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goalkeeper0

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Blog Entries posted by goalkeeper0

  1. goalkeeper0
    In early September, in the very beginning of my time in AP Physics C, I was hesitant about the workload and difficulty of the course. When Mr. Fullerton introduced integrals to us for the first time, I knew from then on that the class would be no piece of cake. The funny thing looking back is that I enjoyed the calculus parts of physics by the end of the year very much. With a solid calculus background, the "hard math" aspect of the AP did not seem so hard. For me, the hardest part of the class was reading the problems and deciding in which direction to think. I had trouble reading the questions and immediately knowing which equation to use first, which equation to use second, and so on. I tried helping myself by reading the textbook and taking notes, along with making flashcards for the equations. By the time the AP rolled around, I was nervous, but felt prepared to do well. After taking the AP, I am happy to say that Mr. Fullerton prepared us very well as he made our tests harder than the AP itself. All in all, I look forward to the physics I take in college. I hope that from the AP tests I get some college credit; but if I do not, I know that I will at least have the background necessary to succeed in physics mechanics and electricity/magnetism. I wish the best to all of my AP Physics C classmates and the future students of AP Physics C! Go Physics!
  2. goalkeeper0
    As graduating seniors, we are getting old. No more high school, it's off to college! But, just how old are we? On the earth we are about 18 years old, give or take a few months. Because the other planets are different distances from the sun, they have different periods of revolution. Therefore, in relation to many planets we are very young (Neptune) or very old (Mercury).

    A planet's period is given by:

    = distance from planet's aphelion to sun
    = distance from planet's perihelion to sun

    Periods of planets (in Earth years):
    Mercury: 0.241
    Venus: 0.615
    Earth: 1
    Mars: 1.881
    Jupiter: 11.86
    Saturn: 29.46
    Uranus: 84.32
    Neptune: 164.8

    Age of 18 year-old earthling on planets:
    Mercury: 74
    Venus: 29
    Earth: 18
    Mars: 9
    Jupiter: 1
    Saturn: 0.6
    Uranus: 0.2
    Neptune: 0.1

    As period increases, one's relative age on that planet decreases.
    So, as seniors, we may be walking the stage soon; but on Mars, we would only be half-way there!
  3. goalkeeper0
    In the realm of “big” things there is the world, the solar system, the universe, and then the…? Some scientists, primarily physicists, now believe in the existence of a multiverse. The idea of a multiverse has not been proven, but there is substantial evidence toward the theory. Some of the main points include:

    1.) The observable universe goes on for as long as light has had the opportunity to get in the 13.7 billion years since the proposed Big Bang. Beyond the visible universe there can be other universes lasting to infinity. This is because space and time are thought to go on to infinity.

    2.) Other universes could arise from something called “eternal inflation.” Inflation refers to the universe expanding very quickly after the Big Bang. Some believe that certain pockets stopped inflating, while others never stopped. As a result, separate “bubble universes” were created. In our universe inflation has ceased, and galaxies and stars formed as a result. Other bubbles may still be inflating.

    3.) It is possible that more dimensions exist to our world than the three of space and one of time that we know. The idea of parallel universes that remain just out of reach of our own universe is a theory. In a higher-dimension space other three-dimensional universes could exist.

    4.) Quantum mechanics support the existence of multiple universes. Quantum mechanics deal with probabilities and the idea that all outcomes of a particular situation occur somewhere in separate universes. In one universe you may chose to go left at a fork in the road, and in another universe you may go right.

    5.) Some believe that math is a “fundamental reality,” and our perceptions of the universe are "imperfect observations" of the mathematical nature of reality. Hence, many mathematical structures exist. The mathematical structure that makes up our universe may differ from mathematical structures in other universes.

    It’s hard to imagine that other universes may make up a multiverse; but, it is also hard to imagine that other universes don’t exist. Who is to say that we are part of the only universe? People may never really know or fully prove that we are part of a grand multiverse, but the topic will continue to intrigue scientists of all kinds.

    http://www.space.com/18811-multiple-universes-5-theories.html
  4. goalkeeper0
    Happy (belated) National Donut Day! This American day of celebration for sugary breakfast rings occurred yesterday on June 7. Yesterday, people from across the nation stopped by Dunkin Donuts to receive a free donut. These consumers devoured the sticky treats without thinking about the history or science behind the donut. But, the history and science, particularly physics, is interesting. So, I will now discuss the connection between donuts and physics.

    The Dutch brought the idea of deep-fried balls of dough over to the western hemisphere. Originally, the dough balls were spherical, solid, and small. Over time, as American confidence grew, potion sizes also increased. Donut makers tried making bigger and bigger donuts to attract more customers. The physics of heating, and heating efficiently then came into play. The large donuts burnt on the outside and remain uncooked in the middle. The dough wads did not heat evenly. Producers couldn't match the demand for larger donuts, because they couldn't prepare larger donuts. One man by the name of Captain Hanson Gregory then changed donut history. Captain Gregory made a circular cutter and removed an inner circle from the dough. And, the ring shape of donuts today was created!

    The modern donut with an extracted center exists solely because one man thought about physics. Captain Gregory knew about thermodynamics and heating. He knew that for Americans to eat larger donuts, larger donuts needed to become more spread out. By increasing surface area, the donut heats and cooks faster and more evenly. To all of those donut lovers out there, thank Captain Gregory for the design of the classic ring donut.
  5. goalkeeper0
    Population concerns on Earth are leading scientists to inquire whether colonizing Mars is possible. As of now, over 78,000 people have applied to leave Earth forever and live on Mars. Mars One, a nonprofit organization, is sponsoring the colonization with a take-off date sometime in 2023. Out of the applicant pool, four will be chosen to send first to Mars. The first four will lay the groundwork for a permanent colony. Two years after the first four land, Mars One would send up more people to the colony. With the application process underway, it seems as though scientists have discovered ways for humans to survive on Mars indefinitely. However, this is not the case. Many, many concerns exist such as how will the colonists feed themselves? Will crops which grow on the Earth also grow on Mars?

    The first settlers of Mars will most likely be farmers. Yes, they will be astronauts; but, if survival is of any importance to them, they will learn to farm in order to eat. Research which has been conducted supports the idea that growing crops is possible in microgravity. However, those working for NASA do not know to what extent the gravity of Mars will effect crop growth. Also, Mars' surface only receives about half of the sunlight that the Earth's surface receives. Will plants be able to grow with limited sunlight? On top of the already limited sunlight, pressurized greenhouses would be necessary to grow crops. The greenhouses would block out more light. So, additional light would be necessary from other sources than the sun. What would power additional light sources? How would that power be generated and sustained?

    Radiation would also be a problem faced by those on Mars. Mars does not have as strong of an atmosphere as the Earth. More radiation reaches the surface of Mars than the surface of the Earth. Inhabitants would need a way to reflect the radiation or shield themselves from the rays.

    To live on Mars, man must master the art of agriculture in microgravity. Feeding the inhabitants of Mars is one among many more necessary tasks of survival. As of now, research is still being conducted. The 78,000 who have already showed interest in living on Mars are a bit stupid or extremely bold. With current technology man would not survive on Mars. I do not doubt though that technology will develop in the near future for man to successfully live on Mars.
  6. goalkeeper0
    Pale people of the world, beware of the shining, warm sunlight! UV radiation, with a shorter wavelength than visible light, is absorbed by skin causing a sunburn and long-term skin damage. The Earth's atmosphere filters the majority of UV rays before they reach pasty humans; however, UV rays still penetrate the atmosphere. Exposure to UV radiation changes based upon altitude, distance from the equator, time of day, season and amount of cloud cover. At noon, with the sun high in the sky, sunscreen is heavily advised. How does sunscreen protect people from UV radiation?

    Sunscreen includes organic and inorganic compounds to reflect, scatter, absorb and release UV rays. Inorganic ingredients such as titanium dioxide and zinc oxide form a physical barrier between UV rays and skin. Because of this barrier, less rays penetrate deep layers of skin. Organic ingredients absorb UV rays and release them as heat.

    There are two different types of UV rays. UVA rays penetrate multiple layers of skin and cause long-term skin damage. UVB rays cause the visible sunburn and effect top layers of skin. Both types of UV radiation are bad. The SPF of a sunscreen is the measured UVB protection of the formula; there is no standard for UVA protection. A broad spectrum sunscreen protects against both types of rays. A sunscreen with a SPF of 15 means that one could spend 15 times as long in the sun before getting burned compared to the time necessary to get burned without sunscreen.

    Why wear sunscreen? Well, besides the fact that prolonged exposure to UV rays can lead to skin cancer and eye damage, UV radiation also can reduce the effectiveness of one's immune system. This fact seems strange. But, since UV rays displace or kill some cells necessary to trigger immune system responses, the body's ability to fight infections decreases.

    So, as we all await the end of school and the sunny days of summer, remember the importance of applying sunscreen!
  7. goalkeeper0
    As senior year comes to a close, brain space previously reserved for memorizing lists of vocab or challenging physics concepts has been filled with plots for senior pranks, senior runs, and so on. As of now, our senior runs have been quite brief, but I remember the senior runs of the past being both long and successful. As a freshman, I remember being caught in the hallway as I heard the shouts and footsteps of hundreds of seniors coming my way. Senior runs, or more like senior stampedes, can be heard from far away which is good so that small, tiny freshmen have time to hide in the bathrooms and not get trampled. Potentially, one caught in the middle of a senior run could get seriously bruised and battered. Stampedes are dangerous. I touched a bit upon stampede physics in my Black Friday post a very long time ago, but I found some more information about how physicists are studying crowd dynamics.

    Physicists look at fluids to help them understand crowd dynamics. Physicists have found that crowds behave as fluids with three different types of flows. The first type of flow is laminar flow. Laminar flow is a steady flow which resembles crowd dynamics when an area is undersaturated with people. The next type of flow is stop-and-go. Stop-and-go flow causes spurts of people to leave an area at a time. Waves are created in the crowd. The worst flow type is turbulent flow. Turbulent flow is the result of pressure buildups. Turbulent flow leads to "shock waves" which can push people up to 3 meters forward.

    I'd say that most senior runs do not reach the turbulent flow stage. However, given the velocity of the crowd, and the combined mass of the people in the crowd, these runs can definitely cause damage. The momentum of the stampede is enormous, and tiny freshmen are wise to seek shelter in nearby restrooms.

    http://physicsbuzz.physicscentral.com/2013/01/brazil-nightclub-stampede-trampling.html
  8. goalkeeper0
    Even though we launched our bottle rockets a few weeks ago, I thought I would reflect upon team Brazanah's rocket performance.

    With prior knowledge in the field of building bottle rockets, team Brazanah was determined to succeed in the bottle rocket competition this year. We mainly focused on constructing a well-made parachute. We knew that especially on a windy day, a parachute can greatly slow down the rocket during its fall. Just as we put parachutes on rockets for the Kerbal Space Program to salvage parts and save Kerbals, we put a parachute on our bottle rocket. As a result, the drag force (F=-bv), resisting the pull of gravity as the rocket plunged downward, was greater for our rocket than for others. Parachutes seem simple, but to have them actually deploy is another story. Luckily, with guidance from another group, we learned the proper parachute folding technique. We also weighted the nose cone to make sure it fell off as the rocket hit its peak and flipped. The rocket's descent definitely was longer than its climb, primarily due to our successful parachute.

    We did not have time to add fins to the rocket; however, if we did, the rocket would have been more stable on the way up. This is because the fins would counteract the sideways motion of the rocket as water escapes. Fins are similar to adding a SAS on a Kerbal Space Program rocket . Even without the fins, our rocket seemed to climb pretty straight. All in all, for Physics C team Brazanah finished on top with a time of 5.85 seconds in the air. Go Brazanah!
  9. goalkeeper0
    In Physics class we are currently working on a space exploration computer game named Kerbal Space Program. The purpose of the game is to build rockets or airplanes, think about money management, learn about space exploration, and achieve preset checkpoints. Lately, as our groups attempt longer and longer missions, the Kerbals are stuck in space for a considerably long time before returning home. The question has arisen, what do Kerbals eat while in space in order to survive? I am no Kerbal expert, and I have no idea what the Kerbals consume if they consume anything. However, this prompt inspired me to research a bit about space food in general.

    Typically, when one thinks of space food, tubes of unidentifiable jellies and freeze-dried snacks come to mind. Space food isn't known for receiving 5 stars. Food scientists have designed space food to be easily prepared, provide nutrients, and be edible while in low gravity. Foods which leave crumbs are not well-suited for space. Crumbs can float around the space craft and fly into unwanted areas. Loose debris such as crumbs can be harmful and dangerous to the crew. Today, the selections for space food are numerous in comparison to the tubed-applesauce of the past. To list some of the most popular space foods here they are-- Scrambled eggs, Chocolate pudding, Macaroni and Cheese, M&Ms, Pineapple, Swedish Meatballs, Yogurt, Tortillas, Shrimp Cocktail... So, if the mystery of space food turned your interest away from becoming an astronaut, think again. The food today isn't so bad. Food scientists with the help of physicists have mastered the art of eating in low gravity environments.
  10. goalkeeper0
    As advised by Mr. Fullerton, I did the Coat-hanger bubbles experiment to further understand flux!

    Pre-experiment preparation:
    First, in my closet I found a nice metal coat-hanger suitable for the trial. After attempting to reshape the coat-hanger, I learned that my hangers are very strong, or that I lack strength; so, I went to my brother's toolbox and grabbed pliers to help bend the wire into a slinky-like shape. My coil ended up having four turns. I then ventured into my kitchen to fill the sink with soapy water. With the bubbly solution complete, I was ready to start the experiment.

    The experiment:
    I dipped my wire coil into the water, and slowly pulled it out. I found that the bubbles didn't form well to the structure. So, I compressed the coil by pushing the turns closer together. When I tried again with the compressed coil, the bubbles formed nicely between each turn and along the outside of the coil. The formation of the bubbles between each turn demonstrated how the number of turns matter when calculating flux. Therefore, the more turns, the greater the flux. Hence, the equation for magnetic flux is:





    N=number of turns



    A=area within one loop



    B=magnetic field



    =angle between magnetic field and positive normal direction


    Everyone should try this experiment before the test on Wednesday!
  11. goalkeeper0
    While exploring this lovely APlusPhysics site, I came across an article titled, "How Fast Would the Earth Have to Spin to Fling People Off?"
    I never thought about this question, but now wonder why I didn't. Oh wait, it's because the idea seems incredibly silly and impossible. Well, someone actually came up with an equation to answer this question.

    Here is the physics thought process:
    [ATTACH=CONFIG]644[/ATTACH]
    Ffake=an added force used to fix the accelerating reference frame
    Really, just two forces exist:
    Fground= normal force and Fgravity=mg
    [ATTACH=CONFIG]645[/ATTACH]
    If you want to solve using other locations on earth other than equator:
    [ATTACH=CONFIG]646[/ATTACH]
    [ATTACH=CONFIG]647[/ATTACH]
    So....Since changes in longitude impact this problem, every person on the world would not fling off at the same minimum rotational speed of the Earth. Those at the equator would fly off most easily. Luckily, we are not near the equator as seen by the weather today. At the equator the Earth's rotational speed must be 0.0124 rad/sec for people to tangentially fling off. The actual rotational speed of the Earth is 0.0000727 rad/sec. We should have nothing to worry about.

    source: http://www.wired.com/wiredscience/2013/03/neil-degrasse-tyson-still-complains-about-the-daily-shows-globe/
  12. goalkeeper0
    As APs are nearing closer, caffeine seems like the secret to success. Staying up late takes a toll on the body, and drains you of energy. Therefore, in the morning, it is very common to see kids and adults carrying around a cup of coffee or tea for the caffeine boost. Nobody wants to fall asleep in class. For those who do consume these beverages here is a disclaimer:

    Beware of water heated in a clean container in the microwave. Unlike when water heats up on the stove, water heated in a microwave can reach a temperature above its boiling point, and remain in liquid phase. This is called "superheating." Normally, when the temperature of the water exceeds its boiling point, the water slowly becomes a gas. But, in the microwave, boiling is hindered by lack of nucleation sites to form bubbles. A nucleation site can be a scratch in the container, a spec of dust, or any place where there is high surface area relative to volume. Also, the surface tension of the water in the mug suppresses the growth of bubbles. When the timer buzzes, and the mug is removed from the microwave, the water in the cup may appear placid, without bubbles (So, you think that the water's temp. is below 100 degrees Celsius). You are wrong, the water may be well above its boiling point. As soon as a powder such as a sugar or teabag is added to the water, the sudden addition of many nucleation sites can trigger an explosion of froth. Instantaneous boiling is induced. This can cause nasty burns to your skin.

    The "superheating" of water is easily preventable. First off, do not set the timer on the microwave for very long (over five minutes). Also, you may leave a nonmetallic object in the glass while it heats such a wooden stick to add nucleation sites. Lastly, stay away from heating and then reheating the same water multiple times in the microwave. Don't let this post scare you into never using a microwave again. Superheating isn't too common unless you set the microwave timer for 20 minutes instead of two, and then come back and find a very hot cup of water. Moral of the story: be safe when using the microwave.


  13. goalkeeper0
    If you ever find yourself in Las Vegas with nothing to do, $100 to burn, and gambling isn't your forte, head over to the Stratosphere Casino/tower.
    At the Stratosphere, you can experience the thrill of free fall as you descend 108 floors to the ground. After taking the elevator to the top of the building, you receive a brief "safety lesson." Then you saddle into the harness, say a prayer, and jump! (Ok, this isn't true free fall. A long cord is attached to your back which slows you down for the last 20 ft of the drop.)

    But, for physics sake, let's say that a person jumping off the Stratosphere was in perfect free fall. What would the maximum speed of the brave yet stupid jumper be?

    Vmax occurs as the person hits the ground
    h= height of the building, ~260 meters
    g= acceleration due to gravity, 9.8 m/s2
    Conservation of energy: mgh=(1/2)mvf2
    vf=(2gh)1/2
    vf= 71.4 m/s which is about 159.7mph...This is the speed the jumper would hit the ground at if the cord snapped..ouch

    The Stratosphere SkyJump claims that its jumpers reach speeds up to 40mph which is much different than 159.7mph! The attached cord and drag force work together to slow the person down during the jump--it's a good thing!
    [ATTACH=CONFIG]633[/ATTACH]
  14. goalkeeper0
    In college, I plan to major in biomedical engineering. Biomedical engineering combines biology, chemistry, physics, and math into one field of study. The field is very broad; so a biomedical engineer usually focuses on one specialization, some of which include medical imaging, biomechanics, bioinstrumentation, genomics, robotics, clinical engineering, tissue engineering... I am not sure which specialization I will follow yet; however, I think that tissue engineering is extremely fascinating. Tissue engineers are constantly finding new ways to grow skin, bones, cartilage, and even organs. The theory behind tissue engineering and regenerative medicine is that an organ made by a patient's own cells should be easily received by the patient's body. With typical transplants (transplanting an organ from human to human or animal to human), there is always risk of rejection. As strides are made in the field of tissue engineering, the results are promising. If tissue engineers can streamline the process of growing organs, people would not have to wait on transplant lists and pray for a suitable organ to turn up.

    The process of "growing" organs involves many steps. One of the first steps is called electrospinning. In this process, positively charged nanofibers are transferred from a syringe which is positively charged to a spinning cylinder which has a negatively charged plate behind it (physics ) . The nanofibers travel along the electric field lines, and accumulate evenly on the spinning cylinder. After enough fibers have accumulated, the engineer stops the machine. The deposited fiber is removed from the tube; and a thin sheet is end product. The engineer uses the thin polymer to construct a scaffold. Cells are placed on the scaffold which multiply, differentiate, etc. to form the intended organ. The scaffold provides a structure for the cells to form around. Once in the body, the organ slowly develops around the scaffold. Due to the composition of the scaffold, it slowly is absorbed by the body over time, leaving just the organ in place. Ta-daa! An organ has just been made!

    This is a glimpse at one step in the long process of creating an organ. Many chemical and biological steps come next, but this is physics so I will stop here.
    All in all, three cheers for E-fields which allow super thin nanofiber sheets to form!
  15. goalkeeper0
    After laying low for awhile, cross products have suddenly became very important in our current independent unit on Magnetism. For those who may have forgotten how to find a cross product, here are some reminders.

    1. Cross products are needed when the multiplication of vectors is involved in the problem
    2. To find cross product of a x b [where a is (ax,ay,az) and b is (bx,by,bz)]
    cx=(aybz-azby)i
    cy=(azbx-axbz)j
    cz=(axby-aybx)k
    3. The cross product is then written:
    a x b = (cx,cy,cz)
    [ATTACH=CONFIG]625[/ATTACH]
  16. goalkeeper0
    Most people think of magnets as a solids. But, think again. A "liquid" form of magnet exists.

    Ferrofluids contain magnetic particles in a liquid carrier, and act like a "liquid magnet." Ferrofluids do not clump together to form solids because of a surfactant, which coats the magnetic particles. The surfactant overcomes the magnetic forces between the particles and keeps the solution a liquid. A ferrofluid is primarily made of a liquid carrier, and contains relatively small amounts of magnetic particles and surfactant. Depending on the ratio of liquid carrier: magnetic particles: surfactant, ferrofluids range in viscosity and magnetization.

    How do ferrofluids work?
    When a magnetic field is applied to a ferrofluid the magnetic particles quickly align themselves along the magnetic field lines. Ferrofluids can be precisely positioned and manipulated by an external magnetic field. When a magnetic field is not present, the particles of the fluid are randomly distributed in no particular arrangement.

    How are ferrofluids used?
    Ferrofluids are applied in a variety of ways. Some ferrofluids are used as adhesives, particularly in the speaker industry. In the computer world, ferrofluids act as lubricants. For machine tools, ferrofluids come in the form of a liquid spray. Ferrofluids can also plate and protectively seal materials from the atmosphere and harmful contaminants. When correctly used, a ferrofluid can improve a product's performance.
    [ATTACH=CONFIG]620[/ATTACH] [ATTACH=CONFIG]621[/ATTACH]
  17. goalkeeper0
    The Law of Conservation of Energy: Energy may neither be created nor destroyed.

    One of the most simple transformations of energy occurs when a ball is dropped from height, h. Before being released, the ball possesses potential energy equal to mgh with m=mass, g=gravitational constant, h=height. While the ball is in motion, before it reaches the ground, its kinetic energy= (1/2)mv2 increases and potential energy decreases. When the ball hits the ground, some energy is converted to friction. So, when the ball rebounds off the floor, it will not exceed the height it was released from.

    Well, Disney broke this fundamental law in their 1997 film, Flubber, which was a remake of the 1961 film, The Absent-Minded Professor. In Flubber starring Robin Williams, Flubber-- aka green flying rubber, bounces to the sky when dropped from 4ft off the ground. Obviously, Disney threw the law of conservation of energy out the window to create this funny fictitious substance. Flubber, when applied to the soles of the shortest, whitest, weakest, worst basketball players, allowed the athletes to jump remarkably high. The best part in the film comes right before the buzzer of the basketball game when a player with Flubber on his shoes jumps from mid-court to do about eight somersaults in the air and fly head down through the basketball hoop with the ball for the win. Best buzzer-beater ever.

    I'd like to see this happen in a March Madness game. But, for now and probably forever, physics restricts both the idea and creation of Flubber.
    [ATTACH=CONFIG]622[/ATTACH]
  18. goalkeeper0
    Displayed in his videos for our current independent unit, Professor Walter Lewin has a strong interest in magnetic monopoles. Lewin repeatedly stated that proof of the hypothetical magnetic monopole would win the brilliant scientist a Nobel Prize. Because of his excitement toward this topic, I have researched a bit about the mysterious magnetic monopoles.

    Currently, it is believed that a magnet must have a positive, and a negative pole; the existence of magnetic dipoles has been elementary and common for years. No experimental evidence has been found to prove the existence of magnetic monopoles. However, many physicists still believe they do exist for theoretical reasons.

    New leads and ideas have led physicists to probe polarized rocks for magnetic monopoles. Polarized rocks buried deep within the Earth’s mantle are thought to contain magnetic monopoles. When the earth formed, and separated into chemically different layers, these researchers believe that magnetic monopoles “bound to matter that sunk towards the core.” This would explain why nobody has found magnetic monopoles in the Earth’s crust. Samples were taken from Antarctic and Arctic regions, but the elusive magnetic monopole still was not pinpointed.

    All in all, the race to find the magnetic monopole may never end. As the hunt stands now, physicists believe they are closer than ever to tracking down the hard-to-find magnetic monopole. Whether these monopoles are bound to matter, or travel freely through space, one can only theorize. If you want to make physics history, find the magnetic monopole.

    http://www.spacedaily.com/reports/Searching_for_magnetic_monopoles_in_polar_rocks_999.html
  19. goalkeeper0
    Circuits with resistors:
    In series:
    Req=R1+R2+R3+R4+...
    I=I1=I2=I3=I4=...
    V=IR1+IR2+IR3+IR4+...

    In parallel:
    1/Req=1/R1+1/R2+1/R3+1/R4+...
    I=I1+I2+I3+I4...
    V=V1=V2=V3=V4=...
    Note: Replacing resistors in parallel with one resistor of equivalent total resistance is very useful when analyzing circuits

    Circuits with capacitors:
    In series:
    1/Ceq=1/C1+1/C2+1/C3+1/C4+...
    Q=Q1=Q2=Q3=Q4=... (Conservation of charge)
    V=V1+V2+V3+V4+...

    In parallel:
    Ceq=C1+C2+C3+C4+...
    Q=Q1+Q2+Q3+Q4... (Conservation of energy)
    V=V1=V2=V3=V4=...
    After a long time, a capacitor acts like an open spot in the circuit; current through the section of the circuit with the capacitor= 0 A

    RC Circuits:
    Time constant=RC, or Greek letter tau
    I=-dQ/dt
    When a resistor and capacitor are in parallel, voltage drop across resistor=voltage drop across capacitor.
    When a resistor and capacitor are in series, current is the same through the resistor as through the capacitor.

    Charging RC Circuit: Current decreases over time. Charge on capacitor and potential drop across capacitor increase over time.
    *In the long run,VC=VT (V-terminal=V-capacitor)
    *I=(VT/R)e-t/RC
    *Q=Qf(1-e-t/RC)
    *Qf=CVT

    Discharging a capacitor: Current flows from the positive plate of capacitor to the negative plate and through the resistor. Current, charge, and voltage decrease over time.
    *I=I0e-t/RC
    *Q=Q0e-t/RC
    *I0=V0/R=Q0/(RC)
  20. goalkeeper0
    Faraday cages shield their contents from Electric fields. How does this work? Charge is distributed on the exterior of the cage, so that the Faraday cage acts as a hollow conductor. Therefore, since charge is only around the outside, the net charge inside the cage is zero; and, the E-field is zero inside the Faraday cage.

    But, what use is a Faraday cage? Well, this video excerpt from National Geographic's television show "Doomsday Preppers" will give you a whole new perspective on the value of Faraday cages and their potential value for the end of the world. When the end of the world does come, do you want your beloved electronics to be spared from electromagnetic radiation? If you are concerned, stop by the local thrift store like this woman and invest in a Faraday cage.



  21. goalkeeper0
    Physics separates the good from the great goalkeepers.

    1. The Understanding of Momentum- A goalkeeper must keep his weight shifted forward, standing on the balls of his feet. When a shot comes, the goalkeeper will try to save the ball while moving forward. Therefore, due to conservation of momentum, any rebounds will deflect away from the goal. A flat-footed goalkeeper (weight on heels) will deflect shots backward, into the goal.

    2. The Analysis of Vectors- While preparing for a shot, a goalkeeper must analyze vectors at all times to determine where he should stand. Given that a forward from the opposing team has the ball on the end line of the field, it is improbable that he will shoot the ball, because he has no angle. So, in this situation, the goalkeeper should stand a step or two off his line, toward the back of the goal, to prepare for a cross.

    3. The Maximization of Impulse- The best goalkeepers purchase the most expensive goalie gloves. Why? One reason is that they can afford them. But, also, the most expensive goalie gloves are made of the softest foam, with premium cushioning in the palms. This foam "absorbs" the shot for a greater period of time (maximizing impulse); so, less rebounds are given up. Cheaper gloves are made of tough foam which decreases impulse, making it harder to hold on to the ball.

    4. The Knowledge of Torque- On breakaways, when the opposing forward is dribbling to the goal uncontested, it is up to the goalkeeper to make a save. A great goalkeeper will strip the ball from the forward's feet, and send the player flying. How is this done? The goalkeeper slides out on the grass, attacking the ball low. Since torque is greatest when applied further from the point of rotation, the low force at which the goalkeeper hits the attacker with causes the attacker to spin and fly into the air. Yeah torque!
  22. goalkeeper0
    While studying for our midterm on Mechanics, I came to this brilliant realization.

    Realization: Physics with calculus is a lot easier when you know calculus

    Ok, this may seem like an obvious statement; but, when it clicks, it feels good. As I looked over some Mechanics Free Response problems involving derivations with drag force, I realized that they are not so bad after all. Now that all of us Physics-C students should understand integrals, differential equations, and integrating with natural logs, the Mechanics Free Response problems with calculus should seem manageable. So, for all of you who have acquired a phobia of drag force, take another look at the problems. It might surprise you that your background in calculus may cure your fear. Don't let drag force hold you back ; have confidence in this previously difficult concept!
  23. goalkeeper0
    Obvious connections between Physics and Calculus, or Physics and Chemistry exist. However, what about Physics and Humanities? Recently, in Humanities class, we continued our Middle Ages unit with a lesson on medieval architecture. We focused on the Gothic Cathedrals built in the Middle Ages, and the advances in architecture which were necessary to build such tall structures.


    The first major advance was the transition from the rounded arch to the pointed arch. The pointed arch distributed the force of the ceiling and walls down toward the ground, and a bit outward. The old, Romanesque, rounded arch focused too much force outward as the columns grew taller. With the rounded arch, as the columns grew taller, the top of the arch would bow under the extreme force. And, as one arch bowed, the entire cathedral would begin to crack and crumble.
    As the pointed arch minimized the outward force, the outward force still existed. So, flying buttresses were created as supports for the arches. These supports connected to the arches about where the columns began and the arch ended. The point of connection was very important, because if the buttress was placed too low, the arch would still bow, and collapse. With the flying buttresses, walls could be supported from the outside; and, the force of the walls was aimed even more downward. The flying buttresses allowed the cathedrals to remain in equilibrium, balancing out all forces.


    And, what was the result of these advances?...................Cathedrals over 48 meters tall!


  24. goalkeeper0
    Don't let four-wheel drive fool you, because any car can spin out on icy, snowy turns. In wintry weather, drivers must slow down or shovel their way out of a snow bank. Why must drivers slow down? The coefficient of friction between rubber tires and snow is much less than the coefficient of friction between rubber tires and dry pavement.
    The coefficient of friction between pavement and tires is about 1.00; whereas, the coefficient of friction between snow and tires is about 0.30.
    So, how much must a person really slow down while driving around a banked turn?

    vmax=(urg)1/2 r= radius of turn, u= coefficient of friction, g=9.81m/s2

    vmaxpavement=(1.00 x 10.0m x 9.81m/s2)1/2= 9.9m/s=22.1mph

    vmaxsnow=(0.30 x 10.0m x 9.81m/s2)1/2= 5.4m/s=12.1mph

    Physics proves you must slow down!
  25. goalkeeper0
    While some are contemplating the end of the world, I am studying for physics. Here are the essential oscillations equations to know for our test tomorrow.

    Oscillations (Includes SHM, Springs, Pendulums):

    F=-kx
    xmax=A
    vmax=Aw
    amax=Aw2
    T=1/f and f=1/T
    w=angular frequency=2(pi)f=2(pi)/T
    v=wr
    Potential Energy= (1/2)kA2cos2(wt)
    Kinetic Energy= (1/2)kA2sin2(wt)
    Total Energy= (1/2)kA2
    x(t)= Acos(wt + phase shift)
    v(t)= Awsin(wt + phase shift)
    a(t)= -Aw2cos(wt + phase shift)
    Tspring= 2(pi)[m/k]1/2

    For use with pendulums only:
    Tpendulum= 2(pi)[L/g]1/2
    w=[(mgL)/(Ip)]1/2
    w=[g/L]1/2

    Also, from past units, the torque equations are handy, along with the moment of inertia equations.

    STUDY!!!
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