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Projectile Motion Trajectory Equation

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This comes up every so often. I get a situation (usually, it’s a video analysis problem) in which I can’t rely on the time data. This usually happens when you can see the motion of a projectile, but the middle part (or all of it) is in “slow motion”.

Before looking at the trajectory equation, let’s review what I would normally do for a video analysis. After collection x,y,t data in each frame, I could make two plots. I could plot the horizontal position vs. time. This should be a straight line (because there would be zero acceleration) and the slope of this line would be the horizontal velocity.

The second thing I could do is to plot the vertical position vs. time. This should be a parabola. From the quadratic equation fit of this data, I can find the vertical acceleration.

So, let’s say I can’t do that. How do we get data from an x-vs-y plot? This is the trajectory since it actually shows the path of the projectile. OK, for this case let’s make the following assumptions:

  • It’s a ball. I’m going to call this projectile object a ball. There is no reason for this choice.
  • The ball starts at some position (x_0,y_0).
  • The ball is launched with some initial velocity v_0 and at some angle above the horizontal \theta.
  • In my mind, the ball hits the ground at some point. I’m going to set the ground to be y = 0.
  • Oh, the vertical acceleration is -g, where g = 9.8\text{ m/s}^2.

Now for the physics. First, the initial velocity can be broken into x- and y-components:

v_{x0} = v_0 \cos \theta

v_{y0} = v_0 \sin \theta

For the x-motion, I have the following kinematic equation:

x = x_0 +(v_0 \cos \theta)t

And in the y-direction:

y = y_0 +(v_0 \sin \theta)t - \frac{1}{2} gt^2

In order to get the trajectory equation, I need to eliminate t from these two equations. I’m going to start by solving the x-motion equation for t.

t = \frac{x-x_0}{v_0 \cos \theta}

Now I can substitute this into the y-motion equation.

y = y_0 +\left( \frac{v_0 \sin theta}{v_0 \cos \theta}\right)(x-x_0)-\frac{g}{2v^2_0 \cos^2 \theta}(x-x_0)^2

Oh, notice that the velocity terms cancel in the middle term. Also, we get sine over cosine which is tangent.

y = y_0 +(\tan \theta)(x-x_0)-\frac{g}{2v^2_0 \cos^2 \theta}(x-x_0)^2

This should be good enough. If I make sure that the ball starts at x = 0, then the x-squared term of the quadratic fit in the format of:

y = Ax^2 + B x + C

Where A, B, and C are fitting coefficients. Now, A should be:

A = \frac{g}{2v^2_0 \cos^2 \theta}

So, if I have data and I plot the trajectory, I should be able to find the acceleration. Of course, this assumes that I know the launch velocity and the angle. But wait! I can get the angle from the B term:

B = \tan \theta

But what about the launch velocity? Honestly, I’m not quite sure. I guess if I new the vertical acceleration, I could solve for the launch velocity. Or maybe I could get the velocity from some other source.

Let’s test this stuff out. I could use some video data—but it’s easier to just make a plot in python. Here is a ball launched (with initial x = 0 meters). I get the following for the vertical position vs. time (like I would expect). Here is the code.

That looks good. Now, I’m going to plot two trajectory lines. The first will be calculated in the normal numerical calculation method (same as above but plotting x vs. y instead of t vs. y). The second plot will be the trajectory equation we solved for above. Here’s what I get.

The plots aren’t identical—but I could easily fix that. This shows that the thing works.

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.

Remote Physics Labs

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This is not a normal semester. So, how can you move your physics labs to a remote learning environment? Here are some ideas.

What is the goal of a lab?

This is what we should always consider when making any changes to a curriculum. What are we trying to do. Or, in the words of Arnold Schwarzenegger:

“Who is your daddy, and WHAT does he do?”

Kindergarten Cop

So, why do we have labs? Honestly, I don’t know. Here are some thoughts:

  • They gives students a “hands-on” opportunity to explore the physics from their lecture class.
  • Students can get experience with certain pieces of important equipment—oscilloscopes, meter sticks (kidding).
  • The nature of science. How do you learn about science without doing science? In labs, students can design and build their own experiments (ideally).
  • Science communication. This is what a lab report is supposed to do—but even having students share ideas in class can be super useful.
  • More time with physics.

I don’t the answer here. Also, if the lab is a service course for some other major then I guess that other department should tell us what they want out of the lab.

Now for some remote lab ideas.

Online labs

What if students had some type of online lab? Maybe they could play around with some virtual lab equipment to collect data. I’m thinking about the PhET simulators. They have some pretty sweet circuit simulators. Students could build a circuit, measure voltage and current and do a bunch of stuff. Not bad.

There’s also the great Pivot Interactives videos. These are pre-made video experiments with measurement tools built in. Students can use the video and measure stuff like the time it takes a ball to fall or the period of a pendulum. This stuff is really nice.

Oh, there’s also Second Life. Physics labs in a virtual reality. I’m mostly joking, but maybe…

Numerical Calculations

This is the perfect time to have students solve some physics problems with python (or some other method for numerical calculations). I honestly think this is great thing for lab anyway—I’ve used these in classes for a while and they are quite successful.

Here is my numerical calculation jump-start guide.

Give them the data

What if you show a video (or two) of the physics and then just give them the data? So, let’s say you are looking at the magnetic field due to a bar magnet or a wire carrying current. Normally, students would use a magnetic compass to plot the magnetic field as a function of distance.

I could record the compass deflection values for different distances and then let them do the analysis. I don’t think this such a bad option. You can use the labs that you already have and then you just need to include some extra pictures or videos and then a data table.

At home labs

This seems like a great idea, but you might have to be flexible. Suppose you want to study pendulums—surely students can find some string with a mass on it to swing back and forth. They could find the time with their phone. What about the length of the string? This might require a little bit of thinking to get it to work—but I would suspect that most students could do it.

Another option is to have students think up their own labs. Maybe they could take inventory of their supplies and use that. Don’t forget of all the sensors on a smart phone—I’ll suggest PhyPhox as a great app.

MacGyver Season 4 Episode 6 Science Notes: Right + Wrong + Both + Neither

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Lifting a glass with fire and suction.

I love this one. MacGyver needs to lift a glass window out of the frame. He uses some glass jars with soap to make a nice air-tight seal. After that, he gets a fire inside of the jar (after it’s up against the window). This fire produces a suction so that he can lift the window.

This is indeed possible (at least plausible). Here, check it out.

Now for some comments:

  • Burning stuff is complicated. Yes, it uses oxygen (O<sub>2</sub>) and creates carbon dioxide (CO<sub>2</sub>). You might think that you don’t lose any gas—but you do. The amount of carbon dioxide is less than the initial oxygen.
  • Since there is less gas after the fire, the pressure inside of the jar is LESS than atmospheric pressure.
  • This lower inside pressure means the atmosphere pushes the jar onto the glass. This is what causes “suction”.
  • The jar would work really well if you lifted a glass straight up. With the jar on the side of the glass it would be more difficult. You would need a large frictional force between the jar and the glass—but it’s at least plausible.

DIY Electric Arc Lighter

The basic idea is to create a homemade arc lighter and use that to destroy the electronic computers in some cars and disable them. I’ve always wanted to build an arc lighter, here’s a nice video.

The basic idea is to create a very high voltage between the two terminals. If the voltage gets high enough, you can create a large spark between them. This spark is hot enough to light a fire or destroy a computer.

Resonance Wall Destroyer

How do you get through a wall with a speaker? Well, if you could have that speaker oscillate at a very particular frequency, it’s possible (but not very likely) that you could set up a resonance.

Here’s an example. Go out to the park and push someone on a swing. The person on the swing will go back and forth with some frequency. Let’s make it easy and say that they complete one oscillation per second (frequency of 1 Hz). Now, how do you make this swing go higher and higher? The answer is to also push with a frequency of 1 Hz. If you pushed every half second, sometimes your pushes would make the swing go higher but sometimes it would be pushing at the wrong time and decrease the amplitude. This is resonance.

Of course, the most famous example of resonance is when someone breaks a wine glass with only a voice—or at least just with sound. If you tap a wine glass (a nice one with thin walls), it will produce a tone at some frequency. Now play an external sound with this same frequency and you can break the glass. It’s awesome (I need to make one of these videos).

Here’s a nice resonance demo.

OK, back to the wall. Could this work? The biggest problem is the frequency. A wall doesn’t have just ONE frequency that it oscillates with—because it’s made of many different parts. If you thump a wall, it doesn’t make a nice tone.

Still, you could claim that this is plausible. Maybe some part of the interior of the wall DOES resonate. That could be enough. Oh, also you could make this a bit better. If you put a microphone on the wall to measure the resonance frequency, then you would know what tone to play.

Knock out grenade

This one’s tough—but again based on something real. Let’s just focus on the water part. When you increase the temperature of water, it does produce water vapor (water as a gas). If inside a closed container, this water vapor would increase the pressure. For a plastic water bottle, this increased pressure could put it at a tipping point. Just a little nudge in pressure and BOOM. It explodes. Don’t try that at home though.

Grenade Launcher

This is basically the same thing as an automatic baseball pitcher—except for the homemade water bottle grenades instead of balls.

It consists of two wheels—at least one of them is powered. In this case, you could use the starter motor from the car to turn one of the wheels. When you put a bottle in between the rotating tires, the frictional force from the tire increase its speed until it goes flying.

COVID-19 Remote Teaching Update

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There’s so much going on right now—so, I think I should post this update about my plans for remote learning. Our current situation at my institution is that we are directed to transition all of our courses to “remote” learning—fortunately, we have the freedom to define how this is done ourselves.

This semester, I have two “lecture” courses and two labs. I’m going to treat these different.

Labs – Algebra-Based 2nd Physics (Electricity and Magnetism) and Calc-Based 1st Physics (Mechanics and Stuff)

How do you do a remote lab? Oh, sure—it’s very possible to come up with some things students can do outside of the lab. Actually, these make great labs in general. However, we don’t have a bunch of time to make this stuff work. So, here’s my plan.

  • Pick a set number of labs to offer the students. There were probably about 6-7 labs left in the semester, so I’m going to try and offer that many to the students. I will recommend that students try to complete 4-5 of these labs. They can pick which ones to finish.
  • For some of these labs, I will simply give the student the data that they would have otherwise collected. If there is some type of complicated equipment, I will hopefully make a short explanation video.
  • For other labs, I will give students suggestions on how to complete the lab at home. For instance—use stuff to measure the speed of sound (with uncertainty). Or measure the strength of a magnet. There’s a very good chance that most students could find material to complete these.
  • Finally, there are labs that focus on numerical calculations. Students can do these anywhere (and they are great).

Oh, what about the lab report and the final exam? For the lab report, they just need to turn in one formal lab report to be graded. The final exam will be on paper and the students can just answer the questions on paper and send me a picture of their test (or mail it to me or something).

“Lecture” Courses—Physical Science and Physics for Elementary Education Majors

Both of these course are only partial lectures. The Physical Science course shows short videos of experiments and then the students discuss the evidence and participate via multiple-choice clicker questions. It works well.

The other course is basically the same thing except that the students conduct small experiments to collect their own data.

So, what am I going to do with these classes? Fortunately, the curriculum has these video experiments online. I’m going to just cut down the material and make a new schedule (removing activities that aren’t completely necessary). With these videos, the students can still do the same activities. Once a week (or when necessary), I’ll have an online group meeting where students can discuss the experiments and ask questions.

Hope that works.

Summary

My remote learning plans can be summarized as two main points.

  • Don’t be a dick.
  • Make things as simple as possible—no need to destroy yourself over this bad situation.

MacGyver Season 4 Episode 5 Science Notes: Soccer + Desi + Merchant + Titan

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It’s not a science comment, but I have to say this: a show is only as good as the villain. In this episode we see James Callis playing The Merchant. Bam. That was pretty good. I like it. I’ll be honest, I didn’t know who was playing the role of The Merchant before the episode. Of course, you might know James Callis from his excellent role as Dr. Gaius Baltar the show Battlestar Galactica.

Now for some science.

Sports Statistics

MacGyver is looking for a way to figure out who is losing soccer games on purpose. You can see the clip right here.

The key to any sports analytics is data. The more data you have, the easier it is to see trends and patterns. Of course, you are still dealing with humans—so they don’t always do exactly what you expect. But really, this is true for most forms of real world data.

If sports stats is your thing, you absolutely need to check out FiveThirtyEight.

Directional microphone

How do you hear people that are far away? What about a directional microphone? MacGyver quickly builds one from a trashcan lid—this is plausible.

Sound is a wave (in the air) and waves reflect when they encounter a boundary (like a trashcan). If the trashcan lid is parabolic, these sound waves from a distant source will reflect in a way that they all meet at the same point. Like this.

Image result for rhett allain parabolic mirror

Actually, this is a diagram of a parabolic mirror (from a blog post about mirrors) —but the idea works for sound also. You would just replace the red dot above with a microphone.

These things are real. They use something similar in NFL games so that you can hear the collisions between football players on TV. Oh, there’s also this great sculpture on the campus of NC State University. It’s basically two parabolic dishes made of concrete some distance away. You get a person to sit in front of each of the dishes and they can hear each other talk. It’s really cool.

Anyway, this is one of those hacks that I want to try out for real. Maybe soon.

Here’s the one that MacGyver made.

He probably should have had the microphone facing the other way (pointing into the trashcan lid)—but maybe he was in a hurry. He WAS in a hurry.

Card counting

Nice. I could explain the basic idea behind card counting, but this video is better.

Magnet and a Roulette Wheel

How do you opposite cheat at the roulette wheel? What is “opposite cheat”? That’s when you do something to the motion of the wheel to make it so you lose. I guess this is still cheating though.

In this case, MacGyver uses a magnet to effect the outcome of the wheel. He grabs a magnet from a purse latch (fortunately, these are pretty common) and holds it over the wheel. Although magnets only attract ferromagnetic materials (iron and most steel and some other stuff), you can get a magnet to interact with any material that is an electrical conductor.

If you have a CHANGING magnetic field, this will create an electric field—this is just the way electric and magnetic fields work. Then, an electric field in an electric conductor creates an electric current. Here, you can see what happens when a magnet is moved into a coil of wire.

Finally, an electric current creates another magnetic field. So, this changing magnetic field makes another magnetic field to interact with the magnet. I know that seems crazy, but it’s true. All of it. Oh, we call these induced electric currents—eddy currents.

For MacGyver, this small magnet creates an eddy current in the wheel such that there is a tiny interaction to slow it down—and cause Desi to lose.

Seeing through skin with infrared

Yup. Again, this one is real. Apparently human skin is partially transparent to near infrared light. This is the wavelength of light just longer than red light (that’s why it’s near infrared). It’s the same stuff that’s used on IR remotes (compared to far infrared that’s used in thermal cameras).

So, if you shine an infrared light on the skin and look at it with an infrared detector, you can see through the skin. At least that’s the idea. Your puny human eyes can’t detect near infrared light, but most digital cameras CAN detect this. In fact, most cameras include an infrared filter so that you WON’T see the infrared light (many cheaper cameras don’t even have this).

If you have a camera without the IR filter, you can even see if your TV remote is working.

Here is a real life version of this to see through skin.

Radio Jammer

You can build a cell phone (or radio jammer)—it’s not too hard. However, it’s also questionably legal. I’ll just tell you the basic idea.

Suppose you wanted to make a sound jammer. You could do this by playing a REALLY loud sound. Then no one could hear anyone else talking. That’s essentially how the jammer works—but it’s with electromagnetic radiation instead of sound.

DIY Glider

Don’t try this—it’s a bad idea. MacGyver grabs some type of light weight sign and uses it as a glider to get down on the field. Oh, sure—it might make you crash, but it’s at least plausible.

It’s not flying—it’s falling with style. But seriously, pretty much anything could work here. This would really work especially if there was any type of updraft.

MacGyver Season 4 Episode 4 Science Notes: Windmill + Acetone + Celluloid + Firing Pin

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Egg Drop

It’s not really a normal “MacGyver-hack”, but the egg drop does have a bunch of physics in it. Oh, you’ve never heard of this? Well, it’s a fairly common activity in science classes. Basically students build “something” around an egg so that they can drop it from some particular height and the egg won’t break.

There are a whole bunch of extra rules—like “no parachutes” and “no rockets” and stuff like that. It’s all good fun (mostly). But what about the physics?

Most stuff that breaks on impact are the result of high accelerations from differential forces. If the egg (or any object) is being pushed on one side more than the other with some force (like from the floor), this differential force breaks the material.

Now for some real physics—the Momentum Principle. This says that the net force on an object is equal to the time rate of change of momentum where the momentum is the product of an object’s mass and velocity.

\vec{F}_\text{net} = \frac{\Delta \vec{p}}{\Delta t}

\vec{p} = m\vec{v}

If an egg is going to hit the ground, you know the change in momentum. It’s going to have some initial value and then it will stop. You can’t change this. But you CAN change the time. Let’s write the Momentum Principle in a different way:

\Delta \vec{p} =\vec{F}_\text{net}\Delta t

So, how do we get a particular change in momentum? You can think of two extreme cases:

  • You can have a VERY LARGE FORCE with a very small time interval.
  • You can have a very small force with a VERY LARGE TIME INTERVAL.

Of course you could go somewhere between these two—but you get my point. This is how the egg drop works. You want to build something that INCREASES the impact time so that you get a smaller force.

Why study science?

MacGyver is right. Scientific thinking is problem solving and critical thinking. These are good in any field—not just physics or working at a “think tank”. So, yes science is good for you. But that’s not why you should study it.

Science is one of the things that makes us human. Some of the other human things that we do: art, music, literature, sports, writing and video games (maybe). So, humans should study things that makes us human. That’s why you should take physics (and art).

One last science comment. The Physics Honor Society has this great page on hidden physicists. These are people with degrees in physics that have jobs that might not be labeled as “physicist”. It’s great.

https://www.sigmapisigma.org/sigmapisigma/radiations/hidden-physicists

Compound Lever

The keys to all simple machines are force and the distance a force moves. If you apply a force over a greater distance, you can produce a larger amount of energy (to lift stuff or something). This is how a basic lever works. You put a stick on a pivot.

The compound lever is just a way to get the push down force to move over a greater distance. Basically, it’s a lever connected to a lever. It’s lever-inception.

Hoist Lift

Here’s another way to lift something heavy—like a WWII bomb. You can use a hoist. It’s essentially the same idea as a lever except that stuff is hanging from it.

Tri-wheel Stair Climber

This is real.

Of course you can make it more MacGyver-ed by adding a power source. Mac uses some cordless drills to assist with the climb. Oh, you don’t think that would work? Well, if you have a big enough battery you can move anything up the stairs—it just might not be very fast.

Bomb Egg Drop

Putting a bomb in a box with bungees might work. As the bomb-box hits the ground, the bungees will stretch and INCREASE the time that it takes the bomb to stop—thus DECREASING the impact force. It doesn’t matter if it’s a bomb or an egg, it’s the same physics.

OK, you want to win at the egg drop competition at school? Here’s a great video from Mark Rober looking at some of the best egg drop options.

MacGyver Season 4 Episode 3 Science Notes: Kid + Plane + Cable + Truck

rhettallain 2 Comments

Can you hear a radio transmission through a fan?

Answer: it’s possible.

So, here’s the deal. MacGyver needs to communicate with this kid on a nearby plane—but he doesn’t have the radio speaker turned on. How do you tell someone to turn on the speaker if they don’t turn on the speaker?

There are two parts to this answer. First, you need to build an AM radio transmitter. This isn’t too difficult—especially for MacGyver and all the stuff he has in the Phoenix jet. Here is a build similar to the one in the show.

Fine. But what about hearing it in a fan? The short answer is that the fan can act like a foxhole radio. Yes, that’s a real thing. It’s a type of radio that soldiers could build using some basic items. But the key to all of this is the diode. A diode is basically a one-way valve for electric current (I said “basically”—so, don’t freak out about that definition). Why do you need a diode? It’s because you can’t “hear” radio frequencies.

Let’s look at AM radios (because FM is a bit more complicated). AM radio stations broadcast at different frequencies for different channels. These frequencies range from 500 kHz to about 1500 kHz. But if you just convert these electromagnetic waves into sound, you wouldn’t hear anything. Humans can only detect frequencies up to about 20 kHz. So, how do you fix this?

The answer is amplitude modulation (the A and M of AM radio). Here is an example of how this would work. Suppose I have a radio frequency of 3333 Hz (I just mostly randomly picked that value to make a pretty graph). Imagine this radio signal is just a cosine function that oscillates with that frequency. Now suppose that I constantly change the amplitude of this radio signal. The amplitude ALSO changes with some frequency—let’s say this amplitude frequency is 150 Hz (typical human voice frequency). Here’s what that would look like (here is the code if you want it).

But this won’t work. You can’t “hear” the 150 Hz signal—the problem is that the average of the AM signal is zero. It goes up as much as it goes down. It won’t work. That’s where you need a diode. This diode only allows the receiving signal to go “one way”. Here’s what that same AM signal looks like when you put a diode in.

Now for that diode. You could use a diode—or an LED light (which is a diode). Old crystal radios use a crystal mineral. If you don’t have that, you could use a pencil with a razor blade. Apparently, this kind of connection acts like a diode. Oh, you could also do this with the metal connection in the brushes of an electric motor—like in a fan.

Here is a story about a guy that thinks he’s crazy because he hears voices in his fan. I guess it’s true. Also, there is the famous (but maybe not true) story of Lucille Ball hearing Japanese spy radios through the fillings in her teeth. Here is the Snopes link for that.

One last comment. If you think “oh, this is awesome—I’m going to go listen to a radio station with my fan.” Nope. It’s probably not going to happen. You need a fairly strong AM radio signal that is tuned to your untunable fan. On top of that—the brushes in the motor of the fan have to be JUST RIGHT for it to work. It’s still plausible.

Defibrillator

A defibrillator uses electrical currents to do something with the electrical nerve signals to the heart. I guess they can trick the heart into restarting if it has stopped. Fine—but how do you build one (note: don’t build one)?

Of course as with most things (especially dealing with living humans) this can get tricky. You want to run electrical current through the heart area, but not too high. Also, it’s probably best to have an alternating current—it’s complicated.

The simplest (and oldest) designs use a DC battery along with an inductor and a capacitor to make an oscillating electric current. MacGyver should be able to use the DC power from the plane as the “battery”. If you want to start with a higher voltage, you could charge up some capacitors and then reconnect them in series to pretty much get whatever voltage you want. The inductor shouldn’t be too hard to find either.

Landing electromagnet

Electromagnets are real. I guess you already knew that. The basic idea is that an electric current creates a magnetic field. If you make the wire into a coil, the magnetic field due to each loop will add together to make an even stronger overall field. Oh, more current is better.

But would this work in real life? Of course it depends on many things. The most important thing is the current. How much electrical current could you get out of an airplane?

I’ll be honest—calculating the current needed for an electromagnet is really tough. The magnetic force depends on the type of material being attracted (probably steel), the distance, the size of the coil, and the current. But still, I think you could get at least something like 1000 Newtons (a little bit more than the weight of a person). This might be enough to help a small airplane stick to the top of a truck. It’s plausible.

But let me just leave you with the BEST use of an electromagnet. Allen Pan made this AWESOME version of Thor’s hammer. It uses an electromagnet and a thumb sensor so that only Allen (who is obviously worthy) can pick it up.

Just Enough Physics Video Update

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Perhaps you haven’t noticed, but I’ve been trying to make a bunch of physics videos. Oh, sure—I already have a ton of stuff on youtube, but it’s not linear. For my old stuff, I will solve a problem on work-energy and then do electric field stuff and then go back to kinematics. It was just whatever topic came up in class or online or whatever.

I figured I should start over and do a whole physics course—well, not EVERYTHING. No, I would do just enough to get you through the course. I hope you get the title now. Also, this is the title of that self published ebook I wrote a long time ago—since it really is the video version (but updated).

So, where am I now? I’ve got 4 chapters completed. I think it’s a pretty good start. Here are the chapters (as playlists) along with descriptions.

Chapter 1: Kinematics

Notice that I started off by making a title screen and all that cool stuff. I will end up dropping this so that I can make videos faster. Also, in my previous videos I was in front of a whiteboard. In this case, I’m writing on paper. Still not sure which way is better.

In this chapter:

  • Introduction.
  • Constant velocity in 1D.
  • Example of constant velocity.
  • Introduction to numerical calculations (1D constant velocity).
  • Constant acceleration in 1D.
  • Numerical calculations with constant acceleration (in 1D).
  • Solving the “cop chasing a speeder” problem.

Chapter 2: Forces and Motion

It’s tough to start in physics with forces. There are so many things to cover. This is a shorter chapter that looks at the fundamental ideas of force and motion.

  • Introduction to forces and motion. I really like this first video. It’s a conceptual look at the forces, the momentum principle and “Newton’s 2nd Law”. Guest appearances by Galileo, Aristotle, Newton.
  • Forces in 1D – falling objects.
  • Modeling the motion of a mass on a spring (and finding the model of a spring force). This one is long (but pretty nice).

Chapter 3: Vectors—2D and 3D Stuff.

The goal here is to expand kinematics into using vectors—but then you need to know about vectors.

  • Intro to vectors.
  • Kinematic equations with vectors.
  • Example of constant velocity and position update formula in 3D.
  • Intro to projectile motion.
  • Finding the range for projectile motion.
  • Numerical calculations for projectile motion.
  • Acceleration of a block on an inclined frictionless plane. This is an example of forces in 3D.
  • The physics of flying R2-D2. Using forces and air resistance.

Chapter 4: Calculated Forces

There are really two kinds of forces. There are forces that have an equation to determine the vector value (these are calculated forces). Then there are forces that don’t have an explicit equation (forces of constraint). This chapter just focuses on calculated forces.

  • Universal gravity.
  • Example of gravity—calculating the net force on the Apollo 13 spacecraft.
  • Introduction to visual objects in VPython. This is a setup for the next video.
  • Modeling the motion of an object near the Earth.
  • Modeling the Earth-moon system.
  • Mass on a spring (again) – but this time with visuals AND 3D motion.

MacGyver Season 4 Episode 2 Science Notes: Red Cell + Quantum + Cold + Committed

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Let’s do this.

Metamaterials and Invisible Cloaks

Of course, this is not a MacGyver hack—but it is some science stuff. So, what is a metamaterial? It sounds cool—and it is, but it’s a very broad term. Usually when we say “metamaterial”, we mean some type of engineered structure that’s made of more than one thing.

What about invisible cloaks? The idea here is to use some type of metamaterial to interact with light using a negative index of refraction. Normally, when light interacts with materials there will be an apparent bend in the light ray as it makes a transition between materials. This bend in light is called refraction.

You see refraction all the time. Here’s an example of a pencil in a glass of water.

When light goes into the water, it bends a bit towards a line that’s perpendicular to the surface of the interface. That’s normal. If you had a negative index of refraction then the light would bend PAST this normal line. You don’t normally see that except with special materials—in fact we can really only get this to work with light in the microwave wavelengths (not for visible light).

But what does this have to do with invisibility cloaks? There’s a bunch of stuff to explain here—so, I’m just going to go with a very basic idea. First, in order to see something light has to reflect off that object and then enter your eye. That’s why you can see anything in a room with no light—there’s no reflection.

So, one way to make an object invisible is to bend the light around it. Suppose I have an apple with an invisible cloak around it. If I could trace a light ray around it, it might look like this.

But how do you make light do that? That’s the tough part—the idea is that you can do this with some type of special material (a metamaterial). You might not have that stuff, but you can make something similar with some mirrors. Check this out.

Quantum Computing

Here is my super short description of quantum computing. Current computers use binary numbers. Essentially, these are voltage signals. It’s either some positive voltage (1) or zero voltage (0). From this you can make logic gates and store data and play cat videos on the internet.

A quantum computer uses qubits that can be 1, 0 or a combination of 1 and 0 (that’s the quantum part). OK, now here’s a much better explanation.

Cold Containment Unit

How do you keep cold stuff cold? Really, you just need some type of thermal insulator. Yes, your jacket would work—so would a cooler for your drinks. But for super cold stuff, you need something a little more. One of the most common methods is to use a vacuum. If you have two containers with a space in between them (with no air), then it makes a great insulator.

What about making some cold stuff? It turns out that you can get really cold liquid from a can of compressed air (the kind you use to clean your keyboard).

Check this out.

Picture of an eye for a retinal scan

Can you take a picture of someone’s eye and then use that to fool a retina scan? Probably not, but it might be plausible. https://www.telesign.com/blog/post/can-biometrics-be-fooled/

Lojack Emulator

In order to throw some baddies off their track, MacGyver makes a lojack emulator and puts it in a teddy bear. It’s plausible. But what is Lojack? Here—this is good. https://www.lifewire.com/what-is-lojack-534878

Drilling tool

MacGyver needs to drill through some rock. They don’t show the build, but there are plenty of parts around. Really, he would just need some type of electric motor—after that, pretty much any thing could work as a drill bit.

Rebreather

In order to get through a super old tunnel, Mac needs to breath (there’s not really any fresh air there). The answer is a rebreather. The basic idea is to use a chemical carbon dioxide scrubber that pulls the CO2 out of his exhaled air. You just need some tubes and stuff as well as the scrubber. I bet he could find the scrubber stuff near by.