End of year review techniques: do it yourself, and drill vs. new matieral

This time of year, I'm asked regularly about review -- review for the AP exams, review for the Regents, review for the end-of-year exams, whatever.  The point is, we have covered enough material now that we can be putting it all together, assigning problems which integrate multiple topics, multiple levels of understanding.  And we can expect our students to either get these problems right, or to correct their mistakes.

Today I'll discuss two (of several) features of my April and May review.

Number 1:

During review time, I am stricter than ever about students doing everything on their own, without asking anyone for help until they've completed a problem.  We do a lot of work in class, and I am constantly saying "No, you may not ask me that question, not until the problem is finished.  What?  You say you can't do anything without me answering you?  Really?  So, on the AP exam in a few weeks, you're going to ask the proctor this kind of question?  And when she says 'I can't answer, and I don't know anything about physics anyway,' you're going to give up and stew at your desk for the remaining three hours?  Now go do whatever you can on the problem, and come back with the best answer you can come up with.  THEN we'll ask and answer questions."  Our students must must must get in the habit of working independently, then debriefing.  This process will develop confidence, study habits, and test taking habits all together.

Number 2:

By April, I know my students' strengths and weaknesses.  Review time will help everyone cement the topics and skills on which they were shaky; but no review in the universe is going to magically change a student's raw talent level.  We can use this time to separate our students, to give people work that's appropriate to their ability and progress.

It is always better for a student to get really good at a few topics rather than be sort-of-okay at all the topics on a cumulative exam.  During review time, the difference between an A and a B student should be the amount of material that he's trying to master.  Someone who has been getting top scores on the tests should be reviewing everything, especially those little topics that you didn't have the time, inclination, or energy to cover in the course of the course.  But someone who has been coming up short on tests should FIRST work on cementing some basic topics before moving on to new or difficult material.

In AP classes, I tend to separate out those with consistent As from those with Bs (or Cs) on tests.  The A students would work on atomic physics, nuclear physics, and electromagnetic induction as priorities.  Atomic and nuclear were not covered so thoroughly in the regular part of the class, but A students can generally learn this on their own as well as they could with lecture; electromagnetic induction WAS covered, but always needs careful review, as it's one of the hardest topics on the exam.  

The B (and C) students would instead work on other material.  I start them with some drill on frequently tested topics.  For examples of the kinds of things we do, look at the 5 Steps to a 5: AP Physics book's drill chapters.  You'll see problems on pulleys, inclined planes, electric and magnetic forces, and motion graphs.  I've created a couple more of these this year, as well.  Here's a worksheet on slopes and areas of graphs.  I've done a series of collision problems, and another on graphical analysis for lab problems.

Now, I don't generally believe in "busy work," especially early in the year when we're establishing the idea that physics is about creative problem solving, not about plugging in numbers to equations.  However, this time of year, practice is important for some students.  Which students?  The ones who have shown by their previous performance that they would benefit from more practice.  I don't offer a choice of learning new material or doing drill sheets, because some A students would choose the easy road, some B students would tilt at windmills.  So I assign each student to a review track.

Just the facts -- waves

I've had lots of positive feedback from the "just the facts" series of posts.  Yesterday, my colleague Erik Born asked me if I had such a list of facts for waves and optics.  I've done optics before, at this post.  But I'd not written up waves.

Below are the fundamental facts of physics that Woodberry Honors Physics students need to know for the national Honors Physics exam.  These are all also correct for the AP Physics B exam, but AP B adds in standing waves, and quantitative interference/diffraction for slits and thin films.  I think this is accurate for the New York Regents exam as well; please, New York folks, let me know if I'm missing something.

Enjoy!

Regarding waves, you need to know:

Definition of wavelength, amplitude, frequency, period

v = lf

The speed of a wave depends on the material through which it travels.

When a wave changes materials, the frequency doesn’t change.

Longitudinal waves have particles that vibrate parallel to the wave velocity; transverse waves have particles vibrating perpendicular to the wave velocity.

Sound is a longitudinal wave that moves about 340 m/s through air.

The loudness of a sound is related to the wave’s amplitude; the pitch of a sound is related to the wave’s frequency.

Electromagnetic waves are transverse waves that move through a vacuum, or air, at 3 x 10⁸ m/s.   Visible light is an electromagnetic wave with wavelength in a vacuum of about 400-700 nm.

The brightness of light is related to the wave’s amplitude; the color of light is related to the waves’s frequency.

Electromagnetic waves with frequency lower than visible light are called infrared, microwave, and radio.  Electromagnetic waves with frequency higher than visible light are called ultraviolet, x-rays, and gamma rays. 

The index of refraction n is defined as c/v : the speed of light in a vacuum divided by the speed of light in a material.

When two waves collide, they interfere constructively and/or destructively.  The colliding waves’ amplitudes add algebraically.

Two waves whose frequencies are close together will produce a “beat frequency” equal to the difference between the two waves’ frequencies.

The Doppler effect means that a wave source approaching an observer increases the observed frequency; a source receding from an observer decreases the observed frequency.

Refraction is the bending of a wave at a boundary due to the speed change.

Diffraction is the bending of a wave around an obstacle, which happens when an obstacle is about a wavelength in size.

Mail Time: What experiments do I have to do for AP?

An unidentified reader writes in via email:

I was wondering if you know of a list of recommended labs that Physics C students should do to be prepared for the AP exam.  Does such a list exist?  If not, what are some labs that you recommend AP Physics C students be exposed to?  

The nice part of AP physics is that, unlike in biology, the committee does not list a set of required or recommended experiments which must be understood before the exam.  Rather, the AP exam expects general familiarity with laboraty procedures and data analysis.  The test will ask at least one free response question "posed in an experimental setting," on which pure mathematical problem solving will be worthless.

Physics C students should have done regular experimental work throughout the year.  It doesn't matter what particular experiments you've done; but you should know how standard equipment works, like spring scales, motion detectors, etc.  You should know how to describe an experimental procedure in no more than three sentences.  You should know how to linearize an experimental graph.  You should know how to figure out the physical meaning of the slope and intercept of a best-fit line.  

Physics C experiments don't necessarily have to be different from physics B experiments.  If you're stuck for a good experiment, try looking back on the B and C exams since 1996; most of the experimental problems can be set up in a high school laboratory.  Try actually doing those labs.  Or, pick a free response problem that you know you could actually set up in your lab.  Do so.  Verify the result of the free response question.  

That kind of laboratory experience -- nothing complicated, but complete familiarity with equipment and analysis methods -- will serve you well, both on the exam, and in your future study of physics.

greg

Just The Facts: Magnetism for AP Physics B

I'm running an AP Physics B prep session in Lynchburg, Virginia in a couple of weeks.  I've been asked to discuss magnetism.

Of course I'll bring my demonstrations and practice questions.  But these will be merely confusing without students knowing the background facts.  So, I'll hand out a "just the facts" sheet to everyone for their reference during the demos and practice questions.  Afterwards, they can use this sheet for their own review.

What do you need to know about magnetism for the AP B exam?

I.                  Magnetic force on a charge or wire

The amount of force provided by a magnetic field on a charge is qvBsinq.

·         q is the charge of the particle in the field, measured in coulombs

·         v is the speed of the particle

·         B is the magnetic field, measured in tesla

·         q is the angle between the velocity and magnetic field, usually 90^o

The amount of force by a magnetic field on a current-carrying wire is ILBsinq.

·         same definitions as above for B, q

·         I is the amount of current in the wire, measured in amps

·         L is the length of the wire inside the magnetic field

The direction of force provided by a magnetic field is given by the first right hand rule

·         Do NOT plug in negative signs to qvBsinq.

·         Point toward v (or I), curl fingers toward B, thumb is direction of force on a positive charge or a current-carrying wire

·         (flip the direction for a negative charge)

·         Magnetic force is always perpendicular to velocity; this generally gives circular motion for a charged particle in the magnetic field.

II.               What can produce a magnetic field?

A bar magnet can produce a magnetic field.

·         Its field points out of the north end, and into the south end.

A current carrying wire can produce a magnetic field.

·         Its field wraps around the wire.  To find which way the field wraps, point right thumb with current and curl fingers.

·         The magnitude of the field produced by a straight wire is (μ₀/2π)(I/d).

·         Here I represents the current creating the field, and d is the distance from the wire.

III.           A changing magnetic flux can produce a voltage

Magnetic flux through a loop of wire, F, is defined as BA.

·         B is the amount of magnetic field

·         A is the area of the wire loop through which the magnetic field directly penetrates

·         The units of magnetic flux are T∙m².

·         If the magnetic field is not straight through the wire loop, only use the component of the field that is straight through the loop.

Changing flux produces a voltage

·         This voltage is referred to as “induced emf,” e.

·         The equation for the amount of voltage induced is n ΔΦ/Δt .

·         n represents the number of wire loops.  Dt represents the time it took to change the flux.

·         The induced current in a wire of known resistance can be found using V = IR.

The direction of induced current is given by Lenz’s Law

·         Current must flow through a wire – thus, only two directions are even possible for an induced current.

·         Point right thumb in the direction of the magnetic field.

o   (If flux is increasing rather than decreasing, flip your thumb the other way.)

·         Curl your fingers; this is the direction of the induced current.

Special case: moving rectangular wire entering or leaving a magnetic field

·         The induced voltage in this special case is e = BLv

·         Here, B is the magnetic field, v is the speed of the wire

·         L represents the side of the rectangle that always stays completely in the field, not the side of the rectangle that is entering or leaving the field

·         If the wire isn’t entering or leaving the field, the induced voltage is zero because flux doesn’t change.

Literary Physics: The Cyrano question

Folks, I freely admit to being a bit of a literary heathen.  I firmly believe that the three greatest books I've ever read, and by which I've been influenced, are

1. Harper Lee's To Kill a Mockingbird

2. Terry Pratchett's Night Watch

3. John Townsend's A Modern Approach to Quantum Mechanics

I'm deeply serious.  What, you disagree?  Me, I think the fact that Lee manages to create a heroic lawyer character should by itself send Mockingbird to the top of the literary charts.

I've never read Cyrano de Bergerac, but I came across this wonderful question more than a decade ago.  I think -- though I'm not 100% sure -- I found it in the Tipler 3rd edition test bank.  I've asked it on AP physics C exams for ages.  

Cyrano de Bergerac, in the play by Edmond Rostand, claims to have invented six methods of reaching the moon.  Five of these are listed below.  Select the one that has a physically sound basis.

(A) “Adorn my form with crystal vials filled with morning dew, and so be drawn aloft as the sun rises.”

(B) “Sealing up the air in a cedar chest, rarefy it by means of mirrors placed in an icosahedron.”

(C)“Construct the form of a huge locust, driven upward by leaps and bounds by impulses due to pellets of saltpeter ejected from the rear.”

(D)“Smoke, having a natural tendency to rise, blow in a globe enough to raise me.”

(E)“Seated on an iron plate, I hurl a magnet in the air – the iron follows – I catch the magnet – throw again – and so proceed indefinitely.”

I might have enjoyed Englilsh Class  more had we had fascinating discussions based around such a question.  Got a good literary question?  Post it in the comments.

What is a fundamental, anyway?

So, about a bobzillion years ago, I prepared my class for their first test.  I offered to allow them to use an equation sheet of their own design.  Oops.

These honors students, who were well versed in memorizing but not so well trained in physics reasoning, wrote down every equation in their book.  Including intermediate steps in a derivation; including the solutions to example problems.  No wonder they were confused on the test.

I still sometimes get tripped up in differentiating between what is a fact to memorize, and what is a problem solving process to be learned.  For example, velocity-time graphs are so common that we should simply memorize the physical meaning of the slope and area.  A separate "fundamental" skill is to figure out the meaning of an unfamiliar graph's area.

It's a fool's errand to memorize every possible graph that might be made.  The fact to memorize is "multiply the quantities (not the units) of the axes, then use an equation on the equation sheet to relate the quantities."  So a force vs. time graph has an area that means impulse, because an equation says that impulse is FΔt -- NOT because I can instantly recall "force vs. time graph, area = impulse."

In my senior honors class, I gave a 20 minute, cumulative fundamentals quiz.  You can see the original quiz at this link.  Some folks did quite well... but as you might expect, I had a number of students for whom the questions "just seemed to run all together."

Part of the issue for the lower-level students was the sheer quantity of material.  But another part, one that I too often underestimate, is that some of the questions I'm asking require a step of reasoning in addition to memorization.  When I teach freshmen next year, I'm going to have to differentiate better between fact and process.  For now, though, I need to get all my seniors stone cold solid on these kinds of questions, even if they do require a quick thought.

I've been observing my colleague who does teach freshmen.  He's been making the students write, in their own handwriting, some basic facts of physics.  He gives a fundamentals quiz the next day on which the students can use their notes.  Then he gives ANOTHER quiz the next day with the same material, but with no notes allowed.  He's found that even though it takes several days longer to present material, problem solving skills can be developed far more quickly and correctly.

On this quiz, then, I took a cue from this colleague.  I handed out this document which contains detailed discussion of the answers to this quiz.  I offered another quiz, on which handwritten notes were allowed, but on which students must spit back my detailed discussion WORD FOR WORD on the questions they originally missed.  My hope was that the process of writing the solution in their notebook, and then rewriting on the quiz, would help their memorization issues.

But I also hoped to help differentiate between facts and processes.  On one hand, students can see that "the force of a spring is given by kx, where k is the spring constant, and x is the displacement of the spring from its equilibrium position."  That's a fact.

On the other hand, students can write, "Total power dissipated by a circuit is the sum of the power dissipated by each resistor, no matter how the resistors are connected.  So two resistors in parallel that each dissipate 100 mW will dissipate 200 mW total."  I've started by stating the fact; then I've applied the fact to a specific situation.  Hopefully, next time my students are asked to find the total power dissipated in a circuit, they won't add the power dissipated by parallel resistors inversely.  :-)

  

Mail Time: Hole in an expanding steel plate

Joe Konieczny, who is now at the Walker School in Atlanta, writes in with a question about thermal expansion.

Hey Greg, this is my first year actually teaching thermodynamics to an AP class.  In previous years I just haven't had time (unless we had a Saturday school crash course in thermo) and it is also my weakest area of understanding in physics.

Joe has a class this year with some previous background in physics, so he can move more quickly than he did at other schools.  I've always made a different choice -- I think there's enough material that students of modest ability can handle to justify making thermodynamics a priority.  When I'm pressed for time, I ditch atomic physics, or perhaps induced EMF or magnetic fields created by wires.  But that's me.

  I asked my students a question I thought I understood, but it turns out I don't!  See the question below:

A square steel plate with sides of length 1.00 m has a hole in its center 0.100 m in diameter.  If the entire plate is heated to such a temperature that its sides become 1.01 m long, the diameter of the hole will be

(A)0.090 m         

(B)0.099 m         

(C)0.100 m         

(D)0.101 m        

(E)0.110 m

The answer is D.  The dimensions of the plate increase by 1%, so the diameter must increase by 1% as well.  Is that the correct explanation?

Yes.  By the thermal expansion equation, all of the steel everywhere expands by the same fraction, ΔL/L which equals αΔT.  

  My students expected that the hole would "expand", which to them meant expanding "in", and therefore the diameter would decrease by 1% to 0.099 m.  What is the error in that explanation?  Thanks.  

Yeah, that's a classic question.  The hole expands outward, too.  Three ways to think of it:

(1) Consider a long, thin rod bent into a circle.  Thermal length expansion means that heating the rod expands the rod's length.  Well, the length of the rod is the circumference of the circle.  Making the circumference larger also increases the circle's radius by 2πr.  Increasing a circle's circumference certainly doesn't *decrease* its diameter.

(2) Imagine that instead of cutting a hole, you just drew a circle on the steel.  Would the circle expand or contract?  Of course it would expand!  Turns out, it doesn't matter if you cut that material out, the principle is the same.

(3) I keep a blob of silly putty in the back of the room just for the purpose of answering this question.  Draw a circle on the silly putty.  Then stretch the silly putty out in all directions.  The circle... expands.  Then do the same thing with a cut-out circle in the silly putty.  The circle gets bigger, in an obvious manner that you can watch happen.  Even if students aren't buying the first two abstract arguments above, they'll quit arguing when they stretch the silly putty.

Index of refraction magic trick, I mean, demonstration

Light traveling from material 1 to material 2 is incident on material 2’s surface at an angle q_i, as shown above.  If materials 1 and 2 have the same index of refraction, which path will the light take upon refraction?

(A)  I

(B)  II

(C)  III

(D)  IV

I used this question, adapted from an AP-style question in the newest edition of Serway, on a recent quiz.  I don't think anyone in my class missed it.  Most folks answered it conceptually:  they know that light bends toward the normal when slowing down at an interface, away from normal when speeding up.  They correctly split the difference, recognizing that without a speed change there's no refraction.  A few used Snell's law, knowing that with equal n's, equal thetas are required.

Then I asked, what is the physical manifestation of this quiz?  

                                       

Consider a beaker of water, as shown above.  If I were to put a clear (not cloudy) ice cube in the water, how would we know that the ice cube was there?  Well, the water would look distorted at the location of the ice, because ice has a different index of refraction than water.  The bending of light at each face of ice would provide visual cues that something is inside the water.*

* Well, that and the fact that the ice would float on top of the water.  But still.

  

But what if I were to dunk an object with the same index of refraction as water?  What would I see?

Based on the quiz, the class reasons through the question:  rays of light would not bend at any interface.  Even a laser would pass straight through the object undeflected.  So we would see nothing.

A few years back, chemistry professor Pam Kerrigan of the College of Mount St. Vincent introduced me to Ghost Crystals.  (Follow the link for one place to purchase them, or ask your chem department.)  You place them gently in distilled water overnight, and they grow by absorbing water.  In their fully engorged state, they are solid, but have the same index of refraction as water.  Thus, when you place them in a beaker of water, they disappear -- just like we predicted on the quiz.

Now, the trick is, I've showed the students the "empty" beakers with a discussion of what would happen "if" I were to place a ghost crystal inside one and wait a day.  But after I do so, I reach in... and remove the engorged ghost crystal that no one noticed was already inside.  See -- there it is, now, out of the beaker on the desk.

I've seen (and done) this demo with Pyrex and mineral oil.  I think it's actually more impressive that way, especially if you throw a broken test tube into the beaker and remove the (already prepared) intact test tube that was previously invisible.  But mineral oil is messy messy messy, and I don't feel like paying for dry cleaning every time I do this demo.  So I went to ghost crystals.

GCJ

Experiment: density of mystery fluid, and the audience for a lab writeup

Materials for the "density of unknown liquid" experiment

Fluid mechanics first entered the AP physics B course description in 2002.  That year, the laboratory question (#6, I don't have a legit link, but it's easy enough to look up) asked students to determine the density of an unknown liquid by submerging a mass on a spring into that liquid.  

My own classes did a version of that problem on their trimester exam.  The ones who got it wrong -- usually by conflating the density of the liquid with the density of the submerged mass -- did an exam correction on which they described the procedure correctly.  

And then this week, I had everyone actually, honest to goodness, do the experiment for themselves.  I've often suggested that the AP exams since 1996 provide a wonderful laboratory guide, if you can improvise a bit.  Pick a lab-based question, set it up with whatever equipment you have lying around, and there you have a college-level physics laboratory exercise.  I took my own advice and tried out this new experiment.

I gave each group a beaker of fluid and a mass.  (You can see the cubical masses in the picture -- they all are made of different materials.  I just dug them up in an old storeroom.  I have no idea where they came from.)  The groups were encouraged to pick the spring of their choice.  They could use any other equipment they wanted, including a balance scale; the only action I forbade was to directly measure the mass of the fluid in the beaker.

Now, most of my experiments, and many AP lab questions, call for a linear graph, a best-fit line to copious data on the graph, and interpretation of the physical meaning of the line's slope and intercept.  This particular experiment doesn't lend itself well to a graph, at least not the way it's presented on the 2002 exam.  So I came up with an alternative approach to the writeup.

I used a true mystery liquid rather than water.  I won't reveal what I used (because my students occasionally read this, and the writeup isn't due 'til the end of the week), but I don't even know its density right now.  We're going honestly double-blind here.

I'm asking each partnership to write up one typed page describing their results.  I give no specific instruction other than to imagine that they've been hired to determine this mystery density, and that their financial well-being depends on the quality and accuracy of their work.  They get one shot to impress their potential client with their writeup.

That "client" is Peter, the captain of our USIYPT research physics tournament team, and the rest of his class.  I will collect the typed pages with no names, and hand them to Peter and the research students.  They will rank the papers from best to not-so-best.*  I'll assign grades based on the rankings, and give a prize to the winners.

*Donald Trump would say "worst."  Why is it that teachers tend to get in trouble for such language, while Mr. Trump is lauded for his bluntness?

Sean measures the extension of the spring

Sure, this is a nice cutesy little game.  But there's a real message here.  Too often when students are asked to describe the results of an experiment, they use stilted, overly-formal language that stifles meaning in favor of big-arse words.*  I want them instead to write informally for an audience at their own level of physics.  A major obstacle to improved writing is the faceless audience.  High school students have never published anything; their understanding of a paper's audience is poor even in English class, let alone in a subject where they struggle both with the content *and* the writing skills.

*  "In this experiment, the experimentors carefully and consistently used a decimal-labeled wooden shaft to record precisely the extent to which the PASCO brand spring was extensively extended.  We ensured safety by wearing goggles and grounded electrical outlets." 

So, I put a face to the audience:  Peter.  Everyone knows Peter.  They talk to him in normal language.  They are not in fearful awe of him, but they are all quite clear that he and the research team have no use for incorrect physics.  (I wonder where they got that from...)

I've never done this particular exercise; but I have had students write with a named fellow student as their audience.  Their writing doesn't become perfect, but some of the filler gets filtered out.  And so we focus on the physics... which is what I want, anyway.