Jacobs Physics has moved to a new location!

Hi, all!  The Jacobs Physics blog, archives and all, have migrated to jacobsphysics.org.  I'm escaping Google, for reasons.  Come visit!  I'm still rearranging furniture in the new home, but you should be able to access all the archives there.

All future posts will go to jacobsphysics.org.  You can contact me there with a comment; on bluesky where I'm @jacobsphysics; and via email at my woodberry.org address.  

The 5 Steps books should publish Oct. 15 2024.  

My next possible project is a daily Live Physics Time audio show; still ironing out details, but it would begin mid-August 2024. 

See you on the (new) site!

-- GCJ

Conceptual Physics: teaching the "false calculation"

 In conceptual physics, students are offered three possible ways to justify an answer:

1. Fact: Write a fact verbatim from our fact sheet, then write connecting prose to figure out the answer;

2. Calculation: Write a relevant equation, make a table of known variables (including units) and do math to figure out the answer;

3. Equation: Write a relevant equation, indicate which variable is unchanging and how you know, then draw arrows indicating how the remaining variables increase or decrease.

Education professors might label these approaches as  verbal, quantitative, and semi-quantitative reasoning.  

I've always started the year with fact-based reasoning with reflection, refraction, and lens/mirror ray diagrams.  (A properly drawn ray diagram counts as a "fact".)  Then as we study waves, we do calculations with v=(lambda)f, v=(lambda)/T, and f=1/T.  

A major emphasis of a first year physics class, though, is to get at semi-quantitative reasoning.  "A wave speeds up as it moves from shallow to deep water.  Does its wavelength increase, decrease, or stay the same?"  First, use the fact that says "when a wave travels from one material to another, its frequency stays the same."  Next, in the equation v=(lambda)f, f doesn't change.  Since v and lambda are directly related - mathematically, when one increases, so does the other - an increased speed means an increased wavelength.

Thing is, no matter how hard I tried, 9th grade first-time physics students didn't understand this direct relationship.  They randomly guessed at how v and lambda changed.  Worse, they didn't at all see what the equation meant.  I have them draw up-arrows to show that v and lambda increase, and a line over the f to indicate that frequency didn't change.  But these arrows were clearly meaningless to a large portion of the class.  Even when I drew every possible permutation of the equations and possible relationships on the board, it didn't help.

What was missing was the connection between the equation-in-variables and the underlying arithmetic.  So I made that connection explicit.

Instead of teaching the equation-with-arrows approach to semi-quantitative reasoning, I taught the "false calculation".  What's that?  I'll show you with the above example.

"A wave speeds up as it moves from shallow to deep water.  Does its wavelength increase, decrease, or stay the same?"

Using the relationship v=(lambda)f, make two different charts, one for the wave in shallow water, one in deep water.  The question doesn't require a precise numerical answer for a wavelength - just how the wavelength changes.  So MAKE UP NUMBERS that are easy to work with!

We know that the frequency is the same for each, because when a wave changes material, its frequency doesn't change - so call it 1 Hz for each.  We know the speed is faster in deep water than shallow water - so let's call the speed 1 m/s in shallow water, and 2 m/s in deep water.  (Any speeds/frequencies will work!  The point is to make calculation simple.)

SHALLOW                DEEP                    Using v = (lambda)f

v = 1 m/s                    v = 2 m/s

lambda = ?                 lambda = ?

f = 1 Hz                     f = 1 Hz

******************************

(1) = (lambda)(1)          (2) = (lambda)(1)

lambda = 1 m               lambda = 2 m

Thus, the wavelength is greater in deep water.

Evaluating the false calculation  I expect to see each of the following elements when a student uses a false calculation to answer a question involving semi-quantitative reasoning.  You can "grade" a response that includes a false calculation by awarding one point for each of these items:

1. The relevant equation is written clearly and used.
2. The variable that does NOT change is indicated, with evidence as to why that variable is unchanged.  This evidence usually includes either a fact from the sheet, or direct language in the problem statement.  "The frequency doesn't change because it's constant" is not sufficient.
3. Two charts, like the ones above, filled out with correct units on all values and a question mark indicating the unknown variable.
4. The values in the chart plugged into the relevant equation, and a conclusion drawn.

That fourth point often is awarded even if the calculation is executed incorrectly.  That is, if the student screws up the 5th grade math and gets lambda = 0.5 m and thus says the wavelength is greater in shallow water, that student will get full or nearly-full credit.  The whole purpose of this methodology is to give beginning students a scaffolding to make predictions in a rigorous way rather than using guesswork.  

Of course, my students are often using false calculations to make predictions in the laboratory.  When they do the experiment and find out that the wavelength is in fact greater in deep water, the context is exactly right to show them that they did the math incorrectly - and they've advanced their understanding, which is the whole point of the exercise!

5 Steps to a 5 AP Physics 1 2025 edition RELEASE DATE! And link to request review copy.

Aha!  We have a date... McGraw-Hill says that both the Physics 1 book and the Physics C book will publish on October 15, 2024.  Here is a link to preorder (none in stock yet as of June 2024), and to request a review copy.  

The 5 Steps series has migrated from McGraw-Hill's professional side to their education side.  Which means they are treating the 5 Steps prep book like a textbook for the purpose of marketing.  Awesome!  You can now request a review copy for yourself.  And, you can request to purchase a class set at a discount!  

Fluids for AP Physics 1: buoyant force demonstration and/or lab

I have an aluminum cylinder here.  I hang the cylinder from a string, and attach the top end of the string to a force probe.*  The probe reads 1.1 N.  

*Or a spring scale.  This particular experiment can be done with 1960s equipment.

Next, I am planning to keep the cylinder attached to the force probe, but submerge the cylinder completely in a beaker of water, without the cylinder touching the bottom of the beaker.  What will be the reading in the force probe when the cylinder is submerged?

This is a force problem.  Even though I might be doing this demonstration during the new AP Physics 1 fluids unit, it's still a force problem.  And thus the starting point is a free body diagram, regardless of the exact question being asked.

The free body for the cylinder includes an upward tension T, an upward buoyant force Fb, and a downward force of the earth mg.  The cylinder will be hanging in equilibrium, so up and down forces balance: T + Fb = mg.  I'm looking for the reading in the force probe, which is the tension in the string.  Solving for tension gives T = mg - Fb.  

In this case, we already know mg, the weight of the cylinder, because of the initial force probe reading before we submerged the cylinder: mg = 1.1 N.

The buoyant force on a submerged object is equal to the weight of the displaced fluid.  This is written mathematically by the equation Fb = (density of fluid)(volume submerged)(g).  I write words rather than variables here because it's so easy to get the wrong density, or the wrong volume.  Generally, density times volume gives mass, and mg gives weight.  The mass of the displaced fluid is the density of the fluid times the volume of the displaced fluid.  

Well, we know the density of water: 1000 kg/m^3.  (See the previous post for a brief digression about "as much as you can hug.")

But how can we figure out the volume of this cylinder?  I ask the class for ideas.  There's no one right answer; and this creative experimental brainstorming is exactly the kind of practice that can help students approach AP Physics lab questions.

Idea 1: It's a cylinder, which has volume equal to the area of the base times the height.  So take a ruler and measure the diameter (and thus the radius) of the base; measure the height.  The volume is pi*r^2*h.  Excellent.  Any other thoughts?

Idea 2: Use water displacement.  Pour water into a narrow graduated cylinder.  Look at the initial volume reading when the cylinder isn't submerged; look at the final volume reading when the cylinder is fully submerged.  Subtract those volumes to get the volume of the cylinder.  Great.  Any further thoughts?  Anyone?  

Idea 3: You said it was an aluminum cylinder.  We can look up the density of aluminum; we know the mass by dividing the cylinder's weight by g, meaning the mass is 110 g.  The cylinder's volume is its mass divided by its density.  Fantastic!  Any OTHER ideas?  No?  

My idea: I look at the cylinder, or at least the part of the cylinder that was facing away from the audience.  "It says right here on the cylinder, written clearly in permanent marker, "42 mL".  Okay, okay, it's a trick.  Ha ha ha.  The point has been not to get the right answer, but to have this particular conversation.  I've got the accurate volume pre-measured (I pre-measured using the water displacement approach), the same way a cooking show will have a soufflé pre-baked so the audience doesn't have to sit through the, um, less exciting parts of the cooking process.

I use google to find that 42 mL is equal to 4.2x10^-5 m^3.

And now we can do the buoyant force calculation.  The buoyant force is (1000 kg/m^3)(4.2 x 10^-5)(10 N/kg) = 0.42 N.  The reading on the scale will be (1.1 N - 0.42 N) which should be about 0.7 N.  

Sure enough, I press collect on the app connected to my force probe, submerge the cylinder... and the reading drops from 1.1 N to 0.7 N.  

Physics works.

Extensions:  So many great questions you can ask.  Does submerging halfway down make the buoyant force greater than, less than, or equal to 0.21 N?  

How would the scale reading change if the cylinder touched the bottom of the beaker?

What if you put the beaker on a platform scale and submerged the cylinder, without allowing it to touch the bottom of the beaker?  What would the platform scale read?  This one's rather complex.  I analyze this question here.

Fluids for AP Physics 1: pressure in a static column, demonstration and/or lab

Fluid mechanics is trading places.  Since 2015, fluids has been part of the P2 curriculum, for the 25,000 or so students who take that exam.  But next year, fluids moves over to P1 and its 150,000 students.  So now's probably a good time to share some thoughts about teaching fluids.  

I do recommend coming to an AP Summer Institute, where you can see me do this and other fluids demonstrations live!  You can see my APSI schedule in the left sidebar.

Pressure in a static column

When a tank of fluid is not moving, the pressure anywhere in the fluid is given by P =P0 + ρgy. Here P0 represents the pressure at the surface* of the fluid, ρ is the fluid density, and y is the depth below the surface at the position where you're measuring pressure.  

*Yes, this is *usually* atmospheric pressure... but not always.  Consider one fluid on top of another.  The pressure in the bottom layer is the pressure at *its surface* plus ρgy.

I have one of them giant graduated cylinders filled nearly to the top with water.  My pressure sensor is connected to my ipad under the document camera; I set the Vernier Graphical Analysis app to produce a graph of pressure vs. time.

I attach a long tube to the pressure sensor.  First, I read the pressure when the tube is NOT submerged - this is P0.  The sensor generally reads in kPa; we want a reading in Pa, where 1 Pa is equal to 1 newton per square meter.

Next, I announce that I will predict the pressure sensor reading when the tube is submerged to the very bottom of the container.  The relevant equation is P =P0 + ρgy.  What additional information do we need?

We have the surface pressure - usually around 102,000 Pa, but that varies by weather and especially altitude.  We can measure the depth y with a meterstick - this is usually about 18 cm, i.e. 0.18 m.  We know the gravitational field g to be 10 N/kg.  

What about the density of water?  

AP Physics 1 does not require unit conversions!  The number of times that a student is even asked to give a numerical answer to anything is minimal.  So for this in-class problem where conversions are necessary, I do the conversions in my head and state the result; or I use google ("convert 102 kPa to Pa").  De-emphasize number crunching, and you'll un-de-emphasize concepts.  :-)

That said, thought experiments are well within the scope of AP Physics 1.  Students don't hesitate to volunteer that the density of water is "one."  One what?  The standard units of density are kilograms per cubic meter.  So one kilogram per cubic meter for water, right?

How big is a cubic meter, anyway?  That question provokes several seconds of pure puzzlement, followed by students waving their hands about a meter apart.  "It's as much as you can possibly hug," I say.  Close enough.

So, consider a tank filled with a cubic meter of water - as big a tank as you can possibly hug.  Can you lift that tank?  Oh.  No way.  Well, you can lift a kilogram without trouble - here, catch this 2 pound thing.  That huggable tank doesn't weigh 2 pounds.  No, it weighs a ton.  The density of water is a THOUSAND kilograms per cubic meter.

Back to the calculation.

The gauge pressure at the bottom of the cylinder - gauge pressure means just the ρgy bit, ignoring P0 - is (1000 kg/m^3)(10 N/kg)(0.18 m).  That's 1800 Pa, or 1.8 kPa.  

Thus, the pressure sensor reading should increase from about 102 kPa to 104 kPa.  The actual sensor has a precision in the neighborhood of +/- 0.2 kPa, so this difference will be pretty much dead on when you send the tubing to the bottom.

Follow-up questions include "what's the gauge pressure halfway down?   Greater than, less than, or equal to 0.9 kPa?  Answer?  Equal to: because in ρgy, y is in the numerator and neither squared nor square-rooted, halving y halves the gauge pressure, too.  Sure enough, submerging the tube halfway verifies this prediction.

Physics works.

Make this a laboratory investigation!

Put pressure on the vertical axis, depth on the horizontal.  The slope of the graph should be ρg, and the y-intercept should be atmospheric pressure.  You can use the slope to determine the density of water.  Or, use a different fluid like vegetable oil, and you'll determine the density of the mystery fluid!

Edna meets Mr. Chubbs at the Conceptual Physics Tournament

Will Keay, who teaches in Fairfax, Virginia, came to judge the Woodberry Forest Conceptual Physics Tournament last weekend.  His class pet, Mr. Chubbs, met my pet hippopotamus Edna.  They seemed to like each other.  

We've been doing the tournament as our 9th grade final exam for seven years now.  Feedback from students is universally positive.  They like that they don't sit for yet another two-hour written exam, of course - even though, to a person, they recognize that they work harder to prepare for the tournament than they do for any written exam.  

This year they particularly articulated how much they like the collaborative nature of their preparation.  They get to give presentations and argue about physics with their classmates during their nightly study period.  The process feels social!  It doesn't feel like studying!  Yet, everyone recognizes how much their understanding of their particular physics fight problems - and of physics in general - improves through this social process.

I pointed out that there's nothing stopping these 9th graders from doing similar practice for their history exam as if they were going to have "history fights".  This point met with very confused and skeptical faces.  

The other interesting piece of feedback this year was about the difficulty of the AP-style problems that we posed.  More students than ever said that, once they had dug into the problems for a day or two, they felt easy.  Really!  A couple of students even suggested tougher problems for the following year.  While this peaceful, easy feeling was engineered by design - familiarity over the three-week preparation period breeds comfort - the fact that college-level problems seemed straightforward to general-level 9th graders means the tournament is accomplishing its goal.  We want students to leave physics with a good experience, feeling challenged, but good about meeting the challenge of a difficult subject.  

And, of course, the end-of-year positivity is helped significantly by the invited tournament jurors.  The conceptual physics teachers help students prepare for the tournament, but we don't judge the tournament.  When we give feedback, that feedback is authentic.  "No, you don't *have* to redo your graph, of course not.  But the jurors are more likely to say 'the data points on the graph don't take up anywhere near half a page' than 'oh, I'll bet you spent ten minutes on that graph, you shouldn't have to spend ANOTHER ten minutes making the scale more reasonable.'"  It's always been true that I am the publisher, not the author, of my students' grades.  The large jury, from a pool external to our school, makes my role even more clear.

New online APSI Physics 1 offering - June 24-27, through PWISTA

By popular request, my June 24-27 APSI through PWISTA will now be online.  You can sign up through this link.

Online means you can attend from anywhere, and even bug out for a moment to feed/clean up after the dog/kid.  :-)  Demand was not there for a New York session in person, but we've had a number of requests for another online session!

The PWISTA online session runs synchronously through Zoom from 9am to 3pm each day.  I'm also available for "office hours" from 8:30 each morning, and until 4pm each day.  And I'm happy to arrange for further conversations outside of these times.  As with all institutes, online or in person, you'll get access both to the official College Board materials, AND to my personal files with problem sets, lab activities, quizzes, and tests.  

The AP Physics 1 exam is changing for 2024-25, adding fluid mechanics and a few other minor topics.  And, the exam format will change significantly.  I'll discuss all the changes, but I'll also do all the labs, demonstrations, teaching/culture building tips, etc. that are the hallmark of a Jacobs Physics institute.

Join us in June - you won't be disappointed!  Please feel free to contact me via email with questions.

GCJ

Upperclass AP Physics students in the spring

In the spring, our headmaster reminds us how this is a tremendously emotional time for seniors as they approach a significant ending of one life chapter / beginning of another.  I overheard some parents (from another school) the other day rightly noting how much difficulty their kids are having holding themselves together.  These kids are making a good faith effort to complete so, so many year-end capstone requirements from their classes and their school, on top of life events that matter like proms and sports and social events.  Even seniors who try to be good citizens are being pushed to their mental limits in May.  

What's my reaction to this (unfortunate, I think) feature of 2020s schooling as an AP physics teacher?  I try to make my class one of the most fun parts of the students' day, full of camaraderie.  I'm trying to cash in the culture building I've done for four years with these seniors at our school.  For students who do want to leave the school on a positive note, those who want to work in good faith in each class, they are incredibly happy to be in a comfortable place where they can learn together.  My P2 students are having fond memories of freshman year, when they prepared for AP physics 1 in a similar atmosphere; but their confidence is through the roof now in physics 2, and they know their classmates as true brothers* who've bonded over four years in classes with one another.  

*I'm at a boys' school. You're likely gonna want to use the word "siblings".  :-)

I know, teaching upperclasspeople is not all Care Bears and Smurfs.  Teenagers trying to manage social and parental pressure plus their own boiling crock of hormones can behave in frustrating and nasty ways.  I have to remind myself not to let my seething anger at a few students color my relationships with their classmates who haven't been nasty.  

This year more than ever before, I'm getting the sense that most of my seniors are appreciative of their teachers, their classmates, our school.  This is the class who entered my boarding school in the fall of 2020... right after they had been locked down for months.  They were being denied the social contact that is so critical to all of us, but especially to young teenagers who are developing their sense of themselves and the world.  This senior class seems more grateful than any class I've been around... because, perhaps, they've seen that teachers who care about them are in fact a force for good, not merely a set of jailers.

So in AP Physics 2, we do the "quizzes" that I've been posting each day, but not for grades.  We do experiments where I join in as a regular lab partner.  We sometimes just talk about things other than physics.  This group has learned physics well; they are intrinsically motivated to be as ready as they can be for the exam.  I, and they, can relax and enjoy our time together.

AP Physics 2 - fundamentals review #3

With three weeks to go before the AP physics exams, it's worth remembering that our students don't need MORE practice problems; rather, they need to pay careful attention to the practice problems they do.  This is my application of a John Dewey principle, that we don't learn by doing; we learn by paying attention to what we do.  

My first-year students in physics 1 are in a cycle of AP problem / quiz based on AP problem / corrections to AP problem if their quiz or problem shows they didn't get it the first time.  In AP Physics 2, which is a second-year course, students have already internalized that they must pay attention to what they do.  And, P2 students have a level of earned confidence in their skills that my 9th grade P1 folks lack.  So truly all we're doing is these daily quizzes, in-class experimental and problem solving work, and each week one take-home 25 minute "quiz" with 5 multiple choice and one free response.  Less is more when dealing with upperclasspeople in the spring.

P2 Fundamentals Review #3

21. A battery is connected to two resistors in series.  The resistors each take 20 V of voltage across them.  What is the voltage of the battery?

22. Write the first law of thermodynamics, which is an expression for the change in internal energy.

23. Two waves are initially in phase with one another.  One wave has traveled a small extra distance than the other.  Under what conditions does constructive interference occur?

24. Define the period of a wave.

25. What is the equation relating the image and object distances for a convex mirror?

26. Two light waves undergo constructive interference.  What physical effect will be observed?

27. Name two items that can produce a magnetic field.

28. A battery is connected to two resistors in series.  The resistors each take 20 mA of current through them.  What is the current provided by the battery?

29. A gas consists of molecules moving around.  What feature of these molecules’ behavior causes the macroscopic effect called pressure?

30. What is the physical quantity that means energy produced in one second?

AP Physics 2 - fundamentals review #2

My AP Physics 2 class is an ungraded honors course.  There's not even a contract.  There is a careful selection process - students are selected not based on their previous grades, but holistically based on their demonstrated authentic interest in the subject.  Basically, if a student passed P1, wasn't a jerk, and put forth reasonably consistent effort, we take them into the P2 class.  

Even without published grades, the ground state of our class is to begin with a 4-5 minute fundamentals quiz.  We grade the quiz; students tell me their scores.  The quiz grades have no extrinsic meaning, won't be seen by parents or counselors or universities.  So what!  Motivated students still care about getting things right.  But, with no published grades, the students are insulated from the shame or world-ending dread of receiving a published grade that is not an A.  If someone gets 3/10 - which happens somewhat regularly! - they don't have to fear that someone is waiting with a (hopefully figurative) cane for their poor performance.  They just should try to do better next time.

P2 Fundamentals Quiz #2

11. Light is incident on a thin film.  Under what conditions does the light change phase?

12. An ammeter measures ____.  It is connected in _____ with a resistor.

13. Write the equation for induced emf.  

14. And electric field points →.  A positron moves ← in the electric field.  Sketch the path of the positron, and describe briefly how it moves.

15. An electric field points from position A to position B.  Which position is at higher electric potential?

16. A gas expands adiabatically.  What is the sign of the work done on the gas during this process?

17. Write the units of electric field.

18. Kirchoff’s loop rule is a statement of conservation of _____.

19. A concave mirror has radius 50 cm.  What is the focal length of this mirror?

20. For a convex (diverging) mirror, how does a ray parallel to the principal axis reflect?

(Solutions will be in the comments in a few days!)