) too small to start fusion.
(E) absorb more light than they emit.

Correct answer: (D)

Student responses
Sections 30678, 30679, 30680
(A) : 6 students
(B) : 0 students
(C) : 0 students
(D) : 34 students
(E) : 9 students

Astronomy current events question: Jupiter "hot spots"

Jia-Rui Cook and Elizabeth Zubritsky, "'Hot Spots' Ride a Merry-Go-Round on Jupiter," March 14, 2013
http://www.nasa.gov/mission_pages/cassini/whycassini/cassini20130314.html

Images from NASA's Cassini spacecraft provides evidence that Jupiter's "hot spots" are created by conditions similar to Earth's:
(A) mantle circulation.
(B) atmosphere and oceans.
(C) gravitational fluctuations.
(D) shield volcanoes.
(E) northern lights.

Correct answer: (B)

Student responses
Sections 30678, 30679, 30680
(A) : 5 students
(B) : 28 students
(C) : 12 students
(D) : 2 students
(E) : 3 students

Astronomy current events question: building blocks of life on Mars?

DC Agle and Dwayne Brown, "NASA Rover Finds Conditions Once Suited for Ancient Life on Mars," March 12, 2013
http://www.nasa.gov/mission_pages/msl/news/msl20130312.html

NASA's Mars rover Curiosity shows that ancient Mars could have supported living microbes by drilling into sedimentary rock and finding:
(A) DNA fragments.
(B) fossilized microorganisms.
(C) chemical building blocks of life.
(D) water-bearing crystals.
(E) air pockets.

Correct answer: (C)

Student responses
Sections 30678, 30679, 30680
(A) : 0 students
(B) : 6 students
(C) : 31 students
(D) : 11 students
(E) : 2 students

20130323

Presentation: advanced electricity

Gum wrapper (foil-covered paper), cut into a strip, with a narrow center section: check. AA battery: check. Completing an electrical circuit to start a fire: priceless. (Video link: "How to Make A Prison Lighter From a Bubble Gum Wrapper. MUST SEE! :)")

In this presentation we introduce a few additional concepts as we further implement Kirchhoff's circuit rules in analyzing electrical circuits.

The videos shown in this presentation, as with many videos shown in this class, should never be attempted at home. Even if many of these videos use items commonly found at home. Even if these items are found, well, within the very walls of your house itself!

First, using the digital multimeters used in laboratory to measure current, or to measure voltage.

You have already used these digital multimeters to measure the resistance of Christmas light bulbs, when isolated from an electrical circuit, when the proper plugs and correct dial settings are used. These digital multimeters can also measure current or electric potential rises/drops of items wired in an active electrical circuit, provided the proper plugs and correct dial settings are used. And since measurements are being made on an item while the circuit is "live," some care must be taken in not only using the proper plugs and correct dial settings, but also in properly connecting the digital multimeter to the item of interest.

When measuring the current passing through a light bulb (or any other circuit element), the current that passes through the light bulb must also pass through the digital multimeter. This means that the wiring in the circuit must be "broken" open to connect the digital multimeter to measure current (making it an ammeter).

Does it matter whether the ammeter is connected to measure current before it passes through the light bulb, or to measure current after it passes through the light bulb?

Why must an ammeter have a resistance that is ideally zero (or at the very least, a very low resistance value)?

When measuring the amount of electrical potential used by a light bulb (or any other circuit element), the digital multimeter must be connected to both before and the current flows through the light bulb. This means that the wiring in the circuit is not modified in order to connect the digital multimeter to measure electric potential (making it an voltmeter), as it "feels" the amount of electric potential before and after the light bulb, and reports the difference (whether a drop or rise).

Why must a voltmeter have a resistance that is ideally infinity (or at the very least, a very high resistance value)?

Second, the rate of energy per time (power) used by a circuit element.

"Joule heating" is the historical term for the power (or rate of energy used per time) continuously used by a circuit element of resistance R due to the amount of current I flowing through it, as in these radiating coils.

(For the purposes of this class, we will consider the resistance R of materials to be constant with respect to temperature, although the resistivity of many materials will typically be strongly dependent on the temperature.)

Recall from a previous presentation that a change in electric potential ∆V represents the "potential" potential energy used by a charge. For each charge q that uses a certain amount ∆V of electric potential, the amount of electric potential energy used is ∆EPE = q·∆V. For a continuous flow of charges per time as in a current I, the rate of electric potential energy used per time (that is, power) is ∆EPE/∆t = (q·∆V)/∆t = (q/∆t)·∆V = I·∆V.

(If instead the ∆V represents a rise in electric potential (as in a battery) instead of a drop, then I·∆V represents the continuous rate of electric potential energy per time provided by the battery.)

Substituting in Ohm's law (I = ∆V/R), the two parameters I and ∆V in the power equation can each be substituted out, yielding two other equivalent equations for power, most notoriously, the "Twinkle, Twinkle, Little Star" form:

Twinkle, twinkle, little star
Power equals I-squared R.

Believe me, you won't get this out of your head. Ever.

So endless hours of amusement await you when solving power dissipation (or source) problems, so use caution when you use these equations, and more importantly, use only the equation you really need.

All household electrical outlets provide 120 volts of electric potential and operate independently of each other, and thus are wired in parallel to each other to the same 120 volt electromotive source. Recall that from a previous presentation that as more resistors are added in parallel to a circuit, the equivalent resistance decreases. This means that as more and more appliances are plugged into the same household circuit and turned on, then the equivalent resistance may become dangerously low.

This may result in a very large runaway current flowing through the wires leading to the overloaded outlets. Even though the wires ideally have a low resistance r, a large enough current I will cause the wire to heat up appreciably (as the rate of joule heating is I²·r), resulting in the insulation around the wires, and the joists and walls in contact with it to catch on fire.

In order to prevent runaway currents from happening in a household circuit (well, should common sense fail to prevent overuse of the outlets), a circuit breaker is designed to "trip" and interrupt the current should it become dangerously high. If this should happen, protocol is to first unplug any and all appliances in that part of your house before resetting the breaker to re-complete the circuit. (Video link: "A 6 Amp AC breaker trips on DC at 240 Volts 30 Amps.")

Remember the gum wrapper and AA battery fire starter at the start of this presentation? That is an analog for an older-type fuse that would have a slightly greater resistance than the wires, such that the fuse would experience higher joule heating and sacrificially melt first before the wires would themselves heat up, breaking the circuit. Unlike modern circuit breakers, a fuse is no longer functional after melting, and must be completely replaced. A highly dangerous, but unfortunately common workaround for when a replacement fuse was not readily available was to push a penny (or other small piece of conducting metal) into the fuse socket in order to re-complete the circuit--hopefully after unplugging any and all appliances in that part of the house!

Physics midterm problem: microscope construction

Physics 205B Midterm 1, spring semester 2013
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 24.42

The converging lenses available from a commercial optics supplier have focal lengths f = +0.30 cm and f = +0.45 cm, respectively[*]. A Physics 205B student would like to use these two lenses to construct a microscope with a "tube length" L (the distance from focal point to focal point) of 5.0 cm, where the f = +0.30 cm lens is used as the objective. Solve for (a) the angular magnification of this microscope, and (b) the distance from the object to the objective lens. (The near point of the Physics 205B student is 25.0 cm.) Show your work and explain your reasoning.

[*] edmundoptics.com/optics/optical-lenses/double-convex-dcx-spherical-singlet-lenses/uncoated-double-convex-dcx-lenses/1748.

Solution and grading rubric:

p:
Correct. Determines (a) angular magnification to be –930×, and (b) the object must be placed 0.32 cm in front of the objective lens.
r:
Nearly correct, but includes minor math errors. Determines angular magnification, but does not explicitly solve for the distance for the object in front of the objective lens, but instead understands that it must be held very near outside the focal point (0.30 cm) of the objective lens.
t:
Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. At least has magnification, and some attempt in finding the distance for the object in front of the objective lens
:
Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner.
x:
Implementation of ideas, but credit given for effort rather than merit.
y:
Irrelevant discussion/effectively blank.
z:
Blank.

Grading distribution:
Sections 30882
Exam code: midterm01p0C4
p: 19 students
r: 2 students
t: 4 students
v: 6 students
x: 2 students
y: 0 students
z: 0 students

A sample "p" response (from student 1224):

20130321

Astronomy quiz archive: sun/spectra/star properties

Astronomy 210 Quiz 4, spring semester 2013
Cuesta College, San Luis Obispo, CA

Section 30674, version 1
Exam code: quiz04Ni7E

Section 30674

0- 8.0 :
8.5-16.0 :	*** [low = 10.0]
16.5-24.0 :	***********
24.5-32.0 :	********* [mean = 24.6 +/- 6.7]
32.5-40.0 :	***** [high = 36.5]

Section 30676, version 1
Exam code: quiz04sGf6

Section 30676

0- 8.0 :
8.5-16.0 :	*** [low = 8.0]
16.5-24.0 :	****************
24.5-32.0 :	**************** [mean = 24.7 +/- 7.0]
32.5-40.0 :	******* [high = 40.0]

20130319

Found astronomy: photosphere granulation

2013-03-18_18-39-47_245
http://www.flickr.com/photos/waiferx/8574333012/
Originally uploaded by Waifer X

Convection currents in miso soup, as an analog for photosphere granulation on the sun. Photo by Cuesta College Physical Sciences Division instructor Dr. Patrick M. Len.

Astronomy current events question: Comet C/2013 A1 close approach to Mars

Andrew Fazekas, "Monster Comet May Have Mars in its Crosshairs," March 6, 2013
http://newswatch.nationalgeographic.com/2013/03/06/monster-comet-may-have-mars-in-its-crosshairs/

Comet C/2013 A1 (Siding Spring) may __________ in September 2014, according to calculations from NASA's Jet Propulsion Laboratory.
(A) come close to impacting Mars.
(B) pass through Earth's upper atmosphere.
(C) plunge into the sun.
(D) escape from the solar system.
(E) disrupt GPS signals.

Correct answer: (A)

Student responses
Sections 30678, 30679, 30680
(A) : 37 students
(B) : 8 students
(C) : 0 students
(D) : 0 students
(E) : 1 student

Astronomy current events question: Curiosity rover computer memory problem

Guy Webster, "Curiosity Rover's Recovery on Track," March 4, 2013
http://www.nasa.gov/mission_pages/msl/news/msl20130304.html

NASA's Mars rover Curiosity is __________ due to an unknown problem with its computer's memory.
(A) trying to get its drilling arm unstuck.
(B) using its back-up computer.
(C) continuously rebooting.
(D) streaming corrupted data.
(E) only able to drive in reverse.

Correct answer: (B)

Student responses
Sections 30678, 30679, 30680
(A) : 2 students
(B) : 31 students
(C) : 7 students
(D) : 8 students
(E) : 0 students

Astronomy current events question: end of Herschel space telescope mission

United Press International, "Space Telescope Nears End of Mission," March 5, 2013
http://www.skyandtelescope.com/news/wires?id=183042792&c=y

The European Space Agency's Herschel infrared space telescope will end its observing mission due to:
(A) no more liquid helium coolant.
(B) software that cannot be upgraded.
(C) misaligned solar panels.
(D) cracks in its primary mirror.
(E) a reactor radiation leak.

Correct answer: (A)

Student responses
Sections 30678, 30679, 30680
(A) : 37 students
(B) : 1 student
(C) : 1 student
(D) : 8 students
(E) : 2 students

Student scribble: "What's up, P-dog?"

2013-03-16_14-32-55_929-tiltshift
http://www.flickr.com/photos/waiferx/8566689049/
Originally uploaded by Waifer X

Student scribble, Astronomy 210 Midterm 1, Cuesta College, San Luis Obispo, CA. Photo by Cuesta College Physical Sciences Division instructor Dr. Patrick M. Len.

20130316

Astronomy midterm question: evening star planet visible later?

Astronomy 210 Midterm 1, spring semester 2013
Cuesta College, San Luis Obispo, CA

A view of the horizon is shown below, as seen from San Luis Obispo, CA at a certain date/time. Carefully note the positions of the sun, and an unknown planet in the sky.

[Version 1]
Discuss why this this planet would not be visible at sunrise for an observer in San Luis Obispo, CA, and how you know this. Support your answer using a diagram showing the positions of the sun, this planet, Earth, and an observer on Earth.

[Version 2]
Discuss why this this planet would not be visible at midnight for an observer in San Luis Obispo, CA, and how you know this. Support your answer using a diagram showing the positions of the sun, this planet, Earth, and an observer on Earth.

Solution and grading rubric:

p = 20/20:
Correct. Correct and complete diagram, with observer at sunrise on Earth and a planet (either inside or outside of Earth's heliocentric orbit); shows and discusses how the planet just above west horizon at sunset (as an evening star) would not be visible anywhere in the sky at sunrise/midnight.
r = 16/20:
Nearly correct (explanation weak, unclear or only nearly complete); includes extraneous/tangential information; or has minor errors. Diagram and/or explanation has minor errors.
t = 12/20:
Contains right ideas, but discussion is unclear/incomplete or contains major errors. Problems with either diagram or discussion. At least understands that any planet near the sun in the sky cannot be seen at sunrise/midnight.
v = 8/20:
Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Diagram and discussion problematic. May have planet orbiting Earth, but still discusses how planet visible at sunset could not be visible at sunrise/midnight.
x = 4/20:
Implementation/application of ideas, but credit given for effort rather than merit. Misconceptions or non-relevant concepts.
y = 2/20:
Irrelevant discussion/effectively blank.
z = 0/20:
Blank.

Grading distribution:
[Version 1] Section 30674
Exam code: midterm01n4sT
p: 17 students
r: 1 student
t: 3 students
v: 9 students
x: 0 students
y: 0 students
z: 1 student

[Version 2] Section 30676
Exam code: midterm01sAb1
p: 33 students
r: 1 student
t: 3 students
v: 9 students
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 1686), explaining how the planet would not be visible at sunrise:

A sample "p" response (from student 0317), using another type of diagram to explain how the planet would not be visible at sunrise:

A sample "p" response (from student 4336), explaining how the planet would not be visible at midnight:

A sample "t" response (from student 7580), identifying the planet as a morning star rather than an evening star (but still discussing how it would not be visible at midnight):

A sample "v" response (from student 1162), with some semblance of using the "snowboarder model" for identifying the local horizon for an observer: