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Kodėl dviratis negriūna, o lakūnas džiaugiasi? Kalta precesija!



Pratęsiant temą apie lėktuvus, norėčiau paklausti: kas bendro tarp lėktuvo, dviračio, žaislinio vilkelio (to, kur įsuki ir ilgai sukasi nenuvirsdamas) bei tokio šaunaus įrenginio, kaip SegWay?

Ogi giroskopas! Šaunus žodis, ane? Dar šūstresnį galiu pateikti: precesija.

Arba precesuoja :) Kad dar labiau apžavėti liktumėt, pažėkit filmuką:



Na, kai jau baigsis nuostabos šūksniai, skaitykit toliau.

Pradėkime nuo terminų: giroskopas yra toks diskas, kuris gali laisvai suktis, o ašis įtaisyta per centrą. O štai tas procesas, kai įsuktas ratas ne nusileidžia į horizontalią padėtį, o sukasi aplink šniūrą ir yra vadinamas precesija.

Na, pagal visus logikos dėsnius, mum jokio skirtumo, ratas sukasi, ar ne -jei jis, pakabintas ant šniūro per savo centrą, turi nusileisti į horizontalią padėtį, kai jo niekas nelaiko. Tačiau pasiaiškinkime, kodėl fizikos dėsniai šiuo atveju sako ką kitką.

Kadangi šįkart internete neradau manęs tenkinančių animacijų, teko papaišyti pačiam. Tikiuos pavyko padaryt pakankamai aiškiai.




Įsivaizduokime, kad turime ratą. Jis tiesiog kaba erdvėje, neveikiamas jokių jėgų. Jei pabandysime paveikti jo ašį mėlynai pažymėtų rodyklių kryptimi, jis pradės virsti žalių rodyklių kryptimi, nes bus veikiamas tos krypties jėgos (paspauskit trikampuką pažiūrėti, kaip atrodo judesy).



   

Daba žėkit žemiau esantį paveiksluką. Paleiskime tą ratą suktis. Ir taip pat mėlynų rodyklių kryptimi veikime ašį. Ratas vėl bus veikiamas jėga, nukreipta žalios ir raudonos rodyklių kryptimi ir norės virsti. Bet kas vyks toliau? Viršutinė rato dalis, paveikta raudonosios jėgos, iškart pajudės žemyn ir kartu nusineš jos sukeltą impulsą.  Kai ta jėga nukeliaus pusę rato iki apačios, atsitiks toks dalykas: apatinį tašką veiks iš viršaus atkeliavusi raudona jėga, bet tuo pačiu ir žalia jėga (ji niekur nedingo!). Jų dydžiai yra vienodi, tačiau kryptys - priešingos. Manau, iš mokyklos žinote, kad tokiu atveju galime sakyti, kad kūno neveikia JOKIA jėga. Pažiūrėti viskam, ką surašiau, paspaudžiam trikampuką:



     





Žinoma, tas pats vyks ir su jėga, kylančia iš apačios į viršų ir ten sunaikinančią esančią rodyklikę :) 

Kodėl mums tai įdomu? Ogi todėl, kad šitaip panaikiname priežastį rato virtimui ant šono - viršuje ir apačioje esančias jėgas. Tačiau kiekvienu laiko momentu iš viršaus žemyn ir iš apačios viršun keliauja krūvos tų rodyklių - gi ratas nuolat sukasi ir perneša impulsą iš apačioje ir viršuje gautų taškų. Bendrai paėmę gauname, kad kūnas veikiamas tik vientisomis rodyklėmis pažymėtomis krpyptimis (žr. paveikslą žemiau). O punktyru nupieštos viena kitą panaikina, tad jos neegzistuoja:


 

Viso šito reikalo galutinis rezultatas: jėgos verčiančios ratą virsti ant šono panaikintos, o verčiančios jį suktis juodos rodyklės kryptimi veikia. Tai ir yra vadinama precesija, mano brangieji!

 

Uh, net padusau aiškindamas :)

 

Atsipalaidavimui pažėkit, kokį gražų šposą galima su ta precesija iškrėsti, jei giroskopo masė ir stovo ilgis yra gerai parinkti:

 

 
   

Šitą dalyką tyriau per laboratorinius darbus. Labai šaunus aparatas pas mus labėj stovi precesijai tirti. Šiandien specialiai ten įsiveržiau ir pafilmavau :)

   


     

Kairėje pusėje įtaisytas pats giroskopas, o dešinėje - svertas. Kol diskas nesisuka, svertas nulenkia kairę pusę. Kai įjungiame sukimą, giroskopas stipriu judesiu ištiesina visą sistemą - atsistoja į jam malonia padėtį :) Žinoma, svertas vistiek nori atlikti savo darbą, tačiau giroskopas priešinasi ir vykstant precesijai visa sistema pradeda suktis aplink vertikalią ašį. Beje, būtent šio sukimosi (precesavimo) greitį man ir teko tirti. Tiksliau, to greičio priklausomybę nuo disko sukimosi greičio. Labai fainas darbas ;)

     

Ok, o daba grįžkime prie to, nuo ko pradėjome, t.y. klausimo: kaip giroskopas sieja lėktuvą, vilkelį, dviratį ir segvėjų? Na, apie vilkelį pasakot, turbūt, nereikia. Patys puikiai suprantat, kad tai pats paprasčiausias giroskopas, kuris įsuktas, nebenori virsti dėl precesijos. Dviračio giroskopiškumą jau irgi matėt pirmame video. Kai sukasi, pats ratas nebenori griūti. Ir kuo greičiau sukasi, tuo labiau stengiasi stovėti statmenai žemės. Todėl vaikai, besimokydami važiuoti ir bijodami nugriūti, vos bejudėdami patys sau daro meškos paslaugą: važiuojant greitai, dviratis pats laikytų lygsvarą! Kai mokysit savo vaikus važiuoti dviračiu, pirma paaiškinkit apie precesiją :D Štai lėktuvuose toks įtaisėlis labai pasitarnauja nustatyti, kiek jis yra pakrypęs. Jei giroskopą įtaisysime laisvai judančioje laikiklių sistemoje, jis vistiek suksis statmenai žemei, nepriklausomai, kaip vartysis lėktuvas. Tie laikikliai matuoja ir disko pakrypimą lėktuvo atžvilgiu (o tuo pačiu ir lėktuvo pakrypimą žemės atžvilgiu). Tad pilotas visada žino, kokioje padėtyje yra jo valdomas paukštukas. O štai segvėjuje giroskopas reikalingas tam pačiam, kaip ir lėktuvui: nustayti padėtį žemės atžvilgiu ir taip padidinti/pamažinti greitį, kad visas prietaisas sėkmingai važiuotų nenuvirsdamas!

     



Rodyk draugams

Komentarai (144)

  1. mishkas:

    :)

    jėga.. jamam tą fiziką :)

  2. Anonymous:

    "Jei giroskopą įtaisysime laisvai judančioje laikiklių sistemoje, jis vistiek suksis statmenai žemei, nepriklausomai, kaip vartysis lėktuvas."

    Aš ne fizikas, bet taip pamislijau, jei pakabinčiau bumbulą ant siulo, tai jis taip pat visada bus statmenai žemei, tai kodėl lėktuve naudojamas būtent giroskopas?

  3. Saulius:

    Jei lėktuvas apsivers aukštyn kojom iš tavo bumbulo mažai naudos bus :)

    Ale vat dabar gailiuos biški, kad man neišpuolė tas giroskopo darbas savo laiku :[

  4. eziukassukedais:

    turbūt nevisai aišku, kaip tas giroskopas lėktuve įtvirtinamas :)

    štai kaip: http://www.gyroscopes.org/showfull.asp?imagename=39.jpg

    kai diskas sukasi, stovą (arba lėktuvą) galime vartyti kiek širdis geidžia - giroskopas vistiek išliks toje pačioje padėtyje. o ties žeidų sujungimais įtaisius jutiklius, bua aišku, kiek kurioje ašyje lėktuvas yra pasviręs

  5. Andrius:

    Nepamirškit, kad ir kosminiuose laivuose, palydovuose bei zonduose navigacijai taip pat naudojamas giroskopas. Tskant, nustatei kursą ir skrisi tiksliai kaip galima. Tiksliau, negu naudojant bet kokią elektroniką (nenaudojant precesijos privalumų).

  6. Originalas:

    gaminam pigesnius lėktuvus ir ypač SegWay'us su bumbulais, tokius po toną pakabinam, ir ok, tikrai atsvers, bet ar pakils, tai… :DD

    Tarkim, kai lėktuvas sukas, jį dar veikia ir išcentrinė jėga, tai tavo bumbulas pieno riebumą rodytų, tikrai ne į žemę, atliekant manevrą. jis veiktų, jei lėktuvas stebuklingai kabėtų ore ir nejudėtų, tik vartytus apie savo ašį.

    mačiau kažkur internete 10kart pigesnį SegWay, visą mandravojimą su giroskopu ir kompu, pakeitus 3 ratu. genialu - kas paprasta. :DD

  7. eziukas:

    Originalai,

    perteikiu bazine info, kuri reikalinga suprasti pagrindiniams procesams. kai pats gaminsiu lektuvus, galesiu papasakoti ir apie atskirus giroskopo veikimo atvejus inercinese/neinercinese sistemose bei kitas subtilybes ;) deja, dabar zinau tik tiek, kiek surasiau cia

  8. Originalas:

    Čia Anonymous siūlė bumbulą ant siūlo vietoj giroskopo kabint, tipo į žemę rodytų.. :D

    Giroskopas daug greičiau sukas už patį lėktuvą, todėl ta lėktuvo išcentrinė jėga nieko nereiškia jam.

    Redagavo Originalas 2007-07-28 12:48

  9. ramulis:

    Atsimenu dariau laboratorinį darbą su giroskopu pirmam kurse. Tikrai įdomus dalykas ir įvairiai panaudojamas.

  10. tikiuosi nesupyksi, man labai referatui sita temyte tiko :D

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