Just the facts: Fluids for Physics 2

I'm doing a one-semester AP Physics 2 intensive course for some very dedicated students.  On a typical day we take a fundamentals quiz; we do a demo or three; then we spend lots of time doing problems and playing with the demo setups.*

*We did copious lab work in the first half of the year as part of our research projects.  And these students had a Physics 1 course in which we got hands on equipment during something like 75% of our classes.  I don't do so much formal lab work in this intensive, 'cause these folks have been there and done that; but they know how to play with equipment on their own.  At least when they're in person rather than online. :-)

I've had to construct an AP Physics 2 fact sheet.  Some of the facts can be found in other blog posts, like this one for magnetism or this one for capacitors or this one for optics.  

I've never published a fluids fact sheet.  Here's what I handed out today before I started lab work...

FLUIDS

Static fluids

The pressure in a static column of fluid is P = P₀ + rgh

            Here the rgh term is called the “gauge pressure,” meaning the pressure above atmospheric.

Density is defined as mass/volume.  Thus, mass can be expressed as rV.

The buoyant force on an object is equal to the weight of the fluid displaced.

The equation for the buoyant force is F_B = rVg, where r is the density of the FLUID and V is the volume SUBMERGED.

Flowing fluids

The continuity principle is a statement of conservation of mass: the volume flow rate (or mass flow rate) must be the same everywhere.

The continuity principle for flow of cross sectional area A and speed v says A₁v₁ = A₂v₂.

Bernoulli’s equation is a statement of conservation of energy.

Bernoulli’s equation says P + rgh + ½rv² is constant at any two locations.

Atwood Machine: what if the rope is massive?

The question was asked on a physics teachers message board: How do you deal with a rope-and-pulley situation if the rope isn't truly massless?

I'm giving the AP Physics 1 answer here today.  This video by Pasco's Dan Burns gives a seriously intense mathematical solution.  You don't need that unless you're in and beyond AP Physics C, or unless you're solving the 2022 US Invitational Young Physicists Tournament problem on "rope and chain fountains."

I'm thinking of a modified atwood - one cart on a horizontal low-friction track, connected by a rope over a pulley to a hanging object.

Consider the entire cart-rope-hanging object system.  The unbalanced external force on the system is the weight of the hanging object.  (The force of the ropes on the objects is internal, because the rope is part of the system.)  Then set the system acceleration equal to this unbalanced force divided by the system mass.

But now give the rope a significant mass, still smaller than the mass of either object.  The unbalanced external force doesn't change (much)* - still the weight of the hanging object!  But with a larger system mass in the denominator, the acceleration becomes smaller.

*Okay, okay, the weight of the rope that's dangling contributes to this unbalanced external force.  So start the system with most of the massive rope horizontal.  And the rope's mass is still small compared to the hanging object's, so this is a good approximation.

Test this in class!  Use a smartcart on a track, connected by a thread over a pulley and onto, say, a 50 g hanging object.  Use the smartcart to measure acceleration.  Then remove the thread, and instead use a chain - like a bike chain, maybe? - to connect the smartcart to the hanger.  I'll bet you get a smaller acceleration!

This AP live video from April 2020 shows me doing this experiment with a low-mass rope, if you need ideas of how to make the acceleration measurement experimentally.  

Teaching rotation as a cumulative mechanics review in AP Physics 1 or C

Where do you start with AP Physics 1 (or C) rotation, especially in a Pandemic Year when you might have a lot of virtual students?

Think of rotation as a vehicle for review-in-context of mechanics concepts.  Your class has studied the three main mechanics approaches:

• Forces/kinematics, where we start with a free body diagram and/or a kinematics chart
• Impulse/momentum, where we write the impulse-momentum theorem or p conservation
• Energy, where we start with an annotated energy bar chart

The whole point of the rotation unit, to me, anyway, is to give students a new context in which they can review these three main approaches.  The AP Live videos in 2020 started with a focus on rotation, precisely because rotation is a great way to start a cumulative review.

So what do I do for each of these topics in rotation?

I personally don't do anything significant in class on rotational kinematics, since this is such a straightforward extension of linear kinematics.  I ask a few released AP multiple choice questions dealing with rotational kinematics graphs, and demonstrate the solution with the PASCO rotary motion probe. That's it.  

For newton's second law for rotation, I use the rotating platform and an in-class problem set.  By changing the lever arm for torque, the force for torque, or the rotational inertia, students predict how the angular acceleration changes.  This is essentially word-for-word what I did in the AP Live Newton's Second Law for rotation video, except as a come-and-show-me activity where they check their prediction in the back of the lab with the rotating platform.  This year, since we were 100% virtual in February, I just showed the linked video to the class over zoom.*

*Short rant: you've gotta watch the video with the class.  You can't just assign the video as homework.  How do I know?  I tried assigning some short - 8 minute! - AP Daily videos earlier this year via AP Classroom.  In class, it became apparent that very few had watched carefully.  Sure enough, the stats from AP Classroom showed that only about a third of my class had even opened the videos.  This in a class where I get better than 95% completion for daily problem sets!  The moral I drew was, don't ask students to watch videos on their own, 'cause that way madness lies.

For angular momentum and rotational kinetic energy, I use Pivot Interactives.  I've sometimes spent a full week on the "marble collides with block and can" activity, without much preamble beyond the fact sheet and 15 minutes showing demos about what rotational inertia and torque mean.  In the video, just asking "is linear momentum conserved?" gets students to think about center of mass motion and reviews linear momentum; then "is angular momentum conserved?" teaches them how to deal with angular momentum (especially for a point object) better than any lecture.  And finally, "is mechanical energy conserved?" forces them to draw an energy bar chart and include rotation.  I mean, truly, this is all I do to intro rotation.  We get straight into problem solving with rotational kinematics and N2L for rotation.  They don't need any presentation, because they already know the concepts and simply apply them.  

As you can see, most of this rotation introduction can be done virtually.  In my classroom after spring break - that's March 24 this year - I have students just doing independent lab work.  We do quizzes and short problem solving homework assignments that help not only review but also help teach rotation.  But that's it.  Between the AP live videos, Pivot Interactives, and some very open-ended lab work, my students get all the resources they need.  At this point, the class is full of experienced physics students.  They do well learning rotation sorta on their own, as I guide them to use rotation as a means to overall AP Physics 1 content and skill review.

Not physics - question about English Pie.

In 2015, I was in London for a month on sabbatical.  I went to three football games, one Victorian pottery factory, toured several sports cathedrals and one school, and sat with the radio commentary team during a Manchester United-Aston Villa game.  As I looked through my notes recalling this amazing trip, I found a question about pies.  Perhaps an Englishperson could help me.

We went to Sainsbury's to shop for groceries for dinner on our second night in town.  My wife loaded up with all sorts of green things, but I found the counter with fresh pies.  I bought one of every variety of pork pie that was available.

Problem was, back at the flat, the oven started smoking when I turned it on.  (Don't worry, I turned it off.  No London Fire of 2015.)  I wanted a warm pie, not a refrigerated pie straight from the grocer's cold case.  

So, um... I used the microwave to heat each pie.

Was this a tremendous breach of Pie Etiquette?  Am I any less of a good person for having eaten microwaved pork pies?  

And when is Food Lion in Virginia going to start stocking these?  I'd probably keep them in business by myself.  

Incentive other than a grade: exemptions.

Does every student need to do the same number of practice problems?

Early in the year, yes.  Even the best students need practice.  Even Allen Iverson needs practice.  And the top students gain confidence not just by doing their practice problems well, but also by helping their classmates. The not-top students gain confidence by occasionally being right when the top students are wrong.  

But as the year wanes?  Especially now, in Pandemic Times?  Awarding exemptions from practice problems can be a powerful incentive to students to take their work more seriously.

It's not the doing of the practice problems that develops physics skills - it's doing the practice problems carefully.  Even, especially, incorrect practice problems can help students learn physics.  But only if the student's incorrectness was born of a misconception, not of laziness or fatalism.  And only if the student cares about being correct.

When my students are all living together on dorm, when they can come to my classroom to work together the night before a problem is due, then it's easy to convince students to put forth serious effort on each problem.  The incentive isn't the grade - the incentive is, no one wants to see their name on the board.  The name on the board means to come in during an assigned free period to redo the problem.  It's not a punishment, but nevertheless... students work carefully the first time so that they're not likely to have to visit me for a second bite of the apple.

I can't use the name-on-board incentive method when we're online.  And since the students don't have in-person contact with any of their classmates, they don't work together; they don't incentivize each other through their presence.

So, I've taken to exempting students from the next assignment if they do well on today's assignment.  

Aren't these exempt students missing out on important practice?  Maybe.  Perhaps they are.  But is it really *important* practice for someone who's shown they can do the previous problem perfectly or near-perfectly?  I think a lot of teachers, parents, and students take it on faith that more practice is always better.  I disagree.  It's okay to let a student earn a break.

It's early March.  I already know which students care about grades and which don't, which students tend to get problems done for the sake of being done rather than for the sake of understanding the material.  These folks have already shown that the incentive of a job well done, the incentive of a high grade, isn't important to them.  So I need a different incentive.

I've seen students suddenly, for the first time all year, show tremendous effort, skill, and willingness to collaborate when they know that good performance will get them out of future work.  It's not a good idea to shame these folks with "you know, if you worked that carefully on every assignment, maybe you'd be doing better in this course."  They know.  Rubbing their noses in it is condescending and counterproductive.  I just congratulate such students on their exemption, and move along.