A Wonderous Wormhole - Honors Geometry Picture Graphing Project

In the field of cosmology and particle physics, the possibility of wormholes is a very mind-boggling and exciting subject. In essence, a wormhole is a hypothetical "shortcut" through spacetime, a theoretical "tunnel" with its end at two different points in spacetime. Even though there has never been any physical/observable evidence of wormholes in physics, there are some solutions to the equations of general relativity that could support wormholes. One possibility for a real wormhole is the Schwarzschild wormhole. However, this was discovered to be too unstable to last long enough to allow any matter to pass through it. Traversable wormholes, wormholes that someone/something could travel through, would only be possible if some type of exotic matter with negative energy density could be used to make it stable.

When I was assigned a project in Honors Geometry to create an image solely by writing equations and graphing them, a wormhole immediately came to mind. I knew that it was going to be a challenge with the many ellipses parabolas, and curves. However, I knew it was something I could do, and wanted to do. I worked on it by hand and on the computer. For the sake of giving due credit, the final picture was graphed and colored with the application GeoGebra.
 

 Thanks!!!!

Attributions:
Some Wormhole Information: http://en.wikipedia.org/wiki/Wormhole
Wormhole Photo: http://lnns.webs.com/lnns/tema8eng.html

AC/DC - Not the band!?!?

When you hear the acronym AC/DC, what is the first thing that pops into your head? Is it the Australian rock band formed in 1973 by brothers Malcolm and Angus Young? Possibly. For me, however, it has to be electricity, for AC/DC also stands for Alternating Current and Direct Current.

Ok. So we're talking about electricity here, an obscure subject for some but an important one nonetheless.

For all intensive purposes, electricity (electric current) can be defined as the flow of charges (typically electrons) from one place to another with a capability of doing work. For an electric circuit to be present, there must be a closed path in which an electric current can travel from an energy source (positive terminal), to an element in the circuit, and back to the energy source (negative terminal). Conventionally, the direction of the current is considered to be the movement of positive charges from + to - when in reality, it is the movement of negatively charged electrons from - to +. The common elements of a circuit are a battery (energy source), wires, and loads (lights, resistors, etc.) that are arranged in a closed loop with no breaks or gaps.

A DC (Direct Current) circuit is one in which the current travels in one direction continuously (a constant flow of electrons).  An AC (Alternating Current) circuit is one in which the current is continuously and rapidly changing directions (the electrons are moving back and forth).

A Series Circuit:
A series circuit is one in which the elements in the circuit (lights, in this example) are arranged in line with each other, from end to end. Take, for example, the circuit below:

In a series circuit, the current is the same along all points in the wire.  This is due to the fact that there is only one path for electrons to take (like cars traveling along a one lane road; they cannot pass each other).  The equivalent (total) resistance of the circuit equals the sum of all the individual resistances of all the elements in the circuit.  Even though the current is the same at all points, the voltage (potential electrical difference) across two points in the circuit is not.  The voltage drop across each individual element in the circuit equals the voltage drop across the entire circuit (the voltage drop of the energy source).  Basically, the voltages of the batteries are distributed between the elements in the circuit. In this example, the total voltage of the circuit is 75V. Because the two lights have the same resistance, they both have a voltage of 37.5V. Note: If elements in a circuit have different resistances, the distribution of the voltage will not be equal.

A Parallel Circuit:
A parallel circuit is one in which the elements are connected in parallel, meaning that each have a direct connection to the energy source (the lead from the energy source is split into many paths that lead to the elements).

In a series circuit, the voltage drop across each "branch" equals the voltage drop of the total circuit (voltage drop of the energy source).  Even thought there are multiple paths, the voltage in each path is the same because it has, in essence, a direct path to the energy source (battery). However, the current drawn by each branch varies with the the resistance of each branch. Furthermore, as can be derived from Kirchhoff's current law (Conservation of Charge), the total current of the circuit equals the sum of the currents through each branch.  The equivalent resistance of the circuit can be found by taking the inverse of the sum of the inverses of each individual resistance (each new resistance added decreases the equivalent resistance).

A Complex Circuit:
A complex circuit is a combination of elements in series and elements in parallel into one circuit.

In a complex circuit, things become more complicated. To find the equivalent resistance you combine the resistances of individual components (parallel segments and series segments). For this example, the equivalent resistance would be found by adding the resistances of the two series lights and the resistance of the parallel segment (as described above). The total current would be found by dividing the voltage drop of the energy source by the equivalent resistance of the circuit. To find individual voltage drops and currents at specific points, look at each component as a single entity and incorporate it into the larger arrangement. In this example, the parallel segment can be considered in series with the two other lights. In general, in situations similar to the one pictured above, to find the voltages of series elements multiply the individual resistances by the total current.  To find the voltage of the parallel branch, subtract the series voltages from the total voltage. Now, you can find the different currents in the individual branches of the parallel segment: divide the voltage of the parallel branch by each individual resistance.

When working with circuits, do not memorize a certain method that can be used in every situation. Circuits are like puzzles; they take thought to work through every situation.

Have Fun!!!


Attributions:
AC/DC Photo: Photo by Yannick Croissant - http://www.flickr.com/photos/yannick-croissant/3315343302/
Lightning Photo: Photo by Fort Photo - http://www.flickr.com/photos/70619288@N00/3638881022
Electric Circuit Pictures: Screen shots while working in PhET simulation: http://phet.colorado.edu/simulations/sims.php?sim=Circuit_Construction_Kit_DC_Only 

A “Green” Idea: Optical Phenomena with a Green Laser

Warning!!!! Laser Ahead!!!!

When beginning to think about what to do for my photo project, lasers immediately entered my mind. From hand held lasers that can be seen for miles and miles, to extremely high powered lasers used for science or military purposes, something about lasers peaks my interest. Interestingly, the word laser originates from the acronym LASER, or Light Amplification by Stimulated Emission of Radiation. The basic premise of lasers is that they emit "coherent" light, or light that has waves of identical phase (in-step), polarization, and frequency, rather than "incoherent" light that is totally random, in various phases, frequencies, and positions at various times. The common components of a laser are a gain medium inside of a reflective optical cavity (a mirror on each end, with one mirror having a small hole or being semi-translucent).  As light travels through the gain medium and bounces back and forth between the mirrors, it is exponentially amplified and is released as a narrow "beam" of light.  Simply, energy (typically electricity) is "pumped" into the gain medium, causing all of its atoms to be at a higher energy state. Next, "ignition" photons are tuned to a specific frequency (a similar wave function), so when they skim the atoms in the gain medium, they stimulate the release an additional photon in the same direction as the incoming photon. These two photons go on the stimulate further atoms, and they will stimulate even more atoms, etc., creating a chain reaction. Affter emmiting these photons, the atoms fall back down to a ground state to be re-energised by the energy being pumped in. Through this process, the light can be exponentially amplified, creating powerful "rays" of electromagnetic radiation (light).

Here is my photo:

A “Green” Idea: Optical Phenomena with a Green Laser

This contrived image demonstrates common optical phenomena that are not typically observed with conventional light sources (incandescent lights, fluorescent lights, or sunlight) because the rays are too spread out. The image was created using a 5mW, 532nm green laser, water tank, small mirror, and light bulb. Greater visibility of the beam was created with the dispersal of a small amount of milk throughout the water and the introduction of fog into the air above the tank. The laser demonstrates several optical concepts: reflection (Law of Reflection), refraction (Snell’s Law), and diffraction. When the ray strikes the water, two things occur. First, the majority of the ray passes through the air-water boundary, refracting (bending) and traveling through the water at an angle less than the incident angle of the aerial ray (with respect to the normal, perpendicular to the waterline). Second, a substantial amount of the ray reflects off the water’s surface, obeying the Law of Reflection (angle of incidence equals angle of reflection). Next, the ray is reflected off a mirror on the tank’s bottom where it then hits the water-air boundary again, some of the ray reflecting back into the tank (barely visible) while most passing through, refracting, and striking the light bulb. Some of the beam reflects off the bulb’s shiny surface while the rest is transmitted through the glass where it is refracted, reflected, and diffracted (due to the frosted coating), making it visibly illuminated from the inside; a “green” idea comes to “light.”


For your enjoyment, here is a fun puzzle game on laser reflections: http://games.erdener.org/laser

Attributions:
Laser Radiation Picture: http://chemistry.about.com/od/labsafety/ig/Radiation-Warning-Symbols/Laser-Radiation-Symbol.-QVX.htm
Some Laser Information: http://en.wikipedia.org/wiki/Laser

March 14th: Pi Day and Einstein's Birthday Celebration: A "Mysterious" Quote

Now that its March 14th (3/14), Pi day and Albert Einstein's Birthday have fallen upon humanity for another time. To commemorate these two events, I have written a little description of one of my favorite Einstein quotes and have given you a little "pie" treat:

Albert Einstein - "The Father of Modern Physics"

"The most beautiful thing we can experience is the mysterious.

It is the source of all true art and science.

He to whom this emotion is a stranger, who can no longer pause to wonder and stand rapt in awe,

is as good as dead: his eyes are closed."

-Albert Einstein

Discussion:
        Despite his mind-blowing achievements in the field of physics and cosmology, Albert Einstein was a profound philosopher and intellectual on life. He put in writing many thoughtful quotes about science, education, the universe, and life; many of which are based around the concept of “imagination and creativity.” In 1931, the quote above was published in one of Einstein’s essays, “The World As I See It,” that was originally published in “Forum and Century,” the thirteenth in the Forum series, Living Philosophies. In this quote, Einstein explains that it is human nature to seek answers to problems that arise or things that humanity does not understand; he is showing how mankind is inclined to be curious and how it is this curiosity that drives people to hunt for justifications and explanations for the many complexities of life.
        In the first two sentences, Einstein describes how mystery is beautiful because it makes people engage their mind and actively think, search, and look for answers to the most complex problems in life. Furthermore, it is this unwavering desire to solve problems and explain mysteries through graceful inventiveness and ingenious, tedious scientific research that causes spectacular discoveries in science and works of art to be discovered or created. For the problem-solving scientist, although the best achievement would be to find a life changing answer to a long debated question, true fulfillment and pleasure arises from the path and steps that one takes to move toward the final goal. Artists, nonetheless, use their mind, imagination, and creativity to create wondrous works of art for generations to take pleasure in. Both are trying to answer humanity’s favorite question, “What if . . .?” It is that small spark of curiosity and intrigue that is inside every human being that allows for the creation of magnificent pieces of art, the pursuit of the highest levels of education, the solving of complicated puzzles, and the discovery of new scientific inventions. Mystery is beautiful because of the wonderful things that are created when humans engage on a quest to find answers.
        In comparison, the last two lines of the quote has Einstein issuing a warning to all of mankind about what will happen to humanity if people refuse to see the wonder in everything around them. For human beings that do not have curiosity or any interest in solving mysterious occurrences, the world to them may well be dead, and thus, they are dead to themselves. If people do not see any beauty in mystery or any remanence of grace in the unknown, then what is there to motivate or drive them to achieve something great? Why should an artist pour out his/her soul into a work and try to express themselves to others? Why should a scientist spend hours scouring his/her mind, trying to find the solution to a snag in the research? The answer to these questions is “human nature.” Humans strive, desire, and need to find meaning in the things they comprehend and even in those things that cannot be easily observed. If people are not able to just stop their busy schedule and stand for a moment, amazed with the “awe”-some world, then their eyes are closed; they cannot see the world in its true value or make any contribution to society.

And now sit back, grab a piece of pie, and enjoy the first 500 digits of pi:

Pi = 3.
1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 5058223172 5359408128 4811174502 8410270193 8521105559 6446229489 5493038196 4428810975 6659334461 2847564823 3786783165 2712019091 4564856692 3460348610 4543266482 1339360726 0249141273 7245870066 0631558817 4881520920 9628292540 9171536436 7892590360 0113305305 4882046652 1384146951 9415116094 3305727036 5759591953 0921861173 8193261179 3105118548 0744623799 6274956735 1885752724 8912279381 8301194912

Smells good!!!!
: )

Attributions:

Albert Einstein Sitting: Public Domain - http://commons.wikimedia.org/wiki/File:Albert_Einstein,_by_Doris_Ulmann.jpg
Albert Einstein Signature: Public Domain - http://commons.wikimedia.org/wiki/File:Albert_Einstein_signature.svg
Pie Symbol: Public Domain - http://en.wikipedia.org/wiki/File:Pi-symbol.svg
Apply Pie: Public Domain - http://commons.wikimedia.org/wiki/File:FoodApplePie.jpg
Information:
When quote was published - http://www.aip.org/history/einstein/essay.htm
Digits of Pi - http://www.subidiom.com/pi/pi_10k.txt

"The Fastest Ice on Earth" - Conservation of Momentum in Short Track Speed Skating

On February 12, 2010, the stunning opening ceremonies to the 2010 Vancouver Winter Olympics were held at BC Place in British Columbia. This ceremony opened the 21st Olympic Winter Games in which the USA was awarded over 37 medals and Canada got its first gold on home land (over 14 golds, leading the gold count for the Olympics). For me, one of the most exciting sports to watch and one that I knew little about was Short Track Speed Skating. These athletes need to have speed, agility, athleticism, and aggression in order to excel in the races. Not only is Short Track exciting to watch, but it is also filled with physics, like all of the other sports in the winter Olympics.

Below is a link to and an embedded "Prezi" that gives a little history of Short Track, describes its rules, equipment, winners, and illustrates how the Conservation of Momentum and the Conservation of Energy apply to the sport that moves at a lightning speed:

Link for full screen:  Short Track Speed Skating "Prezi"

I could not have done this project without my partner Cyrus. Thanks so much for your help and collaboration. It was such an enjoyable experience. Here is his Blog: "A Phlight Through Physics"

Reflection: Energy - The Fuel of the Universe

"Hubble Ultra Deep Field"

A look back in time nearer to the "Big Bang" 

According to the commonly accepted theory of the big bang, approximately 13.73 ± 0.12 billion years ago, the universe started expanding from an infinitesimally small point into the visible universe that we know of today, over 93 billion light years wide. After one Planck time (about 5.39124*10^(-44) seconds), gravity separated from the electronuclear force. After one picosecond (1.00*10^(-12) seconds), the “weak” force separated from the electromagnetic force resulting in the four forces we know today. By one hour, helium nuclei formed. In 370,000 years, hydrogen and helium nuclei captured electrons and formed stable atoms. By 100 million years after the big bang, the first stars began to shine. It may seem surprising, but all of the energy in our universe at this moment, was present from the very beginning. Some of what I have learned during this unit about energy is explained in the following "Glog":

Energy - The Fuel of the Universe

Attributions:
Big Bang Technical Information: http://en.wikipedia.org/wiki/Big_Bang, http://en.wikipedia.org/wiki/Graphical_timeline_of_the_Big_Bang
Hubble Ultra Deep Field Photo: http://en.wikipedia.org/wiki/File:Hubble_ultra_deep_field_high_rez_edit1.jpg

Extra!! Extra!! Read all about it! Finally the secret behind the death-defying "Sphere of Fear" explained!

Have you ever been to a circus, amusement park, or stunt show? Well, all of those air defying and gravity smashing stunts are just good applications of physics and an understanding of motion. Not to say that these tricks are not dangerous and don’t risk life and limb, they do. However, the physics principles behind them are rather simple. Take for example the “Sphere of Fear,” “Globe of Death,” or “Circle of Doom” that is a staple in many circus acts. The stunt is fundamentally composed of a large spherical metal cage with one or more motorcycles and riders driving around on the inside. Created by Herb “Daredevil” Durkin after WWII, he and his wife believed that the public would pay good money in order to see the death defying “double loop.” For more than 30 years, they continuously added new tricks to their repertoire such as sidecars, more riders, and eventually, they decided to cut off the bottom half of the sphere in order to increase the risk and make it more exciting for the audiences. In the early 70s, Herb Durkin and his wife retired and left their “Sphere of Fear” to rust into scrap metal. From then on, fresh and innovative performers, entertainers, and daredevils have created similar acts and amazed audiences with their fearless acts of bravery.

Now onto the Physics!!!
Here is a “Prezi” that can explain everything: "The Sphere of Death" - Prezi
 In this "Prezi," you will find a description and analysis of the motion of the riders and motorcycles when riding in the "Sphere of Death." It includes a detailed description of both vertical and horizontal loops, what would happen if the riders go too fast, too slow, or just the right speed, and multiple FBDs and diagrams in order to help you understand what is the physics behind this amazing feat. To navigate the "Prezi," move the mouse to the bottom right of the "Prezi" and use the arrows to step forward or backward in the path.

Now that you know how it works, test you skills with the Homer Simpsons "The Ball of Death Game".


Attributions:
Pictures:
Filmstrip: http://www.accoll.se/default.aspx?id=1249
Black and Blue Colorful Fractal: http://www.shutterstock.com/pic-43038823/stock-photo-colorful-abstract-fractal-background.html
Blue and White Waves: http://www.shutterstock.com/pic-32752504/stock-photo-animated-waves.html
Dark and Gloomy Sphere of Death: http://picasaweb.google.com/lh/photo/3_vtdoqr_isY-Q69Qq8o6w
Green Sphere of Death in Motion: http://www.flickr.com/photos/mikerollerson/3332074252/
Blurred Motorcycle in Motion: http://www.flickr.com/photos/mikerollerson/3344932877/in/pool-fairgrounds
Sphere of Death in Daylight: http://www.sciencejoywagon.com/physicszone/03circular-motion/sphear/
Inside Sphere of Death: http://www.sciencejoywagon.com/physicszone/03circular-motion/sphear/
Bright Colorful Blue Fractal: http://www.shutterstock.com/pic.mhtml?id=41864677
Roller Coaster: http://sciencefair.math.iit.edu/projects/forces/
Softball: http://softballtips.wordpress.com/category/softball-pitching/
Diagrams: http://www.sciencejoywagon.com/physicszone/03circular-motion/sphear/
LED Circle: http://hacknmod.com/hack/goliath-killing-led-bola-slingshot/
Snail Cartoon: http://www.toonpool.com/cartoons/Globe%20of%20Death_9499#
Specific Tricks: http://www.acmecompany.com/Pages/Urias.html
Videos:
YouTube Long: http://www.youtube.com/watch?v=PVaKxNDNF-Q
YouTube Short: http://www.youtube.com/watch?v=e3nqUUGWx4o&feature=related
Information:
http://www.sciencejoywagon.com/physicszone/03circular-motion/sphear/
http://www.physics.uni.edu/chanceyclass/GPI/Chapter%206%20part%202.ppt
Game:
Homer Simpson Ball of Death Game: http://www.gamesplz.com/play/457/homer-simpsons-the-globe-of-death.html

Reflection: Newton's Second Law of Motion including Friction

In this Prezi (a "digital napkin/ presentation tool" if you will), I give my reflections on Newton's Second Law of motion including friction and describe some of what I learned, some of my difficulties during this unit, and some of my problem solving skills as well.



Attribution for Prezi: http://prezi.com/

Physics Carol

In this glog is the lyrics for a song "Wondrous Physicsland" written by me, sung to the tune of "Winter Wonderland."  I hope that you enjoy!
 Wondrous Physicsland Carol Lyrics Glog

PS: I also wrote a short carol entitled "Hark - Newton's Second Law of Motion" written by me, sung to the tune of "Hark the Herald Angels Sing."  It is short, but it is sweet!


"Hark - Newton's Second Law of Motion":
Newton’s second law of motion,
Describes how objects accelerate,
Sigma f equals ma,
That is what helps us to say.

That the intensity of a force,
Depends upon the mass of course.

The cause and effect linked in a definite way,
That is what this law can say,
Understanding bodies moving away,
The second law now saves the day.

Reflection: Newton's First Law of Motion

During this lesson about Newton's First Law of Motion, I have learned numerous concepts which are expanded upon in the following Glogster.  The Glogster contains information about some of what I have learned about this lesson, what I have found difficult to understand, my problem-solving skills, and some connections between the learned concepts and real world situations.

Newton's 1st Law of Motion & Translational Equilibrium

Content: Pixton - Reindeer Flight School

This comic strip gives some introductory material about projectile motion to Santa's reindeer in training.

Content: Glog- Santa's Fun with Objects in Motion

This Glog gives a brief overview of motion in general, helping to describe the development of projectile motion at an angle.

Santa's Fun with Objects in Motion

Fun Game with Santa as a Projectile

Just for kicks. A little game concerning Santa and projectile motion. Click anywhere on the screen to start the elves running. Then, click on catapult to pull back Santa and release to launch.  The goal is to achieve the greatest distance that is possible.

Projectile Santa

Attributions: http://69.93.193.34/~egg1com/Games-D5-140406/slingshot_santa.swf

Content: Blabber- Santa and Rudolph discuss projectile motion

In this Blabber, Santa and Rudolph are discussing the concepts of projectile motion after Rudolph's 1st day in Reindeer Flight School. I have tagged on something on the end just for fun. Have a good time!!!

Part 1 of 3 Blabbers of Projectile Motion

       


Part 2 of 3 Blabbers of Projectile Motion

            


Part 3 of 3 Blabbers of Projectile Motion

           


Just for Fun!!! We Wish You A Merry Christmas


       


Attributions:
Reindeer-Rudolph: http://blogs.nationalgeographic.com/blogs/intelligenttravel/2008/01/the-running-of-the-reindeer.html
Santa: http://www.squidoo.com/write-a-letter-to-santa-claus
Reindeer-Dancer: http://blather.net/abroad/archives/2007/07/barren_ground_caribou_wild_reindeer_denali_nationa.html
Singers:  http://www.nyca.org/victoriancarolers.htm
We Wish You A Merry Christmas: iTunes - Mormon Tabernacle Choir

Content: The Night Before Christmas - Physics Style

In this Glog, you will see a remix of the poem "The Night Before Christmas" in a physics point of view.  The equations in the ornaments to the side of the poem are equations used when working with objects in projectile motion at an angle above the horizontal.  The "Finding Components" equations discuss how the find the x and y components of a velocity if the have the resultant velocity.  The second set of equations named "Position Components" discusses how to find the range and height of a projectile if you have the time and the original component velocities.  The last set of equations named "Velocity Components" discusses how to find the component velocities of an object at any point in time if you have the original velocities and time.

Content: Glog: The Night Before Christmas Physics Style

Content: Projectile Motion- Santa's Knowledge

The fact that Santa knows the acceleration due to gravity of objects on earth (9.8m/s/s, down) is crucial in understanding and being able to use the equations in projectile motion.

Attributions:
Falling reindeer picture: http://www.myspace.com/82335731

Wordle: Feeling like a Mega Physics wordle has to be made

Here is another try at a Wordle that is entitled "Everything Learned in the First Trimester": Physics Skills, Kinematics in one and two dimensions and a thouch of Dynamics (I have make it large so you can see everything. :) )

My first wordle!! It has to be about physics...Duh!

When writing a wordel, the topic can tell a lot about its creator. For me, physics is the way to go.

Ben Voki

Get a Voki now!