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29 March 2021

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 FB = 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.


5 comments:

  1. Hi, I have a small question relating to the 5 Minutes to a 5 section in your AP Physics 1 book. I get that this is a Fluids page but I dont really know where else to post it.
    This is problem 101 in the 2020 edition, relating to the motion of a particle given its initial kinetic energy, its initial position, and a potential energy vs. position chart.

    I get how the particle move towards x=5m with varying levels of kinetic energy, but how come it doesn't just stay at rest at that mark, instead of accelerating to the right and reaching its original position and continuing to move right with 1J of kinetic energy. Thanks in advance.

    PS: How should I go about finding questions relating to electricity + waves in my practice tests, now that they are no longer covered in the exam. I still want to keep the original time constraint of 1.8 minutes per question, and skipping the irrelevant problems breaks that ratio.

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    1. Reading my PS at the end shows me how I need to improve my English haha. I mean how should I go about taking the practice tests without the electricity + waves problems in the practice test, to keep them relevant to the 2021 exam. Sorry for any confusion that caused.

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  2. Rohan, I'm not in my classroom now, so I'll check on that problem later. (Others are welcome to comment!) As to timing on multiple choice, you're right about 1.8 minutes per problem. So for now, I'd just count up the number that are about circuits or waves, multiply what's left by 1.8, and that's your time limit! (Or have a friend do that if you don't want any spoilers!) The best estimate I can give is that the old exam was about 1/3 circuits and waves... so instead of 90 minutes, give yourself an hour and skip the circuits/waves questions!

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  3. Rohan, thanks for the ping. I looked at problem 101 in the "5 minutes" section. It's a potential energy vs. position graph. In one of these, assume that potential energy will convert to kinetic and vice-versa. Like an object oscillating on a spring... which would not stop permanently just because the spring got fully compressed! Same deal here. The object converts all its potential energy to kinetic energy at the x=5 m position. So then it's time for the object to convert that potential energy right back to kinetic energy. That's how this sort of graph works! Hope that helps...

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    1. Ok, that makes sense. As a final clarification: for problems like this, I should assume that potential energy is continuously being converted to kinetic energy and vice versa. If so, thanks!

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