# MacGyver Season 3 Episode 21 Science Notes: Treason + Heartbreak + Gum

Breaking Window Bars with a Bicycle

This is another classic MacGyver hack. There is a window with bars on the outside and Mac needs to get IN. Simple, just pull off the bars. Obviously you can’t do this with your hands, you need to build something.

I guess you would call this a hand-crank winch. That probably best describes what he builds. Actually, it’s a hand crank winch WITH a compound pulley. Here are a couple of pictures.

The main idea here is the same for ALL simple machines. It’s really about force, distance and work. Let’s start with a super basic definition of work (physics work).

$W=Fd$

In this expression (which isn’t technically correct—but that’s OK for now), W is the work, F is the force applied and d is the distance over which the force moves.

Now imagine I have a simple machine. I can put work into it and get work out of it. Assuming it is 100 percent efficient, the work in can’t be less than the work out (or you would get FREE ENERGY).

So, if you want to pull (or push) with a smaller force then you need to pull over a larger distance. For the output force, you need to have it move over a shorter distance to get a larger force.

With the winch, MacGyver turns a hand crank (part of the bike). If the garden hose (used for a rope) is wrapping around something with a smaller diameter, then for each rotation of the hand the rope will move a small distance. This is the key to a winch. Remember—smaller distance means larger force.

With the compound pulley, the same thing happens. By using multiple pulleys—you can make the pull force move over a larger distance thus increasing the output force.

Here is my initial diagram for how this might work.

Spark Gap Generator

You don’t get to see much detail here—so let me just explain the idea behind a spark gap generator.

First, I guess I should say what it is used for. Originally, a spark gap was a radio transmitter. It turns out that although it’s simple to build, you can only use one at a time because they don’t really use channels. In the case of MacGyver, he is using a spark gap to jam a phone signal (to prevent data transfer).

All of the wireless data works by broadcasting and receiving electromagnetic waves. Radio, microwave, visible light, x-rays…these are all electromagnetic waves (but with different wavelengths). Still, they are electromagnetic waves.

So, what about this spark gap? The idea is to create a repeating spark across some small gap. This spark is a very violent (electromagnetically speaking) event. It has accelerating electric charges which create EM waves. These EM waves are high enough intensity that they can make it such that other (more well behaved) devices can’t send or receive a signal.

But how do you make one of these spark gap generators? Really, you just need a battery and some wires. If you use the wires and battery you can create an electromagnet. That doesn’t make a spark, but if you can turn it on and off really quickly, then it will indeed make a spark. I built one using a moving metal switch. When the electromagnet is on, it pulls the metal and turns off the switch. Once the switch is off, the metal is no longer attracted to the electromagnet and it moves back in place to turn the electric current on again. This just repeats to make the spark.

Here is a video.

Here are some more details on this.

Oh, here is another way to make one of these spark gap generators.

Gum Wrapper Switch

The key to this episode (it’s in the title) is gum. MacGyver activates the spark gap by taking out a piece of gum. How would this work?

The purpose of a switch is to do something such that two wires are connected. In this case, the two ends of the circuit could be the foil wrappers for two pieces of gum. If you put an insulator (gum) in between them, then the circuit will be closed. Pull the gum out and then two foil pieces will touch and complete the circuit.

Here is a diagram I created for this.

# Basics: Work Energy

**Pre Reqs:** [What is a Force](http://blog.dotphys.net/2008/09/basics-what-is-a-force/)

[Previously, I talked about the momentum principle](http://blog.dotphys.net/2008/10/basics-forces-and-the-momentum-principle/). Very useful and very fundamental idea. The other big (and useful) idea in introductory physics is the work-energy theorem. Really, with work-energy and momentum principle, you will be like a Jedi with a lightsaber and The Force – extremely powerful.

Well, what is work? What is energy? How are they related? In [another post, I talked about energy.](http://blog.dotphys.net/2008/10/what-is-energy/) I think it is interesting to look at how most textbooks define energy:

*Energy is the ability to do work*

This is really a stupid definition. Kind of circular logic, if you ask me. In the post I mentioned earlier, I claim there are two kinds of energy, particle energy and field energy. At low speeds (not near the speed of light), particle energy can be written as:

Where *m* is the mass of the particle, *c* is the speed of light. So, if you just look at a particle, that is it for the energy. Now, what about the “work” portion? Work is defined as:

Where *F* is the net force on the particle, ?r is the vector displacement of the particle. The “dot” in between F and ?r represents the “dot product” operation between vectors (also known as the scalar product). In a [previous post](http://blog.dotphys.net/2008/09/basics-vectors-and-vector-addition/) I showed that you could multiply a scalar quantity by a vector quantity. Here I need to do “something” with two vectors. You can’t multiply two vectors in the same sense that you multiply scalars. A general definition of the dot product for two vectors:

That looks a little more messy than I wanted, but it can not be helped. Really, it is not that complicated. The dot product is simply the projection of one vector on the other. Let me explain in terms of work.

# What is Energy?

I think it is time for me to talk about energy. My ultimate goal is to give some insight into the many stories about perpetual motion. To do this, I will first talk about the fundamentals of energy.

**What is Energy**

I started thinking about this, and at first I realized that I did not have a good, short explanation of energy. The most commonly used definition in science text books is:

*Energy: the ability to do work (or something dreadfully vague like this).*

But what is work? It may be no surprise to find that many college level physics texts avoid defining energy. After some serious contemplation, I think I have this energy figured out.

**There are only two types of energy**

I don’t need a general definition of energy, since there are only two types I can just describe those two. ALL energy is either:

• Particle Energy: Energy of particles (obviously). I was originally going to just say kinetic energy (energy of things that move) but I forgot about mass (of course you remember E=mc2). This is sort of complicated, so I can perhaps summarize it by saying a particle can have energy because of its mass and because of its motion (really this is just one thing). So, particle energy can be an electron moving, a water molecule moving, or a car (a car is a collection of atoms that are mostly moving in the same direction). For the rotational kinetic energy of the Earth, this is really the same thing. Imagine all the pieces of the Earth (atoms) they are moving and thus have kinetic energy. The idea of rotational kinetic energy is to simplify the calculation. Instead of summing the kinetic energy of each of the atoms of the Earth, one can use the radius, mass, and the angular velocity of the Earth to do the same thing. But realize this is mostly just a short cut.
• Field Energy: Energy in the fields associated with the fundamental forces – gravity, electric, magnetic, strong nuclear and weak nuclear. Suppose I hold a ball above the Earth, it has particle energy (because of its mass) and there is also energy in the gravitational field associated with the ball and Earth. A chemical battery has energy stored in the electric field due to the configuration of atoms. A final example of energy in fields would be the energy from electromagnetic radiation.

But wait! What about ….. What about …. (insert some energy). All these other energies you read about are one of the above two. Other energies (for example thermal energy) are short cuts. They allow us to deal with large collections of particles without having to calculate ALL the particle energies and the field energies.

**Conservation of Energy**

There have been many many experiments in the history of science. In all of these experiments, the total energy of the situation as been conserved. Well, this is to say that there has not been an experiment where clearly the total energy before something happened was different than the total energy after something happened. Most experiments don’t look at this “energy accounting” directly. Energy conservation isn’t the law, its just what we see. How about a couple of examples of everyday things and I explain where all the energy is?

**Example: A cup of hot tea sitting on a table**

First, where is all the energy in this hot cup of tea? The cup and the tea both have particle energy. The particles (carbon and stuff) have mass energy. If I somehow annihilated this cup and tea it would turn all this mass into field energy. In this case that energy would be in the form of electromagnetic radiation. In fact, this would be so much energy in electromagnetic radiation that it would create pairs of particles (matter and antimatter pairs).

The particles also have energy because of their motion. If we assume the cup is stationary, the particles in the cup are still moving. The hotter something is, the more they move. For the particles that make up the cup, these particles are essentially just vibrating and staying in the same general area. For the tea, the particles are moving around and mostly staying in the cup (but some are leaving at the surface through evaporation). This energy is generally called thermal energy.
The cup also has energy in fields. There is energy associated with the gravitational field of the Earth-Cup(and tea) system. This would be called gravitational potential energy. There is also energy associated with the electric field is the interactions between the electrons and protons in the atoms of both the tea and the cup. People usually call this chemical energy, you could see this energy change forms if you burned the cup or had some other chemical reaction.

As the cup is sitting in the room, it gets cooler. That corresponds to lower particle energies. Where does the energy go? In this case, the stuff surrounding the cup gains energy. The table gets a little warmer (particle energy) and so does the air. This energy transfer takes place by the higher energy particles of the cup and tea interacting (through the electric field) with the particles of the air and the table. You might ask, why is it that the table gains energy and the cup loses energy? Couldn’t it happen the other way and energy would still be conserved? Yes, it would. But the probability of this happening (remember that there are on the order of 1025 particles in this cup) is so near to zero that you have a much greater chance of winning the lottery.
What if the cup were in outer space with nothing touching it? It would still cool (unless the sun was shinning on it). The particles in the cup still radiate electromagnetic energy (usually in the Infra Red region). This IR radiation could causes something else to increase in energy, but the cup still loses energy. The tea would all evaporate and lose energy to IR radiation.

I didn’t think it would be possible to take a simple thing and make it so boring, but I did it. I know that was painful (and likely in some places technically wrong) but it was necessary. Don’t make me do it again. Hopefully, you have an idea of conservation of energy and of the fundamental ideas of energy.

# How much gasoline could we save by stopping drive-throughs?

Gas prices may be trending down, but they are still quite high. How can we save gas? One of my colleagues suggested we can save gas by getting rid of all drive throughs. This means it is my job to estimate how much could be saved.

**Starting Assumptions (estimations)**

How many drive-throughs are there in the U.S.A.? When I think of drive-throughs, I think of McDonalds. [Wikipedia](http://en.wikipedia.org/wiki/Mcdonalds) says there are 31,000 restaurants world wide. I am going to say there are around 20,000 in the U.S. that have drive-throughs. So then, how many total drive-throughs? In my town, there are two McDonalds and probably 8 other major drive-throughs (Wendy’s, Burger King, Taco Bell etc….). This will give an extremely rough estimate of 100,000 drive-throughs in the U.S. (drive-through fast food).

There are also other kinds of drive-throughs. Drive-through banks, starbucks, pharmacy, liquor (yes, they exist). All of these will have different times, so I will first just deal with the fast food drive-throughs.

How many cars go through the drive-through a day and how long do they idle? I am going to estimate that the average over 8 hours a day is 2 cars in the drive-through line with an average wait time of 2 minutes. Yes, at lunch time there is a longer line, but sometimes there is no line. This is my estimation and I am sticking to it.

**Calculating the hours of idle time**

From this, I can calculate the average idle time. If there are 100,000 drive-throughs and for 8 hours there are two cars idling (I guess the wait time does not matter), that would be 1,600,000 idle-hours per day (100,000 x 8 hours x 2 cars). How much fuel does this use? Anecdotal claims from the internets say that cars use around 0.3 gallons per hour idling (I would have guessed higher than this). For this calculation, I will use 0.25 gallons of gas per hour idling. So, the total fuel per day wasted in drive-through (just restaurants) would be: 400,000 gallons.

**Comparing to the U.S. oil used per day**

Now to compare this to the 20 million barrels of oil used per day. 1 barrel of oil produces about 20 gallons of gasoline. So 400,000 gallons of gas saved would be 20,000 barrels of oil saved. This is just 0.1% of the oil used per day. Not nearly as much as the claimed 3% savings from tire pressure (although that is for people that don’t already have properly inflated tires). Also, that 3% is for individual savings, not for the whole nation.

**Slow Down**

I still think the best way to save oil is to drive slower.

Either way, the real issue is (as stated in the time article) how much would we get from off shore drilling? How much can we save by changing stuff.

# Turn off daytime running lights, or reduce speed? Which saves more?

Which wastes more fuel? (and thus produces more carbon dioxide). This is a difficult to question to answer for a variety of reasons. The main reason is that a speed change from 71 mph to 70 mph is different than a reduction from 56 to 55 mph.

First, let me be clear that the question of how much fuel is wasted using daytime running lights (or DRL as they are called) has already been addressed. The first source I found was howstuffworks.com

**Assumptions**

• The daytime running lights on a car run at about 100 watts (for the pair)
• The energy density of gasoline is 1.21 x 108 Joules/gallon.
• A car is 20% efficient at converting this energy to mechanical energy.
• The alternator is 70% efficient at converting mechanical energy into electrical.
• At highway speeds, air resistance is the dominating factor in fuel efficiency (this might be wrong)
• The air resistance can be modeled as Fair = (1/2)?CAv2
• I will assume an “average” car that has combined CdA of 9 ft2 or 0.84 m2 (where Cd is the coefficient of drag and A is the cross sectional area. Also ? is the density of air, about 1.2 kg/m2)
• An average trip of 50 miles (I completely made this up).
• My mythical “average” car gets 25 mpg when going 70 mph

# Energy issues are like the reverse Y2K problem

There was this commercial on the radio about Trane heating and cooling units. The ad claimed that the units could use up to 50% less energy than your existing unit. This started me thinking (because before that I was in a complete state of non-thinking). Do you remember the Y2K problem? Basically, when people started writing programs back before Star Wars they had to be very conservative. The hardware of the time did not afford the programmers to have frivolous code. To conserve, they only used the last two digits to represent the year (1970 was represented as 70). Obviously this became a problem in 2000. So, for computers and programs, people started very conservative and the hardware became less conservative.

Now look at appliances. When people first started getting electricity in their house, it was a completely new thing. But how much electricity would a household use? At one point (I read somewhere) that it was projected that electricity could be so cheap it would be free. In this case, why make an efficient AC unit? Look at many of our energy uses today (including cars). They seem to have the legacy of being extremely inefficient.

To summarize: Computer programs start out being efficient and then go to not needing to be efficient (because computer processing is relatively cheap). Appliances start out being inefficient and are moving towards being more efficient. Really, that is all I wanted to say.

# How about a massive catapult to replace the space shuttle

I recently saw a comment on a blog somewhere about putting satellites into space (I think it was from a post about a rocket that blew up). The poster suggested using a giant catapult to put things in space instead of rockets. Maybe he or she was kidding, or maybe not. But I have heard this idea before. Would it work?

# Heat. It’s a four letter word

Heat. You have heard it before. You have used it. I have even used it. Do we need this word? No. Is this a useful word? No.

Let me start with the definition as usually stated in a physics type text: (this is from [dictionary.com](http://dictionary.reference.com/browse/heat))

*heat:* a nonmechanical energy transfer with reference to a temperature difference between a system and its surroundings or between two parts of the same system.
This definition is fine. It is not wrong, but is it needed? Not really. Couldn’t we just say energy transfer? Actually, I like to use this in the following equation: