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Capacitor Lab

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Note: This is for me and anyone else that needs remote physics lab data. My goal is to keep this as simple as possible.

What is a capacitor?

The very basic idea of a capacitor can be two parallel conducting plates with an insulator between them. It could literally just be two metal plates with air between them.

When a capacitor is connected in a circuit, negative charges move onto one of the plates, but they can’t jump to the other side because of the insulator gap. However, these charges DO create an electric field that can interact with the negative charges on the opposite plate. This pushes those charges off the plate such that it appears there is a continuous electric current. Also, with negative charges leaving that plate, it now becomes positive.

Remember that I is the direction of positive moving charges —but it’s almost always negative moving charges.

This build up of charge creates an electric potential difference from one plate to the other. The ratio of charge to voltage is defined as the capacitance.

C = \frac{Q}{\Delta V}

Where Q is the charge on just one plate (since the total charge is zero) and C is the capacitance. If Q is measured in Coulombs and ΔV is in volts, then C is in units of Farads.

So, what happens when we connect this capacitor to a battery with a resistor? Here is a simulation.

I was going to write a bunch more stuff—but I apparently already did. Here is an older post on RC circuits.

https://rhettallain.com/2019/06/21/rc-circuit-as-an-example-of-the-loop-rule/

Now I will just focus on this lab. Here is some experimental data (in the form of a video).

Here’s what to do.

  • Look at the part where the capacitor is charging. Collect data for the voltage across the capacitor as a function of time. More data is better—but don’t go crazy. If you can get a data point every 1 or 2 seconds, that should work.
  • Now make a plot of voltage (on vertical axis) vs. time (horizontal axis).
  • Repeat this for the discharging capacitor.

But what about a linear plot? For a capacitor (C) discharging through a resistor (R), the voltage should be:

V(t) = V_0 e^{-t/RC}

This is not a linear equation. Divide both sides by V0 and take the natural log. This is what happens.

\frac{V}{V_0} = e^{-t/RC}

\ln \left(\frac{V}{V_0}\right) = -\frac{t}{RC}

Now if you plot ln(V/V0) on the vertical axis and t on the horizontal axis—it should be a straight line. EVEN BETTER, the slope of this line means something. Use the graph to find the value of C if R = 150 Ohms.

Now go back to the other post. See if you can create a numerical model for a discharging capacitor. Here, this might help you get started.

This program is not finished.

https://trinket.io/glowscript/f87df8f621

Questions:

  • What happens if you change the time step (dt)?
  • What happens if you change the capacitance?
  • What happens if you change R?
  • What happens if you change the initial voltage?
  • Can you make a model for a charging capacitor?

Suppose you built your own capacitor and you wanted to discharge it. For this capacitor, you used two sheets of aluminum foil separated by a page in your textbook. The capacitance can be calculated as:

C = \frac{\epsilon_0 A}{d}

where

\epsilon_0=8.854\times 10^{-12} \text{ F/m}

Use this to estimate the value of the capacitance. How long would it take to get halfway discharged using a 150 Ohm resistor? Could you essentially repeat this experiment with your homemade capacitor? Hint: no.

Bonus here is a capacitor that you CAN make.

Course Reflections: Intro Physics Lab (PLAB 193)

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The Course:

This is the lab that goes along with the first semester of the algebra-based physics lecture. That means the students are mostly biology majors, industrial technology, or engineering technology.

This semester, there were only about 13 students enrolled. Here is a link to the course webpage. Over the years, I have learned that you really can just focus on one or maybe two big ideas during the semester. This time, I focused on:

  • Modeling with graphs. Collect data. Make a linear graph. Find the slope and interpret it.
  • Measurement and uncertainty. OK, technically I just used this during the second half of the semester.

The Good.

I can’t remember the exact paper—but there was a research paper that said physics labs don’t really help students. Oh, I found it.

Measuring the impact of an instructional laboratory on the learning of introductory physics (American Journal of Physics)

I feel like this gives me the freedom to do what I think will help the students the most. It doesn’t matter if I cover all the topics in the lecture. Yay.

With this in mind, I decided to start off with the marshmallow challenge. It’s basically a team-building and problem solving exercise in which groups try to create a structure to support a marshmallow as high as possible. I used this modified version – it’s great: https://shiftingphases.com/2019/07/08/hacking-marshmallow-challenge/

Other than that, here are some other things that worked well this semester:

  • Continued using end of class quizzes. Sometimes they seemed forced, but there were a couple of times that I made the quiz a sort of competition – like the projectile motion lab where they have to hit a target.
  • I think the numerical calculation lab went well. This could be better if I included the numerical stuff in more later labs. OK, technically it’s needed for the spring lab and the air resistance lab but normally students are too far behind to get to that part of the lab.
  • I think this lab on acceleration went fairly well. https://plab193.wordpress.com/2018/08/08/constant-acceleration/ . Students use a photo gate and a cart rolling down a track to get velocity as a function of time.
  • Finally, I cut down on the pre-lab instructions. Students weren’t reading them anyway. I tried short presentations – but I don’t think that really worked either.

The Bad:

Let’s just get to a list of notes here.

  • The thing that sticks in my mind is the extreme frustration I had with graphs. I feel like at the end of the semester, there were still many students that still didn’t understand graphing or the slope of a linear function. Help.
  • Lab reports were for the most part super terrible. Maybe I should just stop having them turn in a lab report.
  • The last lab of the semester, I asked them what they wanted to focus on. They said they were interested in a lab where they collect data on their phones (it was an idea I mentioned using the PhyPhox app). I went over some of the experiments, but I don’t think anyone really did anything.

The Future

Here are some ideas for the next time I teach this lab.

  • No more lab reports? Maybe move to some type of worksheet that the students turn in?
  • Maybe more learning activities – stuff like card sorts and speed dating physics problems?
  • More numerical calculations.
  • Go over the PhyPhox stuff and give them an explicit experiment.
  • What about using plickers at the beginning of class?

Teaching Introductory Astronomy

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Through an odd sequence of events—actually, not odd but academically sad, I am going to be teaching the intro astronomy course this semester. OK, if you MUST know the reason, here it goes.

You know I love teaching this Physics for Elementary Education majors course, right? Yes—it uses the Next Gen PET curriculum (which is AWESOME). I put this course together sometime around 2005 for the College of Education. They needed a hands on science course to satisfy their accreditation requirements and this course fit that need. It worked PERFECTLY.

Flash forward to today. Apparently the College of Education decided to drop this course from their curriculum without even telling us. Oh, am I bitter—maybe a little. But since the course isn’t required, I only had 2 students registered. The class was canceled and I picked up an astronomy course. The end.

Now for the astronomy class. This is a class for non-science majors, so essentially no math. I have taught it before, but that was maybe 10 years ago. I want it to be a great course, but I don’t have a lot of time to find some resources. That means I ask twitter for help.

Here are some of the suggestions.

I’ll post more stuff as I find them.

Thanksgiving Physics

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I am honestly not quite sure how many blog posts I have about Thanksgiving.  It’s probably about 1 per year for 8 years.  I’m going to guess it’s 8.  Here goes my internet search.

This is what I found.

Trip Report: Texas AAPT/APS Section Meeting

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Since this is just a normal plain blog, I can do silly things like this report on my recent trip.  Why not?

Where and Why?

I was invited to give the keynote address as well as a workshop on python at the AAPT/APS section meeting at the University of Houston.  Since this isn’t too far away, I decided to just drive there – it’s about a 5 hour trip.  Not bad, plus I can bring as many pairs of shoes that can fit in my car.  I brought one pair of shoes.

I drove in on Friday and arrived Friday evening – I stayed at hotel on the outskirts of Houston.

A note regarding section meetings.

I really like section meetings.  They are smaller, cheaper, and it’s easier to get around and see everyone.  Oh, national meetings are cool too – but sometimes they are just too big.  Also, who likes paying 500 dollars just for registration?  Not me.

Python Workshop

For the workshop, I used my python material.  This is essentially the same stuff I used at the Chicago Section of AAPT.  Here are some notes.

  • The material basically this stuff on trinket.io.
  • I also have instructor materials and other files posted on the PICUP site.
  • It seems there were about 15 participants. The room had computers for people to use – that helps out a bunch.
  • There was an issue with the projector – it wasn’t quite working.  Someone brought in a backup, but it wasn’t bright enough.  It’s funny how small problems like this can make a big difference when people are learning.
  • Another issue for python workshops – variety of people.  Some people have never used python and some have experience. This makes it slightly difficult.
  • Other than that, I think the workshop went well.  I had one person ask me afterwards how to become an expert with python.  My response was to just keep practicing.  The best way to learn is to learn python to solve particular problems.  It’s pretty tough if you try to learn stuff without a purpose.  Oh, also – sloppy code is fine.

Keynote: Science Communication with MacGyver and MythBusters

Normally, I give a talk that focuses on physics of science fiction or video analysis or something like that.  I’ve talked about science communication before – but in this case I wanted to include a bunch of examples from MacGyver and MythBusters – so I had to make a new talk.

Check out the venue (maybe it’s difficult to see from this pic though):

This is the “club level” of the University of Houston football stadium.  No, there wasn’t a game going on at the time (but that would have been funny).  It was a nice place – the screens were in a weird position, but still it was nice.  Oh, I did make one fairly big mistake.  I was having trouble with the projectors and I ended up with “mirroring” on my computer.  This means that I didn’t see the next slide and and I didn’t have a clock. I really like seeing a clock.

For the talk, I focused on 4 “rules” of science communication:

  • You can’t be 100% correct, but you can be 100% wrong
  • Build a bridge from the science to the audience (complicated, conceptual, or shiny physics).
  • Science fiction is still fiction.
  • Use mistakes as a foot in the door to talk about what you want.

Overall, I think it went well.  Oh, there was one great question at the end.  “How do we use science communication to help people understand climate change?”  My response: we need to focus on the nature of science and understanding of what exactly science is all about.

Finally, here is another picture. This is me on the football field (which was kind of cool).

MacGyver Season 3 Episode 4

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Pressure Lift Bag

This one is pretty awesome.  MacGyver needs to lift up a truck to get it un-stuck.  So, he takes a rubber bladder (not sure where he got it – it could be part of a shock) and connects it to the exhaust (or maybe he connects it to the liquid oxygen).  Anyway, he fills the bladder with an expanding gas.  The bladder fills up and lifts the truck.  This would totally work.

Check out this version you can do yourself.

How does this even work?  Ok, so you have a trash bag.  When you blow air into it, you can approximately get a pressure of 2 atmospheres (just a guess).  The force from this pressure depends on the surface area using this formula:

F = PA

If you want to lift a human (mass of 75 kg) with a gauge pressure of 10^5 \text{ N/m}^2, how big of an area would you need?  Solving the above equation for A:

A =\frac{mg}{P} = \frac{(75\text{ kg})(9.8 \text{ N/kg})}{10^5 \text{ N/m}^2} = 0.00735 \text{ m}^2

That might seem like a tiny area – but that would be a square about 9 cm on a side.  So, this is clearly possible (as you can see in the video that I actually did it).

Liquid Oxygen

We normally think of oxygen as a gas – and at room temperature it is indeed a gas.  Actually, it’s a molecular gas of O2 – two oxygens bound together.  I guess we should first talk about air and oxygen.  Yes, we need air to breath – but air is more than just oxygen.  It’s approximately 21 percent O2 and 79 percent nitrogen gas.

If you decrease the temperature of oxygen gas – it will turn into a liquid.  Yes, it has to be super cold at negative 183 C.  How cold is this?  Here is a video that shows how cold this is (and liquid nitrogen) along with some of the cool things you can do with super cold stuff.

High Pressure Air

Humans can survive under very high pressures.  However, there is a problem with breathing high pressure air.

The nitrogen in high pressure air can be absorbed into your tissues and stuff.  When the human then goes back to a lower pressure, this nitrogen comes out of the tissues.  If the change in pressure happens too fast, this nitrogen can bubble and cause all sorts of problems.  This is basically what we call decompression sickness.

The other problem is oxygen.  At 21 percent oxygen at normal atmospheric pressure, everything is fine for humans (since we live in this stuff).  However, as the pressure increases, the partial pressure of oxygen also increases.  At normal cases, the partial pressure of oxygen is 0.21 atm (atmospheres).  If you have 50 percent O2 at atmospheric pressure, this would be 0.5 atm.  The partial pressure is the current pressure multiplied by the fraction of gas.

Here’s the deal.  If the partial pressure of oxygen gets over 1.6 atm, bad stuff happens.  Stuff like convulsions.  Oxygen is bad stuff.  How do you get a partial pressure of 1.6 atm?  If you increase the pressure, the partial pressure of 21 percent O2 is 1.6 atm.

OK, now back to the show.  MacGyver can survive in high pressure one of two ways.  Method number 1: don’t breath air.  If he breathes a gas mixture that has a lower concentration of oxygen, This is what deep divers do when they breath mixed gasses like trimix.  Method number 2: use a constant atmosphere suit so that he stays at 1 atm pressure.  That’s what he does in this case.

What happens if MacGyver pulls out his air hose? Yup.  That would work.  Even at super high pressures.  Oh sure, his lungs would get super small because of the external pressure – but that’s just fine.  This is exactly what happens when a free diver goes deep (breath holding).

Oh, he would have to equalize his ears just like a free diver.

MacGyver Season 3 Episode 3

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Transparent Explosives

Yes, this is probably real – http://www.guns.com/2016/10/21/army-working-on-high-tech-see-though-explosives/

Liquefaction of Sand

This is real.  You can make a simple version of this yourself.

 

 

 

Or you could make a crazy huge version like this.

 

Weather balloon pop

MacGyver needs to get a thermal camera down from a balloon.  The balloon (it’s not actually a weather balloon) is tethered down by multiple lines.  So Mac uses the jumper cables from the car and connects them to the car battery.  Then he connects ONE cable to the wire and the current causes the balloon to burst.

OK, let’s step back for a moment.  Remember that this is a show – this is not real life.  I just want to make sure we are all on the same page there.  So, there’s a small mistake here (you can blame me if you like).  In order to get an electric current from the car battery to go through the balloon, you would need to make a complete circuit.  One jumper cable connected to the line is a start, but there needs to be a path for the current to get back to the battery to make a complete circuit.

One way you could get this to work is to take another line going to the balloon and connect the other jumper cable to that one.  If you look close, it seems like the other cable isn’t connected to anything (in the show).  Of course, that mistake is better than connecting both wires to the same line.

This is sort of the same problem as this double spark in Iron Man 3.

Thermal camera

Yes.  Thermal cameras are indeed real.  Yes, the heat signature of an electric car would be different than an internal combustion engine car.  Actually, I need to see how hot they get in real life (electric cars).  I’m going to test this the next time I see a Tesla.

Oh, and here is an overview of seeing stuff in infrared (also called “thermal image”).

Just for fun, here is a visible and infrared image of me with a bag over my head.

X-Rays from a Vacuum Tube

MacGyver needs to find the transparent explosive.  One of the tools he needs for this is a source of x-rays.  This seems to be real – but it appears you can make x-rays from a vacuum tube, a lighter (the long kind) and a diode.

Here are the instructions from hackster.io (I need to build one of these).

There are so many cool parts of this hack, I could probably write a book on just this one thing – maybe I will write a separate post.  This x-ray device does the following:

  • Uses a vacuum tube from an old radio.  Historically, the vacuum tube was used where transistors are used now.  These things are awesome.
  • The lighter has a piezoelectric in it.  When you apply a pressure to these devices, it produces a voltage – the voltage can get high enough to make a spark in air which lights the gas from the lighter.
  • When you connect the piezoelectric to the vacuum tube, you can make a super high voltage inside the tube.  This can accelerate electrons such that they crash into the other electrode.  This crashing electrons is exactly how you create x-rays.
  • X-rays are just like normal visible light except that they have super small wavelength.  This can make them interact differently with matter.  For instance, they can pass through some materials (like human skin).
  • What is the x-ray used for in this hack?  X-ray fluorescence.  This is essentially the same as glow in the dark (kind of) material except get’s “activated” with x-rays instead of other visible light.

Oh wait! I already have a video on x-ray fluorescence.

 

 

One final note.  In the show, MacGyver says something about shooting ions.  That’s not really what happens here.  X-rays are not ions.

Hydrogen balloon from a trash bag.

Can you fill a trash bag with hydrogen?  Yes.  Will it lift stuff?  Yes.  Could it lift a trash can?  Maybe…just maybe.

Here is my super short introduction to buoyancy.

Suppose you take a box of air – the box is 1 meter on a side such that the volume of this air is 1 x 1 x 1 = 1 m3.  Assuming there is no wind or breeze, this “box of air” will stay in the same location.  Since the box is at rest, the total force acting on the air must be zero.

OK, there is obviously a downward gravitational force on the air puling it down.  Yes, air has weight.  If something has mass, it has a gravitational interaction with the Earth.  Everyone likes to think of air as being weightless – but that’s probably because it has a low density and it’s normally “floating”.  But if there is a downward gravitational force on the air, there must be an upward force pushing to counteract the weight.  This upward force is the buoyancy force.

Since the box of air floats, we know the buoyancy force has to have the same magnitude of force as the weight of the air.

Now let’s suppose I take away that “box of air” and replace it with a sealed cardboard box (it could be a box made out of anything, but in my mind it’s a cardboard box).  The air around this box is going to interact with it in the same way as it did with the box of air (because air is dumb and doesn’t know any better). This means the cardboard box has the same buoyancy force as the box of air – it is equal to the gravitational weight of the air the box displaces – this is essentially Archimedes’ principle for floating stuff.

Oh, this buoyancy force is still the same no matter if the object is floating or not – it just has to displace air.  You can also do this with water or really any substance –  like pudding.  Not sure why you would float something in pudding.

But what if you want to calculate this buoyancy force?  In that case, you need to know the density of the air (which is around 1.2 kg/m3) and the local gravitational field (9.8 N/kg).  With that, the buoyancy force would be:

F_\text{buoyancy} = V_\text{object} \rho_\text{air}g

Finally, we are getting somewhere.  Now you can calculate the size (solve for V) of a balloon needed to lift a trash can.  If you want a simple estimate – you can ignore the mass of the hydrogen in the balloon (but it does indeed have both mass and weight just like the air).  I’m leaving the rest of this as a homework assignment for you.

 

 

MacGyver Season 3 Episode 2

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I’m going to change up my posts on MacGyver hacks.  I’m going to limit the focus on things that I can significantly talk about.  So, suppose there is some hack involving a belt that loops around a pole and something happens.  It might be a great “hack” – but if there’s no fun science to discuss, I will just skip it.

Also, I’m not going over any of the chemical explosions.

Radio Squeal Device

MacGyver does something to a radio to such that it creates a high pitched squeal – a type of sonic weapon.  Is this plausible?  Yes.

Since a radio has both a microphone and a speaker, it’s possible to set up an audio feedback loop.  Here is a short video showing this.

Actually, this demo leads to some interesting questions.  In particular, what does the feedback frequency depend on?  I think that the frequency of the squeal depends on both the audio properties of the speaker AND the mic.  If you change either one of these, the frequency should change.  This would make a great science fair project.

MacGyver Season 3 Episode 1 Hacks

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I’m way behind, but I figured it would be best to go over the new stuff while it’s still fresh.  Don’t worry, I’m still going to do the old stuff.

Episode 301: Improvise

A whole bunch of DIY stuff

(various, mostly real)

I don’t know how much stuff to go over at the beginning of the episode.  Clearly MacGyver has been working hard in this village and there are all sorts of DIY stuff.  Let’s just leave it at that.

Water pump

(mechanics, real)

So, you need water from a well – right?  That’s where a water pump comes into play.  Let’s just talk about pumps in general.  There are really two types of water pumps. There is a suction pump and a spinning pump.

For the suction pump, air is removed from a tube above the water.  This reduces the pressure on top of the water.  There is still air pressure pushing on the rest of the water – and this air pressure (from the atmosphere) pushes the water up the tube.  Once the column of water produces the same pressure as the atmosphere, the column of water stops rising.  This means you can pump water up 33 feet.

For the spinning pump (not its actual name), there is something that spins and pushes the water.  Think of this as a water fan blade.  The blade spins and pushes the water up the tube.

Quartz and steel to make a spark

(chemistry, real)

Note: you can barely see this hack – it’s fast.  But it’s there.

Yes, you can make a spark with quartz rock and steel.  The key thing is that the quartz is strong enough to chip off super tiny pieces of steel.  These super tiny pieces are hot enough and small enough to react with the air and get super hot.

Here is a video.