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AlphaGeek

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  1. AlphaGeek
    So. I was reading my Biology textbook the other day and encountered something called "water potential." A simple summary of this term is water's potential energy , or it's capacity to perform work when free water moves from high water potential to low water potential. What? Physics in biology you say? Of course! :eagerness: Physics is everywhere.

    Let's define water potential in depth. Water potential is given by the equation water potential (symbol = Greek letter psi) = potential due to solute concentration + potential due to pressure, or:
    [ATTACH=CONFIG]515[/ATTACH]
    The potential due to solute concentration, or solute potential, is directly proportional to the number of dissolved solute molecules. Solute binds water therefore reducing the number of free water molecules and decreasing it's capacity to do work. Because of this, solute potential is negative.

    potential due to pressure, or pressure potential, is the physical pressure on a solution. Tension due to pressure is a negative pressure potential, whereas an applied pressure creates a positive water potential.

    The biology part of water potential is that it is essential to a cell's well being (plant cells in particular). The water potential determines the direction of movement of water in/out of a cell. For plant cells, it determines the shape and stiffness of the cell. A plant cell is flaccid initially. It becomes turgid when it intakes free water in that the pressure from the water pushes on the cell wall, making the cell swell. The cell becomes plasmolyzed when free water leaves the cell, causing the cell to shrivel and the cell membrane to pull away from the cell wall. This state is dangerous for a plant (commonly known as wilting) and the plant may die. These conditions are created by unequal water potentials of the cell vs the cell's surrounding environment. If a cell has a lower water potential than the surrounding solution, it will intake free water and become turgid. If the cell has a higher water potential than it's surrounding environment, it will expel free water and become plasmolyzed.

    [ATTACH=CONFIG]516[/ATTACH]


    If you'd like to know more about water potential, didn't understand a thing I just said or would like background noise doing homework, the following link may be of use to you:



  2. AlphaGeek
    Part 2 of the equation posts: E&M. Again, if you see any mistakes or have a few equations to add, make sure to utilize the comment section! I'll add it in right away.

    Electrostatics


    E= Fe/q = kq/r

    λ = Q/L
    ρ = Q/V
    σ = Q/A

    Electric potential

    Ue = kq1q2/r
    F = -dU/dl
    V = k ∑ qi/ri = W/q
    ∆V= Vb - Va = ∫ab E dl = ∆U/q

    Gauss's Law:


    Conductors

    Esurface=

    Vinside =

    Einside =

    Capacitor

    C=Q/V =

    Uc =

    Ue = field energy density =

    Energy = V/d

    C= w/ = Dielectric constant

    Circuits

    I =

    I = V/R

    I = NqVdA = NeVdA

    Current density (J) = NqVd = I/A

    charging up: w = I2V
    charging down: U = CV2

    = RC
    5 = 99% charged/discharged

    Resistance

    R=
    E=
    P=IV
    E= J
    W= qv

    Series Circuit

    Ceq =

    I= constant
    V=IR
    Req= R1+R2+...
    Q=CV

    Parallel Circuit

    Ceq = C1 + C2 + ...
    I = V/R
    V= constant


    Q=CV

    Batteries:

    Videal = V = mf = VT
    V with resistance = Iri = VT
    Pbattery = W/t = = I
    Pexternal resistor = I2R
    Pinternal resistor = I2ri

    Magnetism

    Gauss's Law: dA = O
    Amphere's Law: Ipen
    ...for a wire of radius R, B =
    Biot-Savart law: dB = (dl X r)
    ...for a loop of wire, B =
    Faraday's Law:
    =
    =

    solenoid: B =
    toroid: B =

    Mag. moment () =NIA =NIR2
    Mag. torque=


    ...sorry that took so long to post up, jeez that code takes a while to type up ^-^ Feel free to add/correct in the comments section!
  3. AlphaGeek
    Having trouble on the 4 minute drill? Need to consolidate your thoughts for the Mechanics part of the AP-C exam? Have no fear! I've sifted through my notes to find a good portion of the mechanics equations. If you find anything missing/incorrect, PLEASE give feedback in the comments section! I'll edit the changes in ASAP. Thank you

    MECHANICS

    Vectors etc.

    A B = lAl lBl cos Ө
    A x B = - (B x A)
    lA x Bl = lAl lBl sin Ө

    Kinematics

    V= Vo+ at
    Δx = Vo t + (1/2) a t2
    V2 = Vo2 +2aΔx

    Δx = ∫ v(t) dt
    Δv= ∫ a(t) dt
    Vavg = Δx/Δt = (Xf - Xo)/(tf - to)
    V= dx/dt
    a= dv/dt

    UCM/gravitation

    Fc = mv2/ r
    ac = v2/r = w2/r

    Fg= GMm/r2
    Ug= -GMm/r

    Rotational Motion

    S= Өr
    v= wr
    a= αr

    w= ΔӨ/Δt
    ac= w2r
    Vlinear = 2πr/t

    parallel axis theorem: I = Io +md2

    KEroll= (1/2)Icmw2 + (1/2)mv2

    Angular momentum (L) = r x p = mvrsinӨ = mwr2sinӨ
    dL/dt = Torque
    L= w I
    K= (1/2) I w2

    Moment of Inertia

    I = Σmi(ri)2 = ∫r2dm
    Isolid disk = (1/2) mR2 (also works for a cylinder about its axis)
    Ihoop = mR2
    Isolid sphere = (2/5)mR2
    Ihollow sphere = (2/3)mR2
    Irod about center = (1/12)mR2
    Irod about end = (1/3)ml2

    Torque (T)

    x >> Ө
    v >> w
    a >> α
    m >> I
    F >> T

    ΣF = ma >> ΣT = Iα
    T = rxF = rFsinӨ
    T = (Radius)(tension)

    Center of Mass

    rcm = Σmr/Σm = ∫r dm / Σm
    Xcm = (m1x1 + m2x2)/ (m1+m2)

    Drag force

    Fd = bv = cv2
    VT = mg/b
    V = VT(1 - e(-b/m)t)= (mg/b)(1 - e(-b/m)t)

    Friction
    Ff= μ Fn

    ...As to not get long and confusing, I'll make another blog post with all of the Electricity & Magnetism equations that I have in it. Check that post out, too!

    --Alpha Geek
  4. AlphaGeek
    Hi everybody!

    I haven't done a cookie problem in a while, so here it goes! The problem is related to the current unit. First correct answer gets a cookie. I think Charlie is the only one who answers these things, but I enjoy writing them and he likes cookies, so... It all works out :glee:



    Slinky the dog is bored (since Andy is off at college and all), so he decides to watch Walter Lewin's video Lecture 15. Slink thinks the solenoid example is really cool and decides to try it out himself. If he hooks his middle into a circuit of 1A and stands with his front feet .5 m away from his back feet, what is the magnetic field inside of Slinky? Note: Slinky's center is composed of 100 turns, and each turn is uniformly spaced.

    I love Disney! Bonus question: What is the name of the arcade in Toy Story?

    Have fun!

    --Alpha Geek
  5. AlphaGeek
    PRESSURE'S ON: First person to answer this correctly gets a cookie. :eagerness:

    You're at the playground with a girl you babysit, little Tori McTorque. Being 9 years old and devious, Tori took you wallet and threatened to spend your babysitting money on ice cream and root beer. Kids these days! You chased her over to the see saw, where she and her friend (Lil' Newton) sat happily on one side. You have to think of a way out of this! You don't want all of your hard-earned cash to go to waste, do you? Because physics is always the answer, you decide to make a bet with the little devils.

    You propose to Tori that, if you can make the see saw balance with three people on it on your first try, she must give back the wallet. If you fail, Tori will get unlimited ice cream privileges! D:

    Knowing off the top of your head that the average weight of 9 year old children is roughly 28 kg and that Tori and Newton are sitting 1 m and .7 m away from the center of the see saw, how far should you place a 61 kg teenager with a mullet from the pivot point?

    [ATTACH=CONFIG]553[/ATTACH]
  6. AlphaGeek
    *yawn* It's a beautiful Tuesday morning and you've awoken from camping in the jagged pass. You stow your tent into the key items pocket and continue on your trek to Lavaridge Town. You're on your merry way, thinking fondly of a dip in the hot springs, when the grass in front of you begins to rustle!


    Oh my, a Spoink appeared! Adrenaline pulses through your veins as you shout, "Go, McNugget!" (Mc.Nugget is none other than your lvl 98 torchic).

    You quickly break out your pokedex, which informs you that a spoink's tail can stretch up to .3 m from when it rests at equilibrium. You also remember hearing from a passing hiker that it's angular velocity between attacks is 6 rad/sec. Due to torchic's smaller size, it can only use scratch when spoink is closest to the ground. Asuming that torchic can strike as soon as you order him to attack, how soon after spoink starts oscillating from equilibrium position (moving up first, then down) should you tell torchic to use scratch?

    ...And for those of you who wonder why you didn't delete scratch for a cooler move, I think scratch is the bomb.
    Respond now, a cookie is on the line! (This one is larger than the one awarded from the first challenge )

    --The Geek
  7. AlphaGeek
    How would I determine the drag coefficient of an organic shape, such as a blob of pudding or a chicken or a Looney Tunes character?

    I wanted to do a blog post on the terminal velocity of Wile E. Coyote falling off of a cliff. I went back into my notes and found the following equations:

    Air resistance = Fdrag = bv = cv2
    VT= (mg)/b
    V = VT ( 1 - e(-b/m) )

    Notice the constants, b and c. I turned to google, thinking that the constants would be relatively easy to find.

    It turns out, the equation for Vterminal is a little more complex than I thought.

    [ATTACH=CONFIG]532[/ATTACH]

    Finding V terminal involves the mass of the object, acceleration due to gravity, the density of the medium that the object is traveling through, the area effected, and, of course, a drag coefficient. In my quest to find the drag coefficient, I found that the coefficient is related to the shape of the affected surface area. The lower the drag coefficient, the more easily the object can move through the air. The following table helps illustrate this:

    [ATTACH=CONFIG]533[/ATTACH]

    That's fine and well if you're trying to find the terminal velocity of a UPS box falling from a cargo plane in air of know density, although there are a few complications in the Wile E. Coyote situation. My number one probelm is as follows: unless the furry critter assumes a fetal position and magically transforms his body into a perfect sphere, his coefficient is difficult to determine.

    Any suggestions? :dontknow)
  8. AlphaGeek
    Recently, a friend has confessed to me that he has been diagnosed with stage one senioritis. We've all heard of this virus: common symptoms include drowsiness, in-class headaches, increased social tendencies, and worst of all, characteristic decreases in effort and GPA. Though some have better immune systems than others, this sickness is in fact contagious and most seniors contract a mild case. Because knowledge is the number one prevention factor, I intend to explain--using science and graphical representation-- what is known about this common yet dangerous disease. For those of you who seek protection (at least until the end of AP week), please read on.

    Diagnosis: How do I know if I have Senioritis?

    Illnesses ending in -itis indicate irritation and inflammation. Senioritis specifically refers to inflammation of the "give-a-care" gland, and inflammation seems to increase as the temperature rises outdoors. Senioritis is most common in ages 16-18, however some people are simply born with it. In this case, the illness is refered to as "chronic procrastination," an entirely different animal.

    Though little is known about the causes of Senioritis, there are key variables that contribute to the intensity of the illness. Inflammation level of the GAC gland (I) is directly proportional to t, the amount of time (in hours) left until the end of the year. It can be represented by the equation

    I = (2 π t2 P h) /f3

    where
    P= the constant of procrastination. This constant varies, dependent upon personality type.
    t = time (in hours) left until graduation
    f= the number of friends infected
    h= the amount of homework (in kg) the student is assigned each night.

    For a student with a moderate course load and average amount of friends, the constant of procrastination tends to triple after AP week due to a weaker mentality.

    Observe the below graph exhibiting the relationship between academic wellness over time. The decreasing trends are due to GAC flareups, a common side-effect of senioritis. Students with a high P constant are especially susceptible to the virus. Note how in students with relatively high tendencies of procrastination, the AP period provides a brief spike of academic rigorousness, followed by a devastating relapse. We call this spike of functionality "cramming."

    [ATTACH=CONFIG]618[/ATTACH]

    Cures and Coping Techniques:


    ​1.) Senioritis is highly contagious, like influenza or ring worm. Try surrounding yourself by people with relatively low P constants to avoid infection.

    2.) Create mini-deadlines for assignments as well as allotted time to study. Handling work in small bits reduces the chance of GAC flareups

    3.) Wash your hands before eating finger food.

    4.) Try self-medication: remind yourself that senior year is almost over, and in order to do well on APs you'll only have to fight the -itis a little longer. Stay strong, it's the final stretch!


    Bueno suerte!
    --Alpha Geek
  9. AlphaGeek
    Often times, values in physics are abbreviated using metric prefixes, or SI prefixes. I found this table the other night and thought it would be helpful to post, in that I'm sure I'm not the only one who gets these mixed up sometimes.

    Thanks to wiki for this table:

    [TABLE="class: wikitable, width: 0"]
    [TR]
    [TH="bgcolor: #CCCCFF, colspan: 2"]Metric prefixes[/TH]
    [/TR]
    [TR]
    [TD][TABLE]
    [TR]
    [TH="bgcolor: #EEDDFF"]Prefix[/TH]
    [TH="bgcolor: #EEDDFF"]Symbol[/TH]
    [TH="bgcolor: #EEDDFF"]1000m[/TH]
    [TH="bgcolor: #EEDDFF"]10n[/TH]
    [TH="bgcolor: #EEDDFF"]Decimal[/TH]
    [TH="bgcolor: #EEDDFF"]Short scale[/TH]
    [TH="bgcolor: #EEDDFF"]Long scale[/TH]
    [TH="bgcolor: #EEDDFF"]Since[n 1][/TH]
    [/TR]
    [TR]
    [TD]yotta[/TD]
    [TD="align: center"]Y[/TD]
    [TD]10008[/TD]
    [TD]1024[/TD]
    [TD="align: right"]1000000000000000000000000[/TD]
    [TD]septillion[/TD]
    [TD]quadrillion[/TD]
    [TD]1991[/TD]
    [/TR]
    [TR]
    [TD]zetta[/TD]
    [TD="align: center"]Z[/TD]
    [TD]10007[/TD]
    [TD]1021[/TD]
    [TD="align: right"]1000000000000000000000[/TD]
    [TD]sextillion[/TD]
    [TD]trilliard[/TD]
    [TD]1991[/TD]
    [/TR]
    [TR]
    [TD]exa[/TD]
    [TD="align: center"]E[/TD]
    [TD]10006[/TD]
    [TD]1018[/TD]
    [TD="align: right"]1000000000000000000[/TD]
    [TD]quintillion[/TD]
    [TD]trillion[/TD]
    [TD]1975[/TD]
    [/TR]
    [TR]
    [TD]peta[/TD]
    [TD="align: center"]P[/TD]
    [TD]10005[/TD]
    [TD]1015[/TD]
    [TD="align: right"]1000000000000000[/TD]
    [TD]quadrillion[/TD]
    [TD]billiard[/TD]
    [TD]1975[/TD]
    [/TR]
    [TR]
    [TD]tera[/TD]
    [TD="align: center"]T[/TD]
    [TD]10004[/TD]
    [TD]1012[/TD]
    [TD="align: right"]1000000000000[/TD]
    [TD]trillion[/TD]
    [TD]billion[/TD]
    [TD]1960[/TD]
    [/TR]
    [TR]
    [TD]giga[/TD]
    [TD="align: center"]G[/TD]
    [TD]10003[/TD]
    [TD]109[/TD]
    [TD="align: right"]1000000000[/TD]
    [TD]billion[/TD]
    [TD]milliard[/TD]
    [TD]1960[/TD]
    [/TR]
    [TR]
    [TD]mega[/TD]
    [TD="align: center"]M[/TD]
    [TD]10002[/TD]
    [TD]106[/TD]
    [TD="align: right"]1000000[/TD]
    [TD="colspan: 2, align: center"]million[/TD]
    [TD]1960[/TD]
    [/TR]
    [TR]
    [TD]kilo[/TD]
    [TD="align: center"]k[/TD]
    [TD]10001[/TD]
    [TD]103[/TD]
    [TD="align: right"]1000[/TD]
    [TD="colspan: 2, align: center"]thousand[/TD]
    [TD]1795[/TD]
    [/TR]
    [TR]
    [TD]hecto[/TD]
    [TD="align: center"]h[/TD]
    [TD]10002/3[/TD]
    [TD]102[/TD]
    [TD="align: right"]100[/TD]
    [TD="colspan: 2, align: center"]hundred[/TD]
    [TD]1795[/TD]
    [/TR]
    [TR]
    [TD]deca[/TD]
    [TD="align: center"]da[/TD]
    [TD]10001/3[/TD]
    [TD]101[/TD]
    [TD="align: right"]10[/TD]
    [TD="colspan: 2, align: center"]ten[/TD]
    [TD]1795[/TD]
    [/TR]
    [TR="bgcolor: #EEEEEE"]
    [TD="colspan: 2"][/TD]
    [TD]10000[/TD]
    [TD]100[/TD]
    [TD="align: center"]1[/TD]
    [TD="colspan: 2, align: center"]one[/TD]
    [TD]–[/TD]
    [/TR]
    [TR]
    [TD]deci[/TD]
    [TD="align: center"]d[/TD]
    [TD]1000−1/3[/TD]
    [TD]10−1[/TD]
    [TD="align: left"]0.1[/TD]
    [TD="colspan: 2, align: center"]tenth[/TD]
    [TD]1795[/TD]
    [/TR]
    [TR]
    [TD]centi[/TD]
    [TD="align: center"]c[/TD]
    [TD]1000−2/3[/TD]
    [TD]10−2[/TD]
    [TD="align: left"]0.01[/TD]
    [TD="colspan: 2, align: center"]hundredth[/TD]
    [TD]1795[/TD]
    [/TR]
    [TR]
    [TD]milli[/TD]
    [TD="align: center"]m[/TD]
    [TD]1000−1[/TD]
    [TD]10−3[/TD]
    [TD="align: left"]0.001[/TD]
    [TD="colspan: 2, align: center"]thousandth[/TD]
    [TD]1795[/TD]
    [/TR]
    [TR]
    [TD]micro[/TD]
    [TD="align: center"]μ[/TD]
    [TD]1000−2[/TD]
    [TD]10−6[/TD]
    [TD="align: left"]0.000001[/TD]
    [TD="colspan: 2, align: center"]millionth[/TD]
    [TD]1960[/TD]
    [/TR]
    [TR]
    [TD]nano[/TD]
    [TD="align: center"]n[/TD]
    [TD]1000−3[/TD]
    [TD]10−9[/TD]
    [TD="align: left"]0.000000001[/TD]
    [TD]billionth[/TD]
    [TD]milliardth[/TD]
    [TD]1960[/TD]
    [/TR]
    [TR]
    [TD]pico[/TD]
    [TD="align: center"]p[/TD]
    [TD]1000−4[/TD]
    [TD]10−12[/TD]
    [TD="align: left"]0.000000000001[/TD]
    [TD]trillionth[/TD]
    [TD]billionth[/TD]
    [TD]1960[/TD]
    [/TR]
    [TR]
    [TD]femto[/TD]
    [TD="align: center"]f[/TD]
    [TD]1000−5[/TD]
    [TD]10−15[/TD]
    [TD="align: left"]0.000000000000001[/TD]
    [TD]quadrillionth[/TD]
    [TD]billiardth[/TD]
    [TD]1964[/TD]
    [/TR]
    [TR]
    [TD]atto[/TD]
    [TD="align: center"]a[/TD]
    [TD]1000−6[/TD]
    [TD]10−18[/TD]
    [TD="align: left"]0.000000000000000001[/TD]
    [TD]quintillionth[/TD]
    [TD]trillionth[/TD]
    [TD]1964[/TD]
    [/TR]
    [TR]
    [TD]zepto[/TD]
    [TD="align: center"]z[/TD]
    [TD]1000−7[/TD]
    [TD]10−21[/TD]
    [TD="align: left"]0.000000000000000000001[/TD]
    [TD]sextillionth[/TD]
    [TD]trilliardth[/TD]
    [TD]1991[/TD]
    [/TR]
    [TR]
    [TD]yocto[/TD]
    [TD="align: center"]y[/TD]
    [TD]1000−8[/TD]
    [TD]10−24[/TD]
    [TD="align: left"]0.000000000000000000000001[/TD]
    [TD]septillionth[/TD]
    [TD]quadrillionth[/TD]
    [TD]1991[/TD]
    [/TR]
    [TR]
    [TD="bgcolor: #EEEEEE, colspan: 8"]

    ^ The metric system was introduced in 1795 with six prefixes. The other dates relate to recognition by a resolution of the CGPM.

    [/TD]
    [/TR]
    [/TABLE]
    [/TD]
    [/TR]
    [/TABLE]

    These prefixes were developed to shorten extremely large or small values, such as the teeny tiny mass of an electron (9.11 E -31 kg, or .000911 yg) in contrast to the very large Avogadro's number (6.022E23 atoms, or .6022 yotta atoms in one mole). When tacked onto constants, sometimes we don't realize just how intense these prefixes really are. Here are a few examples to help grasp the largeness and smallness of these constants:

    1. The Earth weighs 5,972 yotta grams, or 5.972E24 kg. It would take over 850 quintillion elephants to match this weight, or just over 81 moons.

    2. The average mass of a human cell is 950 femto grams, or 9.5E-13 g. If you cut a penny into a trillion pieces of equal mass, the human cell would still have a lower mass than the penny bit. AND you would get arrested for defacing US currency. It's simply a lose-lose situation.

    3. On earth, there are an estimated 7.059 G people (or 7.059 billion people). This is roughly 1000 times the number of pigeons in NYC. However, this is roughly 1/3 of the amount of hotdogs Americans consume in a year. (Yes really-- Americans chow down on an estimated 20 billion a year. That's about 70 hot dogs per person).

    Hope that was enlightening if not helpful!

    --Alpha Geek
  10. AlphaGeek

    Test Prep Splash

    By AlphaGeek,

    Hi everyone, just figured that I'd post an accumulation of what I've been studying for the test tomorrow morning. It goes in video order because that's the order that I learned the material in. If something is too vague, I reccomed looking at the video for elaboration

    Circuits

    Current and Current Density
    Resistors and Resistance
    Circuits
    Voltmeters and Ammeters
    Ideal and Real Batteries
    RC Circuits: Steady State
    RC Circuits: Transient Analysis (Charging)
    Current and Current Density:

    Current measured in Amps, or charge per sec.
    An electric field is applied to a conductor and a small field is created that opposes it
    Avg. Velocity of electrons in that field= drift velocity (Vd)
    Vol= Bh = Vd * change in time * Area
    # electrons = Volume * volume density(AKA "N")= N *change in time* Vd * Area
    I= N*q*Vd *A
    Current density = J* N*q*Vd
    I= integral (J * dA)
    J= I/A

    Resistance ("Howdy, Y'all!" made my day in that vid, btw)
    R=V/I
    p = row =resistivity
    R= pL/A
    V= IpL/A
    E=energy=V/L = p (I/A) = pJ
    W=qV
    I= dQ/dt
    P=IV=I2R=V2/R

    Circuits:

    Series: Req= R1 +R2...
    Parallel: 1/Req= 1/R1 +1/R2....
    Kirchhoff's Current Law= sum all current entering = sum all current exiting (conserv. charge)
    Kirchhoff's Voltage Law= sum of all potential drops in a closed loop of a circuit = 0 (conserv. energy)

    Voltmeters and Ammeters:

    Voltmeters: measures v between two points, high resistance, connected in parallel
    Ammeters: measures current, low resistance, connected in series

    Ideal and Real Batteries:

    Ideal: no internal resistance
    V battery = Emf = change in V

    Real: has internal resistance
    V battery = change in V = IR = Emf- (I)®, where r = internal resistance

    For battery:
    W= change in Q * Emf
    P= W/change in time = (change in Q)(Emf)/(change in time)
    P resistor (works for both external and internal) = I2R

    RC Steady State:
    series: 1/Ceq= 1/C1 + 1/C2 ...
    Parallel: Ceq = C1+C2...

    RC Charging:
    W= I2R
    U=1/2 C V2

    Time constant Tao=RC, occurs when quantity is 63% of its final value. 5 Tao= 99% final value (practically final value)

    Note: an uncharged capacitor acts like a wire, a charged capacitor acts like a gap in the circuit (AKA no current)

    ...Okay, bed time. Good luck tomorrow, everyone!
  11. AlphaGeek
    Credit to Mr. Powlin (who read this last year about the same time) and Snopes.com, where I found this humorous commentary once again. For those of you who did not hear this last Christmas or those who want to get into the spirit of the physics-filled holiday season, I thought I'd post this up for a few giggles. Happy Holidays, all! :snowman:

    No known species of reindeer can fly. BUT there are 300,000species of living organisms yet to be classified, and while most of these areinsects and germs, this does not COMPLETELY rule out flying reindeer which onlySanta has ever seen.
    There are two billion children (persons under 18) in the world.BUT since Santa doesn't appear to handle the Muslim, Hindu, Jewish and Buddhistchildren, that reduces the workload to 15% of the total — 378 million according to Population ReferenceBureau. At an average (census) rate of 3.5children per household,that's 91.8 million homes. One presumes there's at leastone good child in each.
    Santa has 31 hours of Christmas to work with, thanks to thedifferent time zones and the rotation of the earth, assuming he travels east towest (which seems logical). This works out to 822.6visits per second.
    This is to say that for each Christian household with goodchildren, Santa has 1/1000th of a second to park, hop out of the sleigh, jumpdown the chimney, fill the stockings, distribute the remaining presents underthe tree, eat whatever snacks have been left, get back up the chimney, get backinto the sleigh and move on to the next house. Assuming that each of these 91.8 million stops are evenly distributed aroundthe earth (which, of course, we know to be false but for the purposes of ourcalculations we will accept), we are now talking about .78 miles per household, a total trip of 75½ million miles, not counting stops to do whatmost of us must do at least once every 31hours, plus feeding andetc.
    This means that Santa's sleigh is moving at 650 miles per second,3,000 times the speed of sound. For purposes of comparison, the fastestman-made vehicle on earth, the Ulysses space probe, moves at a poky27.4miles per second — a conventional reindeer can run, tops, 15 miles per hour.
    If every one of the 91.8 million homes with good children were toput out a single chocolate chip cookie and an 8ounce glass of 2% milk, the total calories (needless to sayother vitamins and minerals) would be approximately 225 calories (100 for the cookie, give or take, and125 for the milk, give or take). Multiplying the number of calories per houseby the number of homes (225 x 91.8 x 1000000), we get the total number ofcalories Santa consumes that night, which is 20,655,000,000 calories. To breakit down further, 1 pound is equal to 3500 calories. Dividing our total number of caloriesby the number of calories in a pound (20655000000/3500) and we get the numberof pounds Santa gains, 5901428.6, which is 2950.7tons.
    The payload on the sleigh adds another interesting element.Assuming that each child gets nothing more than a medium-sized lego set (twopounds), the sleigh is carrying 321,300 tons, not counting Santa, who isinvariably described as overweight. On land, conventional reindeer can pull nomore than 300 pounds.Even granting that "flying reindeer" (see above) could pull TEN TIMESthe normal amount, we cannot do the job with eight, or even nine. We need214,200 reindeer. This increases the payload (not even counting the weight ofthe sleigh) to 353,430 tons. Again, for comparison, this is four times theweight of the Queen Elizabeth.353,000 tons traveling at 650miles per second createsenormous air resistance — this willheat the reindeer up in the same fashion as spacecraft re-entering the earth's atmosphere. The lead pairof reindeer will absorb 14.3QUINTILLION joules ofenergy. Per second. Each.
    In short, they will burst into flame almost instantaneously,exposing the reindeer behind them, and create deafening sonic booms in theirwake. The entire reindeer team will be vaporized within 4.26 thousandths of a second. Santa, meanwhile, will besubjected to centrifugal forces 17,500.06 times greater than gravity. A250-pound Santa (which seems ludicrously slim) would be pinned to the back ofhis sleigh by 4,315,015 pounds of force.
    In conclusion: If Santa ever DID deliver presents on ChristmasEve, he's dead now.
  12. AlphaGeek
    In an episode of Tom and Jerry from 1948, Tom once again has his face smashed in from a falling object. This time, the offender was a half-ounce canary wielding circular cage parts. The bird unfastened the cage bottom and let it drop onto the unsuspecting feline below, making Tom's face into a pancake. How much force does this pan actually make? Could it really damage a cat's face?


    [ATTACH=CONFIG]513[/ATTACH]


    First, we must find the velocity of the pan when it hits Tom's face. We know that the pan falls from rest, its acceleration is 9.81 m/s2, and the time it takes to fall from the cage to Tom is roughly 3 seconds (1:09 -1:12 in the youtube video). Using the equation Vf = Vi + at, we find that the velocity of the pan just before it comes into contact with Tom's face is 29.43 m/s.

    Let's estimate that the pan weighs roughly .1 kg (100 g). Also, let's estimate that the time it takes the plate to go from its initial velocity just before coming into contact with Tom's face and the time when it's final velocity reaches 0 m/s is roughly 1 tenth of a second (.1 s). We know that momentum is conserved in this situation and that (Force)(change in Time) = (mass)(change in velocity). Using this, we know that the change in velocity is -29.43 m/s, so the force of the pan on Tom is roughly 30 newtons. This is equal to roughly 6.7 lb of force.

    It takes anywhere from 7 to 9 lb of force to break a human nose, so even though it's not likely that the bird cage would've smashed the kitty's face in, he might very well lose his sense of smell.

    Here's a blast from the past composed of 40 % physics and 60% pain. Disclaimer: I do not promote domestic animal abuse, nor do I reccomend testing 7 lbs of force on your friend's nose.


    http://www.youtube.com/watch?v=MKyRRP43bh0&feature=related
  13. AlphaGeek
    Have you ever wondered how trampolines work? Anything fun or worthwhile has physics behind it, so let’s take a peek at the gymnast’s best friend:

    [ATTACH=CONFIG]497[/ATTACH]

    I hope you all enjoy my art skills. Read it and weep. :victorious:

    The magic behind a trampoline can be explained in terms of energy. Let’s say that a child is bouncing up and down on the trampoline. When the child is at a maximum height, his/her potential energy due to gravity is at a maximum. Because PE= mgh, with acceleration due to gravity and mass constant, his/her PE is the greatest because height is at a maximum. However, their kinetic energy is at a minimum of 0 because the child has a velocity of zero and KE= (1/2) m v^2. When the child is in contact with the trampoline and is as low as he/she will travel, his/her PE due to gravity is now at a minimum of zero because the height is zero. However, at this point the child’s kinetic energy is greatest because the velocity at this point is at a maximum. In addition, the potential energy due to the trampoline’s springs is at a maximum. Uspring (potential energy of the spring) is greatest at this point because the displacement x of the spring is greatest at this point and Uspring = (1/2) k x^2. In other words, the spring is at its maximum stretch possible for the child and wants to return to its state of rest, so it sends the child back into the air.

    If that AP B review didn't click, try watching the specimen V. vulpes exploring this bouncy apparatus. (CAUTION: Video has sound. If you're in the school library, please adjust volume level accordingly before proceeding).





    Ah, discovery.

    --'Geek out!
  14. AlphaGeek
    For those of you who don't know, there is a video section of the Aplus site that features videos of physics-y origin. You can get there by clicking the word "videos" on the top blue bar of the site.

    http://aplusphysics.com/community/index.php/videos/view-340-vector-despicable-me/

    When I first saw this video, it was floating among intense brain-teasing physics vids and real life examples of the science. I thought it deserved some defense for its place on the site, so let me explain what this despicable me mini clip has to do with physics.

    The most notable physics-feature of the video is that the geeky character's name is Vector, as he explains both verbally and through body language. A vector quantity is a magnitude with direction. For example, velocity is a vector quantity. A velocity of 3 m/s to the right has both units (meters per second) and direction (to the right). 3 m/s alone, a speed, is not a vector quantity because even though it has units, it does not have a direction. We call this a scalar quantity.

    I hope that explains Vectors joke, "I'm committing crimes with both direction and magnitude!" If he were the evil Dr. Scalar, it would only have magnitude. Haha! Ha. Ha... Ha.


    ...And I didn't notice this before, but when Vector first comes into the scene he crosses his arms while doing the "vulcan salute," which is actually the nerdfighter salute (You know! Vlogbrothers on youtube). I thought that was really cool. I wonder if it wasn't even supposed to be there in the first place, but some nerdy producer put it in

    Not familiar with vlogbrothers? Do acquaint yourself via nerd humor:





    ...Just for the record, my favorite part of the movie is as follows:


  15. AlphaGeek
    Many of you are familiar with the children’s movie happy feet, about a whimsical penguin chick that just can’t stop dancing. Why don’t these birds fly instead of dance, you ask? Let’s use physics to figure out why Mumble is aerially challenged:
    There are four main forces involved in avian air travel: lift, weight, drag, and thrust.
    As shown by the diagram of a blue jay in flight (credit to http://www.lcse.umn.edu), lift opposes weight and thrust opposes drag. A bird is able to fly when lift is greater that weight and thrust is greater than drag. Read below for more on these forces:
    1. Weight: Mass x acceleration due to gravity
    2. Lift: This force can be explained using Bernoulli’s principle—as a fluid’s velocity increases, the pressure decreases and vise versa. Bird wings are in an airfoil shape with a bump on the top and a smooth bottom (like an air plane wing). The air is forced to move faster over the top of the wing than on the bottom because it has a longer distance to travel over the bump. Like faster moving fluids, faster moving air causes the pressure on top of the wing to be lower than on the bottom of the wing, allowing the bird to lift upward.
    3. Drag: This force is caused by air resistance. The more aerodynamic the flier, the less drag that will act upon the flier.
    4. Thrust: This is the force created to push the bird forward. Birds create thrust by the backward push of their wing, like humans do when we push backward with our arms to swim in a pool. Plane propellers and jet engines create thrust for a plane.

    In short, the reason why Mumble cannot fly is because penguins store fat to keep themselves warm, increasing their weight. Their wings also are not the correct shape or size to produce enough lift to get into the air. Weight > Lift, therefore Mumble dances.

    Next time, lay off the fish.

    --AlphaGeek

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