Newton's Law of Gravitation : The Probervial Apple

   

The famous story that Isaac Newton came up with the idea for the law of gravity by having an apple fall on his head is not true, although he did begin thinking about the issue on his mother's farm when he saw an apple fall from a tree. He wondered if the same force at work on the apple was also at work on the moon. If so, why did the apple fall to the Earth and not the moon?

Along with his Three Laws of Motion, Newton also outlined his law of gravity in the 1687 book Philosophiae naturalis principia mathematica (Mathematical Principles of Natural Philosophy), which is generally referred to as the Principia.http://physics.about.com/od/classicalmechanics/a/gravity.htm

Johannes Kepler (German physicist, 1571-1630) had developed three laws governing the motion of the five then-known planets. He did not have a theoretical model for the principles governing this movement, but rather achieved them through trial and error over the course of his studies. Newton's work, nearly a century later, was to take the laws of motion he had developed and apply them to planetary motion to develop a rigorous mathematical framework for this planetary motion.

Gravitational Forces

Newton eventually came to the conclusion that, in fact, the apple and the moon were influenced by the same force. He named that force gravitation (or gravity) after the Latin word gravitas which literally translates into "heaviness" or "weight."

In the Principia, Newton defined the force of gravity in the following way (translated from the Latin):

Every particle of matter in the universe attracts every other particle with a force that is directly proportional to the product of the masses of the particles and inversely proportional to the square of the distance between them.

Mathematically, this translates into the force equation shown to the right. In this equation, the quantities are defined as:

• F  = The force of gravity  in newtons
• G = The gravitational constant, which adds the proper level of proportionality to the equation. The value of G is 6.67259 x 10^-11 N * m² / kg², although the value will change if other units are being used.
• m₁ ,  m₁ = The masses of the two particles in kilograms
• r = The straight-line distance between the two particles in meters

Interpreting the Equation

This equation gives us the magnitude of the force, which is an attractive force and therefore always directed toward the other particle. As per Newton's Third Law of Motion, this force is always equal and opposite. Click on the picture to see an illustration of two particles interacting through gravitational force.

In this picture, you will see that, despite their different mass and sizes, they pull on each other with equivalent force. Newton's Three Laws of Motion give us the tools to interpret the motion caused by the force and we see that the particle with less mass (which may or may not be the smaller particle, depending upon their densities) will accelerate more than the other particle. This is why light objects fall to the Earth considerably faster than the Earth falls toward them. Still, the force acting on the light object and the Earth is of identical magnitude, even though it doesn't look that way.

It is also significant to note that the force is inversely proportional to the square of the distance between the objects. As objects get further apart, the force of gravity drops very quickly. At most distances, only objects with very high masses such as planets, stars, galaxies, and black holes have any significant gravity effects.

Center of Gravity

In an object composed of many particles, every particle interacts with every particle of the other object. Since we know that forces (including gravity) are vector quantities, we can view these forces as having components in the parallel and perpendicular directions of the two objects. In some objects, such as spheres of uniform density, the perpendicular components of force will cancel each other out, so we can treat the objects as if they were point particles, concerning ourselves with only the net force between them.

The center of gravity of an object (which is generally identical to its center of mass) is useful in these situations. We view gravity, and perform calculations, as if the entire mass of the object were focused at the center of gravity. In simple shapes - spheres, circular disks, rectangular plates, cubes, etc. - this point is at the geometric center of the object.

This idealized model of gravitational interaction can be applied in most practical applications, although in some more esoteric situations such as a non-uniform gravitational field, further care may be necessary for the sake of precision.

Reference :

http://physics.about.com/od/classicalmechanics/a/gravity.htm

Physics with JAVA APPLETS

Click the following site to view Java Applets for Physics

                 Using Java  applets for Physics

Physics E 101 Lesson 2 : Vector and Scalar Quantities

To find the resultant of vectors click the following site :

Vectors

For an Online Graphing Calculator, click the following site :
( useful in Mathematics for drawing graphs )

Math Graph

Language 102 Vocabulary 1

Vocabulary words :                                   Country                                People

            hata – flag                               Doitsu – Germany                  Doitsujin – German

            hako – box                              Kanada –  Canada                  Kanada jin – Canadian

            neko – cat                               Chugoku – China                    Chugoku jin – Chinese

            uchi / ie – house                      Indo – India                             Indojin – Indian

                                                            Roshia – Russia                      Roshiajin – Russian

 The Parts of the body :

            karada – body                         koshi – hips                             atama – head                         

            ude – arms                              kao – face                               ke – hair

            hana – nose                            te – hands                               kuchi – mouth

            hiza – knees                            hoho – cheeks                        kubi – neck

            hitai – forehead                       tekubi – wrist                           me – eyes

            ashi – legs ( foot )                   ago – chin                               kata – shoulders

            mimi – ears                             kuchibiro – lips                         hifu – skin 

            senaka – back                        hige – beard                            wakinoshita – armpit

            mayuge – eyebrow                 shita – tongue                         mune – chest

            kakato – heels                         hara – stomach                       yubi – fingers

            ha – tooth                                chi – blood                               hone – bone

            iki – breath                              tsume – fingernails                  noo – brain

            shinzoo – heart                      hai – lung                                 chichi – breast

STUDY OF THE FIVE W’s

        Who, what, where, when and why or the 5 W’s in the English language are used in asking questions. The same principles and uses in asking questions in Nihongo and the ka is used in place of a question mark.

           1.  dare – who                         3.  doko – where               5.  doshite / naze – why

           2.  nani ( nan ) – what             4.  itsu – when

  Examples :   

         1.  Dare desu ka or donata desu ka.          Who are you ? ( donata more polite than dare.

         2.  Nan desu ka.                                          What is it ?

         3.  Nani ga arimasu ka.                               What is there or What have you ?

         4.  Doko desu ka.                                        Where is it ?

         5.  Kare / Kanojo wa doko ni imasu ka.       Where is he / she ?

          6.  Doshite kimasu ka.                                Why do you come ?

          7.  Itsu kimasu ka / itsu ikimasu ka.            When do you come ? / When do you go ?

  Exercises :

     1.  Hon wa doko ni imasu ka.                       Where are the book ?

     2.  Ano hito wa dare desu ka.                     Who is that man ?

     3.  Anata wa doko ni ikimasu ka.                 Where are you going ?

     4.  Kutsu wa doko ni arimasu ka.                Where are the shoes ?

     5.  Kami wa doko ni arimasu ka.                  Where is the paper ?

     6.  Ringo wa doko ni imasu ka.                    Where are the apples ?

     7.  Kaban wa doko ni imasu ka.                   Where is the bag ?

  New words :

 1.  kago – basket         7.  heya – room                   13.  omoi – heavy

 2.  hako – box              8.  ringo – apple                  14.  nimots’(nimotsu) – baggage, luggage

 3.  mado – window     9.  mikan – orange              15.  kaban – bag, brief case, traveling bag 

 4.  mizu – water         10. donata  no – whose       16.  ts’tsumi ( tsutsumi ) – a package, a bundle

 5.  kutsu – shoes        11. okii – large, big               17.  shobai – business, trade, profession

 6.  ki – tree                  12.  chisaii – small, tiny       18.  karui – light ( in weight )

Lesson 3 :    PERSONAL PRONOUNS

  Singular form                         Plural form

  1.  watashi  –  I               watakushidomo / watashi tachi   –  we

  2.  anata      –  you          anata tachi / anata gata               –   you

  3.  kare        –  he            karera                                          –   they

       kanojo     –  she          kanojo tachi                                 –   they

Possessive pronouns :  Use  no  to show possession after the personal pronouns :

    watashi no  –  my          watashi tachi no                         –  our

    anata no      –  your        anata tachi no/ anata gata no    –  your

    kare no        –  his           karera no                                   –  their

    kanojo no    –  her           kanojo tachi no                           –  their

  Note:

      1.  “tachi” or “ra” means plural in number.

      2.  “karera” is used when referring to a group composed of males and females. “karera” being the plural male form of “he” ( they ) naturally dominate and encompasses “kanojo” ( they for females ).

 Vocabulary words 

    hoteru – hotel                         shumi – hobby                        kuruma – car

    sekken – soap                        zasshi – magazine                 shimbun – newspaper

    byooin – hospital                    tomodachi – friend                  kabe – wall

    kaisha – company, office        eiga – movie                          hankachi – handkerchief

    tokei – watch                          saifu – wallet                         kaaten – curtain

    doa – door                              kuuraa – air conditioner   

  Examples :  “no”  used as possessive adjective

  1.  Kore wa anata no sekken desu.                This is your soap.

  2.  Are wa watashi no ie desu.                        That is my house.

  3.  Kore wa kare no kuruma desu.                 This is his car.

  4.  Kore wa Tanaka san no kaban desu.        This is Mr. Tanaka’s bag.

  5.  Anata no shumi wa nan desu ka.              What is your hobby?

“no”  used as descriptive adjective

   6.  Kore wa Nihon no kuruma desu.               This is a Japanese car.

   7.  Tani san wa eigo no sensei desu.             Mr. Tani is an English teacher.

   8.  Are wa Amerika no eiga desu ka.             Is that an American movie ?

    

     Note :  The particle “no” placed between two nouns usually makes the first noun the modifier of the second noun. Thus, “watashi no tomodachi” means my friend. This no usually corresponds to “of” or ‘s.

            Anata no tomodachi – your friend.                              Sato-san no kuruma – Mr. sato’s car

            Watashi tachi no shimbun – our newspaper               watashi no tokei – my watch

   

 Common occupations

    kaikei-gakari – accountant         ginkoo-in – bank employee               ten-in – sales clerk

    eiyooshi – nutritionist                 kaisha-in – company employee        shachoo – company president

    gaikookan – diplomat                 isha – doctor                                     ha-isha – dentist

    kangofu – nurse                        taishikan-in – embassy employee     gishi – engineer

    jaanarisuto – journalist              untenshu – driver                              shufu – housewife

    bengoshi – lawyer                    iyayu – actress                                  ongakuka – musician

    danyu – actor                            jimu-in – office worker/ clerk            kookanshu – operator (telephone)

    gaka – painter                            keikan – policeman                            koomu-in – public servant

    bijinesuman – businessman       scholar – gakusha                            gakusei – student

    sakka – writer                            hisho – secretary                             kankoo gaido – tour guide

    gaadoman – security guard       uketsukegakari – receptionist          sensei / kyoshi – teacher

     sojiin – cleaner (janitor)               keeji – detective                             yosaichi – dressmaker

     sejyusi – pilot                               syomin – merchant                        jitsugyoka – businessman

     roodoosha – worker/ laborer      hooka – farmer                              taiku – carpenter

     bobi – waiter                                kasyu – singer                              jugjoin – employee

     gyohu – fisherman                       romusya – laborer                        bengoshi – lawyer

     syosetsuka – novelist                  shimbunkisya – journalist             daijin – minister

     kikaiko – mechanic

Languages: 

   Go – means language. It  is used as a suffix in one’s country denoting his / her native language.

            Chuugokugo – Chinese language                  Nihongo – Japanese language

            Firipingo – Filipino language                           Eigo – English language

            Kankokugo – Korean language                      Supeingo – Spanish language

            Doitsugo – German language                         Indogo – Indian language

            Taigo – Thai language                                    Gaikokugo – Foreign language

   Expression to tell how one looks like :

              1.  mitai desu  –  look (s) like                2.  ni miemasen – do (es) not look alike

  Example : 1.  Anata wa Nihonjin mitai desu.           You look like a Japanese.

                  2.  Anata wa Doitsujin ni miemasen.       You don’t look like a German.

 Basic grammar : 

           1.  Anata wa Kato san desu ka.    Are you Mr. Kato ?

           2.  Hai, soo desu.                           Yes, I am.

           3.  Kore wa saifu desu ka.             Is this a wallet ?

           4.  Iie, chigaimasu.                         No, it isn’t.

           5.  Are wa sekken desu ka.           Is that a soap ?

           6.  Hai, soo desu.                           Yes, it is.

           7.  Kore wa nan desu ka.               What is this ?

           8.  Kore wa hon desu ka.               Is this a book 

           9.  Iie, chigaimasu.                         No, it isn’t.

          10. Kore isu desu ka.                       Is this a chair ?

          11. Hai, soo desu.                            Yes, it is.

          12. Are wa isu desu ka.                   Is that a chair ?

          13. Iie, chigaimasu.                          No, it isn’t.

          14.  Kore wa mado desu ka.            Is this a window ?

          15.  Iie, sore wa doa desu.               No, that is a door.

Note :

            “Hai soo desu”, is use to affirm a statement said by the other party. This is used in reply 

     only to a “be – verb”. For instance, an American is ask “Amerikajin desu ka.”  The American 

     can affirm by answering “Hai, soo desu” or “Iie, chigaimasu” to deny the truth of a statement 

     said by another person.  Literally, “Iie, chigaimasu” means  “No, its different”.

   Daily Expressions :

      1.  Shitsurei shimasu. / Sumimasen              Excuse me.

      2.  Gomen nasai. / Sumimasen deshita         I’m sorry.

      3.  Ojama itaashimasu.                                   Sorry to disturb you.

      4.  Ojama itashimashita.                                 Sorry to have disturbed you.

      5.  Doozo ohaire kudasai.                               Please come in. 

      6.  Doozo okake kudasai.                               Please sit down. 

      7.  Arigatoo gozaimasu.  .                              Thank you. 
      8.  Doo itashimashite. .                                   Don’t mention it.

      9.  Chotto matte kudasai.                                Wait a moment please.

    10.  Koko de matte ite kudasai.                       Wait here till I get back.

    11.  Omatase itashimashita.                            I am sorry to have kept you waiting.

    12.  Sonomama omachi kudasai.                   Hold your line please.

    13.  Hanashichuu desu.                                 Line is busy.

    14.  Sayoonara.                                             Good bye.  

    15.  Oyasumi nasai.                                       Goodnight

    16.  Itte mairimasu.                                         I’m going out  or  I’m leaving.

    17.  Itte rasshai.                                             Good bye, have a nice time.

    18.  Tadaima.                                                 I am back.

    19.  Okaeri nasai.                                          Welcome back.