Friday, October 2, 2009

Fermi Problem Rules of Thumb Part # 1

In order to do Fermi problems, and other back of the envelope calculations with confidence, one must have an few tricks and rules of thumb that can be brought out quickly.

In this entry into Fermi problem rules of thumb, I will introduce a few tricks.






Numbers:

Sqrt(20) ~ 4.5
Sqrt(10) ~ pi
Sqrt(3) ~ 1.7
Sqrt(2) ~ 1.4

2^5 = 32

2^10 ~ 1000

Exp(3) ~ 20
Exp(1) ~ 2.7

Example: (Taken from Back of the Envelope Physics, Clifford Swartz)

Exp(40)= e(e^3)^13 ~ e(20)^13 ~ e(2)^13 *10^13 ~ 2*10^17

Exp(40) = 2.35x10^17 Close enough.

Some Conversions:

1 mi/h ~ 1.5 ft/s ~ 1.6 km/h ~ 0.5 m/s
1km/h ~ 0.3 m/s ~ 0.6 mi/h
1 ft/s ~ 0.3 m/s ~ 1km/h ~ 0.7 mi/h
1 m/s ~ 3.3 ft/s ~ 2.2 mi/h
1 day ~ 8x10^4 sec
1 year ~ pix10^7 sec
1 story (in a high rise) ~ 10 feet

Some "things to know"

Population of planet ~ 7 billion
Population of the USA ~ 3x10^8 people
Population of NYC ~ 8 million
Density of water 1000 kg/m^3
Density of Air ~ 1.3 kg/m^3


Average energy output of resting human ~ 100 Watt
Time light takes to get to the Moon from the Earth ~ 1.3 seconds
Time light gets to Earth from Sun ~ 8.3 min.

That is good for now. =)

Thursday, October 1, 2009

Car vs Pedestrian

Today I am going to talk about a pet peeve of mine, and that is oblivious dumb-ass pedestrians.
Well, to be fair, some of them are not oblivious, just expressing their entitlement to cross the street wherever the hell they want.

I am certain in every college city, drivers are faced with the hordes of students, who after class is over decide that they are going to cross in front of a moving car. They do this in droves, holding up traffic for blocks.

"Hey, the last 20 people just jaywalked across the street, and since the cars are already backed up and stopped then so will I!" They think to themselves.

Well, we all have to deal with that, and it is annoying. But what really gets me are those people who jump out on a crosswalk without even looking!
That's right folks, these people will walk out in front of a large, rapidly moving hunk of metal and not so much as glance upwards from the text they are writing on their cell phone.

In Boulder Colorado, I see this every day on the streets. Some dumb-ass walks out in front of you, and only looks up to give a dirty look and the finger.

The new trend in Boulder are pedestrian walkways.


http://www.bouldercolorado.gov/index.php?option=com_content&task=view&id=9632&Itemid=2973


These walkways either have sensors that detect a pedestrian, and then start flashing a yellow light, or a button that is pressed by the pedestrian to start the lights going.



It seems like perhaps a good idea, but what seems to be happening is that as soon as the pedestrian sees the light flash, they assume that a vehicle will follow state law and yield.
Their mind and sense of self preservation shuts down, then they bomb out onto the cross-walk without hardly sparing a glance upward.

Well, the result of installing these crosswalks are an increase in crosswalk accidents.

Yes, pedestrians have the right of way... but when does having the law on your side mean that you relinquish common sense, or the sense of self preservation? Just because you press a button does not mean a car will stop. Are you willing to put your trust in flashing lights? Or even in the ability of a driver to stop?

Lets consider the physics of an encounter between a moving vehicle and a pedestrian.

To put across why it is a bad idea to step in front of a moving vehicle, regardles if you have the right of way, lets consider some back of the envelope physics.


Persona Dramatis:

1.  A 2007 Toyota Prius.

Stats: 
Weight: 2890 lb (~1300 kg)
Speed: 0 to 100 mph  (0 to ~ 45 m/s)
Composition: 
A butt load of metal, glass, rubber and plastic!

 






2. An oblivious dumb-ass phone-texting pedestrian


Stats: 
Weight: 220 lb (~100 kg)
Speed: 0 to 15 mph  (0 to ~ 7 m/s)
Composition: 
A butt load of stupidity, soft and fragile tissues, bone, and mostly water.












 Of course I will use metric... after all I am a physicist. ;)


 Lets assume that the Prius is moving at a sedate speed of about 15 mph ( ~7 m/s), and the pedestrian, is standing in the middle of the crosswalk like a dumb-ass.
Now, 15 mph is not very fast for a car, go ahead and try it yourself. Heck, the speed limit in a school zone in Colorado is 20 mph, and if that is safe enough for little kids...


First, lets find the kinetic energy of a 1300 kg Toyota Prius moving at 7 m/s. We do this using:



Turning the crank and I get a kinetic energy of:

K ~ 32000 J

(In case you are wondering, the '~' means 'about')


To put this in perspective, to get this energy our 100 kg oblivious dumb-ass phone-texting pedestrian would have to jump off a ten story building. That is a 100 foot fall!

Don't believe me?
We can calculate this by using the equation for gravitational potential energy.



So, the energy of a slow moving Toyota Prius is the equivalent of a 220 lb person falling 100 feet. Who do you think would win, the car or the dumb-ass?

Now, lets approximate collision between an oblivious dumb-ass phone-texting pedestrian and a 2007 Toyota Prius moving at 15 mph.





Here we use the concept of conservation of linear momentum and conservation of energy to calculate the final velocities of both the car and the pedestrian. We will in this initial run assume a totally elastic collision.







Turning the crank and we get a final velocity of the Prius to be about 6 m/s and the pedestrian is now moving at 13 m/s !

The collision transferred about 8500 J to the pedestrian, which is equivalent to the pedestrian jumping off a 3 story building (30 feet).
OUCH!

Lets assume the oblivious dumb-ass phone-texting pedestrian is launched on an optimum ballistic path as described by the equations:



 Turning the crank and we see the oblivious dumb-ass phone-texting pedestrian is launched a distance of about 56 feet.

Now of course in real life, the collision would be relatively inelastic. You see, energy has to go somewhere.
Some of the energy transferred goes into sound waves (no... not the screaming of the oblivious dumb-ass phone-texting pedestrian), as in the sound of bones breaking, metal bending, flesh tearing.
A good deal of energy goes into breaking bones, tearing flesh, compressing and rupturing tissues and bending metal. Any residual energy then launches the pedestrian into the air, and is reclaimed when the body strikes the ground and bounces several times.

The car, after the collision is still moving at a slightly reduced speed, and therefore has an excellent chance of running over the battered corpse of the oblivious dumb-ass phone-texting pedestrian, thus adding insult to injury.

Now, if you double the speed of the Prius, you quadruple the energy! I will let you do those calculations.
You get the point.

Needless to say, legally the oblivious dumb-ass phone-texting pedestrian may have the right of way. But common sense says that the pedestrian should yield to the car.
And PAY ATTENTION!





http://www.thedenverchannel.com/newsarchive/20326913/detail.html

Physics Tower Word Power!

I don't know about you guys, but I have always found restroom graffiti interesting.
Having traveled the country extensively, I have seen a very large range of colorful limericks, words of wisdom, political statements and downright funny jokes scratched or written out on bathroom walls. Also abject stupidity and bigotry. But hey, it is a bathroom wall after all, and the writings usually reflect the users.

What then does one make  of the following, posted in a physics department men's restroom?



Well... whoever said that physicists had to be good at speeling?

;)

Wednesday, September 30, 2009

Energy, pessimisim, optimisim? Youth.

Ah yes, a blast from the past!


In my development as a critical thinker (still developing yo') I was often abrasive and strident in presenting my views. Often, I would latch on to my beliefs and arguments and miss out on those of others. The common case of talking past one another.


In my crackpot bashing days on Usenet, I developed a hair trigger when dealing with what I perceived as ignorant or downright stupid statements.


I will occasionally post some worthwhile examples of my younger days. Some of the assertions I still belive, some I do not or have modified. But the main lessons to take away from these "Blasts from the past" are:


1. Learning to think critically is a life long process.
2. After you have vented your emotions, be willing to go back and look at your assumptions and arguments.
3. Applying critical thinking skills have similar results as applying any skill... namely that since we are imperfect sacks of mostly water, we cannot perform any skill perfectly.


And finally, as a result of the above:
Critical thinking does not 'have' to give us the answers.


 
Below is an excerpt from a conversation I had several years ago on Usenet regarding energy distribution, and resource allocation. This particular post is unedited, but is commented in green!
Use your Google-Fu to find the whole conversation if you wish. (And see hints below for search terms! ;)

Today I am both optimistic and very pessimistic regarding supportable human population. But that is a post for another day.
 

 
 From Star Trek, TOS Mark of Gideon.
 
--- Usenet post ---
 
> It is easy to speculate that the future will bring boundless energy
> sources.
(Oops, hair trigger triggered! I was so quick to jump.)

Only by twits who have no understanding of the basic laws of physics.
Equally so, others pessimistically shortchange the ability of man to
progress scientifically.








(Here I am still pissed about the negative ninnies Luddites I had previously dealt with.)

We all know that there is no free lunch, the second law sets this limit.
However, many do not realize its application to closed and open systems.

Our population problem comes down to a few factors (which interact in an
astoundingly complex manner).
A short list:
1.  Energy
2.  Raw materials
3.  Habitable volume
4.  Distribution.
5. Politics.
6. Technology


> However, getting anyone to take the idea seriously seems
> likely to take more than the handwaving about our uncertainties about
> the laws of physics that Simon appears to offer in his chapter 4.
> I think - in the absence of other evidence - we should go by the laws
of
> physics as they are currently understood.

Currently there are many sources of energy that can be extracted with
technology that exists or can exist in say 100 years.
Be careful when you state "laws of physics", when actually it has more
to do with our state of technology.
Lets consider 1.  Energy:

Lets do a Fermi type problem.

Radiant energy from the sun at earths orbit is around 1400 W/m^2
Surface area of the moon: 4x10^13 m^2
Area exposed to the sun at any one moment: 2x10^13 m^2

Total solar energy available on surface of the moon:  2.5x10^16 W

Say we utilize 1/10% of the surface for solar collectors: 2x10^10 m^2

This would correspond to a band of solar panels surrouning the equator
of the moon with a width a little over 3.5 km

Available solar energy: 2.5x10^13 W
Lets be pessimistic an say we have really crummy solar collectors with
low efficiency broad band spectrum of 1%
Collected energy: 2.5x10^11 W
Conversion to microwave energy, pessimistically 10%
Energy at microwave: 2.5x10^10 W

Transmit collimated microwave energy toward earth, with a pessimistic
90% loss due to atmosphere, inverse square, etc.

Energy at collection stations around earth: 2.5x^9 W

Predicted power usage by 2020: 25 TWh

Therefore we would need a power output of 2.9x10^9 W to meet our energy
needs.

Note that the total efficiency of the plan outlined above is 0.0001%
Which is a exceedingly pessimistic.  For each order of magnitude
increase in transfer efficiency, we can decrease by one order of
magnitude the total collector area and still get our 2.5x10^9 Watts.

How about construction materials on the moon?
The surface is mostly silicates... perfect for constructing solar cells.

http://www.energyadvocate.com/fw54.htm
http://scienceworld.wolfram.com/physics/Power.html
http://whatis.techtarget.com/definition/0,,sid9_gci795904,00.html
http://www.greenelectricitynetwork.org/english/1_5.html
http://www.iht.com/articles/23585.html


(The point here is that, regardless of the tech difficulties of such a construction project, launching, man hours etc. the physics allows this, and who can say what technology will be like in 100 years, or 500 years!  But people are too quick to assume that we are peaked with what we can accomplish.)





> I don't see much hope of extracting unbounded volumes of energy in
> finite times there.

One cannot extract unbounded amounts of energy in a finite time, but of
course we don't need to.
People 90 years ago had nearly the same understanding of physics as we
do now, but do you think we had the technology 90 years ago to supply
the same amount of energy as we can now?  Food?  Distribution?
Transportation? Information?
The key to population support is energy production and usage. And will
be even more so in the future.


(Now... is it really the key to population support?)



> Universal heat death - rather than Simon's "infinite energy" -
> currently seems more likely to me.

In that case, never clean your house.  You are contributing to entropic
heat death of the universe.




Hey... I STILL firmly believe this! ;)  But try convincing my wife of that... [8(

There is no "infinite energy", and we don't need it.

(Currently....)

-------

Blasphemy!




The Center for Inquiry has a blasphemy contest! Read about it here.

My entry? Something I have been saying for years. Examine my blasphemy critically, y'all!

"God offers succor to the soul at the expense of the mind." ~ Michael Varney

Tuesday, September 29, 2009

Ride the Wave!

I make it no secret that I really like many Google products.
Well, a new one coming out is called Google Wave, and this particular product has me very excited!


Copyright Google... of course... =)


What has me jumping up and down in anticipation?
Well, beyond the obvious cool reasons of spending vast amounts of my personal time collaborating (and arguing) with people on the best Bulgogi recipe (and my research in physics and other topics), with respect to teaching critical thinking skills I can see the promise of Google Wave.

For instance, I could use GW to form a collaborative exploration of a topic found on the web, such as a CNN article mistating or sensationalizing opinion as fact. The users could start researching the claims made in the article, and using a group white board with a Google Voice conference call work on determining the real meaning of the data used in the article, and what impact there is on their personal life.

Of course, I can see a lot of arguing over opinions, and ideals etc... but what is new there... at least with GW you can have the ability to see the angry or smiling faces of the collaborators rather than relying on emoticons to convey a j/k. ;)

Monday, September 28, 2009

Google-Fu Introduction (Tools of the Trade #1)

"Approach, students. Close the circle at the feet of the master. You have come to me asking that I be your guide along the path of Google-Fu..."

*ahm* =)  Just kidding

In this day and age, the internet and the world wide web have become the default tool used by most American's (if not most of the 2nd world nations and above) who wish to research a topic, or verify their sources. The "web" is the default go-to resource for searching and researching just about anything.
Only those like my grandmother (may she rest in peace) ever regularly use the physical yellow pages to look up a number, and the days of actual card catalogs in libraries are past in many libraries across the country.

One needs to be web savy to flourish in this modern age, and more than that, one must become proficient in the modern martial art of the web search. Yes... MARTIAL ART!

Hi-Yah!





In this series of Tools of the Trade, I shall introduce you to the basic Kata forms of Google Fu. The path to mastery is long and hard (well.... actually no...) but your efforts will be well spent.
Not only is Google search an indispensable tool in your critical thinking arsenal, but the ability to winnow the wheat from the chaff in your search results is actually an exercise in critical thinking in itself!

Since the path is long and complex (again, not really but I am loath to re-write what is available out there on the net), I will teach you up to yellow belt, at which point you will have the Google basics needed to progress in your art via self study.

Stay tuned for our first lesson: Google-Fu Kata 1. Winnowing the Chaff *

* Yes, I know that strictly speaking a Kata is associated with Japanese martial arts, such as Shotokan and Karate etc.  But Google-Te is not so catchy, and I am studying Karate, and screw it this is my blog and I can mix things up if I want! ;)

Homework:

Read and click on all the links of this page:
http://www.google.com/advanced_search