Popular demand (from a few people – you know who you are) requested another level for the force game. I am open to naming this game. Ideas for levels have been suggested also. There is a new rule change. You must be stopped (or almost stopped) in the red circle.
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Basics: Friction
**Pre reqs:** [Free body diagrams](http://blog.dotphys.net/2008/09/basics-free-body-diagrams/)
Friction is an interaction between two objects in contact that opposes relative motion of those two objects. It is not something fundamental (like gravity, or electromagnetic force), but it comes up enough that it will be worthwhile to talk about it. Let me start with a simple example. Suppose I have a book on a table. Here is the free body diagram for the book:
Simple enough – right? There are two forces on the book. A contact force (the table pushing up) and a long range force (the gravitational force of the Earth pulling down on the book). These two forces have the same magnitude, so when added together, they give a total of zero vector. This means the book is in equilibrium.
Now, what if I push on the book from the side? Suppose I push with 1 Newton. If the book is still in equilibrium, what does that mean? It means the free body diagram must look like this:
If the book is still in equilibrium, then the force of the table on the book (due to friction) would have to have the same magnitude as me pushing on the book. Note: Even though my push and friction are equal and opposite, these are not Newton’s third law force pairs – I talked about that in the free-body-diagram post.
A physics-based Scratch game
I already said I like [scratch from MIT](http://scratch.mit.edu). After building a simple rocket model, the kids said it should be a game. I caved. Here it is:
To play, press the space bar. The arrow keys are rocket thrusts. The goal is to get to the red circle in as little time. If you hit the wall or the sides, you start back at the green circle. Please forgive me masters of scratch (I know who you are – you find something to complain about in my program).
Resonance and a Magic Trick
Magic tricks are cool. Especially when the trick is really physics. In this trick, I can make one of the four balls move more than the others. (When you watch the video, you will see why I am not a professional magician). You could set this up in a variety of ways. I state that if we (me and people around me) all work together with our mind and focus on the same ball, our brain waves can resonate with that ball and make it move. I let the people around me pick. In this video, I make the smallest two move.
So, what is the trick? The trick is not a trick. It is not resonance with brain waves, but it is resonance.
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.
Bullets have a lot of kinetic energy (apparently)
I was recently re-watching a MythBusters episode and I found something I had wanted to explore previously (but accidentally deleted the episode). Here is a short clip from the “shooting fish in a barrel” episode:
Did you see what I found interesting? That big barrel of water left the floor from being hit by a bullet.
The question here is: Does a bullet have enough energy to increase the gravitational potential energy of the barrel to that height?
Continue reading “Bullets have a lot of kinetic energy (apparently)”
Help Me. I can’t stop making scratch programs
I actually have some important things to do. However, I thought I would make another scratch program. Yes, this will all lead to something useful (that is what I told my wife). Anyway, in this program, I made a spaceship with 4 thrusters. The great thing about this is it show what forces do to the motion of an object. I already had a suggestion to make it into a game with a score.
Use the arrow keys to turn on the 4 thrusters.
1-D Motion with a force in Scratch
I can’t remember how I found this, but [Scratch](http://scratch.mit.edu) is a graphical programming language developed at MIT. My kids love this. In order to make sure they don’t know more than I do, I created my own scratch program. I am sure someone from the scratch community will attack it for some reason, but I am ok with that.
The program shows a numerical calculation of the motion of a box with a constant force on it. You change the mass and the force. It “sort of” plots the position as a function of time. Don’t worry python, I still think you are the best.
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
Continue reading “Turn off daytime running lights, or reduce speed? Which saves more?”
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