# MacGyver Season 2 Episode 12 Science Notes: Jack + Mac

Before I get to this science for this episode (there’s some great MacGyver hacks here), let me say something else about the show. The storyline for this episode was great. It had a nice plot, and I really enjoyed the MacGyver and Jack flashbacks. Now for some science.

Photophone

The best Mac-hacks are real. This is real—very real. It is indeed true that this was an early idea for a phone. Here’s how it works.

• You need a directed light. One way to do this is to get a mirror that reflects sunlight. A parabolic mirror works a little better, but still the mirror is a great idea.
• Use your voice to shake this mirror. This changes the intensity of the reflected light to match the wave pattern of your voice.
• Use some type of electrical photo device (solar panel, photo diode, photo resistor) to modulate an electric current to this same sound pattern from the light. Send this to a speaker.
• That’s it.

For MacGyver’s build, he uses a microphone and connects it to a porch light. The idea is that the microphone will modulate the brightness of the bulb. For this to work, I think it has to be an LED bulb. An incandescent won’t work (I don’t think) since the hot bulb filament won’t change brightness quickly enough for sound frequencies.

There is also the problem of AC vs. DC. If MacGyver connects to the AC power line going to the bulb, this might not work. But still—it’s very plausible.

On the other end of the photophone, Riley uses a police car light as her transmitter. Again, if this is LED it should work (plus the car runs on DC, not AC). Finally, the only problem is aiming. In practice, you need your detector to pick up the changing brightness from that one light. Of course it’s daytime, so there are many “lights” outside. Putting a lens on the detector to aim it would help a bunch.

OK, now you want to build one of these yourself. You should. It’s actually not too terribly difficult. Let’s start with the simplest part—the receiver. The easiest way to get this to work is to connect a small solar panel to an amplified speaker.

Oh, do you know where I got that solar panel? Yes, it was from a garden light. You put these small lights outside and the solar panel charges a battery during the day and the light comes on at night. They were old and the battery was bad, so I took it apart.

Now for the transmitting side of the photophone. I tried to do this with a laser instead of a light (so that I could aim it). It mostly worked, but it’s a bit more tricky.

This is something I need to rebuild at some point in the future. Make it better. But still, this should be in my list of Top 10 MacGyver Hacks. I need to make that list.

Gum Wrapper and Battery to Start a Fire

Ok, actually this was to melt a wire. MacGyver takes a foil gum wrapper and connects it to two ends of a battery. The idea is that the foil will make a short circuit.

But there are two questions:

• Is a gum wrapper an electrical conductor? I don’t think they are actually made from aluminum foil—but I suspect that many of these do in fact conduct.
• Would it get hot? Even with a small battery, yes I think it would.

DIY Non-Contact Voltage Probe

MacGyver needs to find wires behind the wall. He puts together this awesome looking probe (or as Jack calls it—a doohicky)

Actually, this prop is great. Here’s why.

• It looks cool and it’s clearly a combination of multiple items.
• It’s not specific—it doesn’t show exactly what MacGyver uses. This is good because that way it could still be plausible.
• Finally, it’s based on something real.

But how does it work? There are multiple ways to detect voltages without touching—I think the most common method measures a super tiny voltage that is created by nearby electric fields. The NCVP is essentially part of a capacitor. When in the presence of an electric field, there is a voltage across the capacitor and you detect this voltage. I need to build one of these—for fun. I’ve seen a very basic version somewhere.

Kitchen Chemistry to Detect Explosives

How do you detect explosives? MacGyver is correct that most explosives are based on nitrogen. If you measure the nitrogen, you can get an estimate of the type of explosive.

There are many things in the kitchen that can be used to detect chemicals. Here is one that you can do at home—it’s a chemical-based pH detector (to determine if something is acidic). The color of this cabbage juice will change color depending on the pH level of the material.

Here’s how to make it.

Laser-Based Wire Cutter

Here’s the problem. There are two bombs that need to be disarmed at the exact same time.

The idea is to use a laser that turns on two identical cutters at the same time. The first thing to use is a beam splitter. This takes a laser beam and breaks into two beams. I guess that’s fairly obvious from the name. Here is a video showing how that works.

For the cutter part, it uses a photocell as the “switch” to turn it on. Here is a rough diagram I created for this hack.

In the end, these two motors might not cut at the exact same speed. But it’s still a fairly fun MacGyver moment.

# RC Circuit as an Example of the Loop Rule

Batteries and bulbs are fun, but they can only go so far. How about a capacitor and a bulb? Yes, let’s do that.

Here is the setup.

This has a battery (2 1.5 volt batteries) connected to a 1 Farad capacitor with a switch. This capacitor is then in parallel with a light bulb. When the switch is closed, the capacitor is charged up to 3 volts. When the switch is opened, the capacitor discharges through the bulb. Notice how it slowly gets dim.

Here, I even made this same (almost the same) circuit in a PhET simulator (java warning).

Of course the full circuit doesn’t really matter. I don’t care about charging the capacitor, just the discharging. So here’s the important part.

Let’s start off by applying the Loop Rule to this circuit. If I start from the lower left corner and then go around counterclockwise, I get the following. Oh, I’m assuming zero resistance in the wires.

$\Delta V = \frac{Q}{C} - IR=0$

Where the voltage across the capacitor depends on the charge.

$\Delta V_C = \frac{Q}{C}$

But wait! The current is the flow of charge. Since there is a current, the will be a decrease in charge on the capacitor. A decrease in charge means there will be a lower voltage. This lower voltage makes a smaller current. Maybe you can see the problem. Don’t worry, we can still solve this.

Let’s create a numerical calculation to model the current running in this circuit. The key here is to break the problem into very small time steps. Let me start by using the loop rule and using the following definition of electric current.

$I = \frac{\Delta Q}{\Delta t}$

Now the loop rule looks like this.

$\frac{Q}{C} - \left(\frac{\Delta Q}{\Delta t}\right)R = 0$

If I use a very small time step, then I can assume that during this time interval the current is constant (it’s not, but this isn’t a bad approximation). From this I can solve for the change in charge.

$\Delta Q = \frac{Q}{RC} \Delta t$

But what does this change in charge do during this time interval? Yup, it decreases the charge on the capacitor—which in turn decreases the capacitor voltage—which in turn decreases the current. I think I already said that.

After this short time interval, I can find the new charge on the capacitor.

$Q_2 = Q_1 - \Delta Q$

Note: the minus sign is there because the current DECREASES the charge on the capacitor.

That’s it. We are all set. Here is the plan. Break this problem into small time steps. During each step, I will do the following:

• Use the current value of charge and the loop rule to calculate the change in charge during the time interval.
• Use this change in charge to update the charge on the capacitor.
• Repeat until you get bored.

OK. Suppose I am going to do this. I decide to break the problem into a time interval of 0.001 seconds. How many of these intervals would I need to calculate to determine the current in the circuit after 1 second? Yes. That would be 1000 intervals. Who wants to do that many calculations? I sure don’t.

The simplest way to do this many calculations is to train a middle school student how to do each step. It shouldn’t be hard. Oh wait, the middle school student is still busy playing Fortnite. Oh well. Maybe I will train a computer to do it instead. Yes, that’s exactly what I will do.

In this case, I’m going to use python—but you could use really any programming language (or even no computer programming language). The idea of a numerical calculation is to break a problem into small steps. The idea is NOT to use a computer. It just happens that using a computer program makes things easier.

Here is the code (below is just a picture of the code—but you can get it online too).

Let me just make a couple of comments on different lines.

• Line 4,5 just sets up the stuff to make a graph. Graphing in super easy in this version of python (Glowscript).
• Line 14 is the length of the time interval. This is something you could try changing to see what happens. Yes, if you use the trinket.io link above, you can edit the code.
• Line 21 looks tricky. It looks like Q will cancel in that equation. Ah HA! But that’s not an algebraic equation. In python, the “=” sign means “make equal” not “it is equal”. So this takes the old value of Q and then updates it to the new Q.
• Line 25—same thing happens with time. You have to update time or the loop will run FOREVER!
• Line 26. This is how you add a data point to the graph.

This is what you get when you run it.

OK. That looks nice. As we see in real life, the brightness of the light bulb dims rapidly at first and then slowly dies down. This plot seems to agree with actual data (always good for a model to agree with real life).

But what does the textbook say about a circuit like this (called an RC circuit because it has a capacitor and a resistor in it)? Note: this is an algebra-based physics textbook. It gives the following equation for a discharging capacitor.

$I(t) = \frac{V_0}{R} e^{-t/\tau}$ $\tau = RC$

In this case the $V_0$ is the initial voltage on the capacitor. Well, then let’s plot this solution along with my numerical calculation. Here is the code https://trinket.io/glowscript/f4a3ff8264—and I get the following plot.

Those two plots are right on top of each other. Winning. Oh, go ahead and try to change the time step. Even with a much larger step, this still works.

Some final notes. Why? Why do a numerical calculation?

• Numerical calculations are real. They are used in real life. There are plenty of problems that can only be solved numerically.
• I think that if physics students create a numerical calculation, they get a better understanding of the physics concepts.
• What if you want to treat the bulb as a real lightbulb? In that case the resistance is not constant. Instead, as the bulb heats up the resistance increases. With this numerical calculation you should be able to modify the code to account for a real bulb. It would be pretty tough if you solved this analytically.
• What is the point of having students (in an algebra-based course) memorize or even just use the exponential solution for an RC circuit. It might as well just be a magic spell if you just use the equation. I don’t really see the point. However, with the numerical calculation the students can do all the physics.

# MacGyver Season 1 Episode 19 Science Notes: 19 Compass

What does “normal” mean?

Honestly, this a great physics joke. MacGyver and Jack are in a trash compactor—yes, there are some Star Wars jokes here too. In order to break the hydraulic pump, Mac wants to put a pole so that it pokes through a particular screw. Here’s the important part.

MacGyver: …if I hold the pipe perfectly normal.

Jack messes up and hurts his arm. According to MacGyver: “I used a technical term that Jack didn’t understand.”

Ok, so what does “normal” mean? In short, it means perpendicular. That’s it. MacGyver needed the pipe to be perpendicular to the wall. That’s what normal means. That’s also why physicists call the force a surface pushes on an object “the normal force” —because it’s perpendicular to the surface.

Yes, we also use “normal” in geometry—but of course Jack wouldn’t get that.

What is a spectrometer?

Not a MacGyver hack, but I want to talk about spectrometers anyway.

My first idea of a spectrometer is a visible-light spectrometer. This is essentially a prism. Light goes into the prism and is then separated into different colors. By looking at the colors in the light you can identify the light source. Oh, but this kind of spectrometer wouldn’t be found in a chemistry lab—at least probably not.

There is also a mass spectrometer. This takes a gas of molecules and shoots them into an area. Using magnetic fields, the path of the molecules is bent. Based on the amount of particle deflection, you can get a value for the mass of the particles.

Also, it’s just fun to say “mass spectrometer”.

Origin of Hacking

Come on. We know that MIT didn’t really invent hacking. Humans have always been able to creatively figure out problems—which is the essence of hacking.

However, MIT might indeed have invented the word “hacking”. The history of this stuff is really interesting. Let me recommend the following book—Hackers: Heroes of the Computer Revolution (Steven Levy). I liked it.

Door Alarm

Another non-MacGyver hack. This is a hack from his friend. She creates a door alarm. You can’t really see it very well, but it would be a small battery with a buzzer. The circuit runs to a clothes pin with aluminum foil on the pinchers and a piece of paper between them. Since the paper is an insulator, there is not a closed circuit. The paper is then attached to the door (with tape) so that opening the door pulls the paper out.

It’s actually a pretty simple design. You can (and should) build one of these yourself. Here is a video showing how to do that.

Electric Whip

In order to make an improvised weapon, Mac takes an extension cord and cuts off one end. Then he strips the wires on that end and plugs it in to the wall outlet. Note: DON’T DO THIS.

When the two bare ends of the wires touch someone, they will get shocked. Oh, and it’s a whip.

So, would this work? I think it would mostly work. It wouldn’t make the lightning stuff, but that just makes it look cool. It does look cool, right?

DIY Centrifuge

This might be the best hack in MacGyver history. Basically, this is a real life MacGyver-hack. It’s a low cost and simple to build centrifuge.

What the heck is a centrifuge? It’s a super high speed spinning thingy. You can put liquids in there and the high rotation rate causes a centrifugal force (yes, I used that term correctly) to separate liquids of different densities. This can be used to process blood.

Here is a real centrifuge.

And here is the DIY version. It’s basically just string and cardboard. However, with this simple version people can process blood stuff in more rural areas. Awesome.

It’s real.

I wanted to build a spark gap transmitter—you know, for fun.  However, things didn’t start off so great.  Here is how it went down.

My first plan was to build this.

I like it, but it uses an ignition coil and some other thing.  However, check out the receiver.  That’s awesome.  It’s a coherer receiver (I think) and it basically detects a spark with those two bolts in the plastic sleeve.  There should be some iron filings or something in between the bolts.  When a spark is detected, the filings jump the gap and make it a conductor.  I’m not sure why the LED light is connected to a 9 volt battery though.

After that, I just did some google searches for spark gap transmitter and attempted to build the designs I saw.  None of them had capacitor values, so I just had to guess.  But they didn’t work.

I honestly thought I knew how to do this.  I tried a step up transformer with a capacitor.  Nope.  Actually, I was getting a spark on the battery side but not the step up voltage side.  How did I even pass physics courses?

Here is my attempt with a transformer.

Finally, I found a page that used an electromechanical bell.  That works.

I decided to build my own oscillator from scratch.

Homework (for me)

• Make this more solid (the connection to the steel plate is iffy.
• Could you replace the steel plate with a paperclip?
• Can you change the buzzing frequency by adding weights to the oscillating bar?
• Use a step up transformer to get BIGGER SPARKS.
• Build a coherer detector.

# MacGyver Season 3 Episode 5: Dia de Muertos + Sicarios + Family

Battery and Solar Powered Fridge

It’s not a big “hack” in the episode, but we see MacGyver walking through the build a refrigerator.  You could use solar power and a battery with a normal fridge, but there is also the peltier cooler option.  The peltier is a small solid state device – when you run current through it, one side gets hot and one side gets cold.  You can use this device to cool the inside of a fridge.  It’s not super efficient, but it’s very simple.

Actually, I started to build one (but I haven’t finished).  Here is my progress so far.

Modify boom box to pick up beacon signal

So, Oversight builds a homing beacon.  He sets the frequency to 457 kiolhertz.  MacGyver needs to modify the radio to pick up this frequency.  He needs to make the modification because a normal AM radio only goes down to about 540 kHz.

So, how do you change the tuning frequency of a radio?  Let’s look at a super basic radio (a crystal radio).

There are two parts to tuning a radio – there is the capacitor (above that would be the tube with the aluminum foil) and the inductor (the tube with the wire wrapped around it).  The radio will amplify the signal with the frequency that matches that of the inductor plus capacitor combo.  So, just change on of those and you can change the minimum frequency of the radio.

Shock vest

I love the parts where MacGyver and Oversight argue about physics stuff.  Here are some notes about their discussion.

• Does shortening the wires reduce the resistance?  Yes.  That’s true.
• You can get a shock by storing electrical charge in a capacitor – that is true (but most taser type things don’t do it that way).  More capacitors means more charge and more shock.

50 foot drop calculation

How fast would you be moving after a drop of 50 feet?  Let’s go over this calculation really quickly.  I hate imperial units, so I am going to switch to metric.  Since it’s about 3 feet per meter, 50 feet would be about 15 meters (rough approximation).

When an object falls, it has a constant acceleration of – 9.8 m/s^2 (assuming no air drag).  That means that for each second that it falls, it will increase its speed by 9.8 m/s.  We can write this as:

$-g = \frac{\Delta v}{\Delta t} = \frac{v_2 - v_1}{\Delta t}$

Since the falling object starts from rest, the initial velocity is zero.  We can then solve for the final velocity.  Oh, this is all in one dimension.

$v_2 = -gt$

Oh, I am assuming the initial time is also zero. But we don’t know the time the object falls.  Let’s look at the two definitions of average velocity:

$v_\text{avg} = \frac{v_1+v_2}{2} = \frac{\Delta y}{\Delta t}$

I can use this with the previous equation to eliminate time.

$v_2 = \frac{2\Delta y}{t}$

$t=\frac{-v_2}{g}$

$v_2 =\sqrt{-2g\Delta y}$

So, the change in y is -15 meters and let’s just say g = 10 m/s^2.  That puts the final velocity at the square root of 300 or about 17-18 m/s.  That’s like 40 miles per hour.

Fan motor as a brake

MacGyver lets a rope wrap around a spinning fan motor.  He then uses that to go down a building (not slow – but slower than falling).  Yes, this is plausible.  It would be better if the motor is on since then there will be a resistance to spinning it.

I could probably say more about this – but it would get complicated quickly.  Oh, how about this – a motor is the same as an electric generator.  It just depends on how you use it.