Kinematics na wani abu aya: na asali Concepts, abubuwa

A topic na mu na yau labarin zai zama kinematics da kayan batu. Mẽne ne duk game da? Abin da Concepts bayyana a gare shi, kuma abin da definition kamata a bai wa wannan kalma? Wadannan da wasu tambayoyi a yau, kuma za mu yi kokarin amsa.

Fassara da ra'ayi

Kinematics abu aya ne fãce da kimiyyar lissafi karamin sashe mai suna "makanikai". Ta, bi da bi, da karatunsa da dokoki na motsi na daban-daban a jikinsu. Kinematics na wani abu aya ne ma hannu a cikin wannan aiki, amma shi ya aikata ba in general sharuddan. A gaskiya, wannan sub-sashe na bincika hanyoyin da bayyana kudirin na jikinsu. A cikin wannan binciken su dace da kawai da ake kira idealized jiki. Wadannan sun hada da: wani abu batu, wani m jiki da kuma wani manufa gas. Ka yi la'akari da matsalolin a daki-daki. Dukanmu mun san daga makaranta cewa wani abu batu ne da ake kira jiki, girman wanda a wani yanayin da ake ciki za a iya bari. Af, da kinematics na translational motsi na wani abu batu fara bayyana a karon farko a cikin bakwai sa litattafai akan kimiyyar lissafi. Wannan shi ne mafi sauki reshe, saboda haka su fara sani da kimiyya, tare da taimakon shi ne mafi m. A raba batun shi ne, abin da suke da abubuwa na kinematics da kayan batu. Su ne quite mai yawa, kuma suka za a iya yanaye kasu kashi dama matakan da daban-daban da wahala ga fahimta. Idan muka yi magana, misali, da radius vector, sa'an nan, bisa manufa, a cikin definition bã kõme ba ne prohibitively hadaddun. Duk da haka, yarda da cewa shi ne sauƙin fahimta shi ne zuwa ga dalibi fiye da talakawan dalibi ko makarantar sakandare. Kuma frankly magana, babu bukatar a bayyana siffofin da kalmar makarantar sakandare dalibai.

A takaice dai tarihi na kinematics

, Shekaru da dama da suka wuce, babban Aristotle kishin zaki ya share na free lokaci karatu da kuma kwatanta kimiyyar lissafi a matsayin mai raba kimiyya. A musamman ya yi aiki a kan kinematics, kokarin gabatar da shi ga babban maki kuma Concepts, ko ta wani hanya amfani a yunkurin warware m, kuma ko da mundane ayyuka. Aristotle ya ba da farko ra'ayin abin da suke da abubuwa na kinematics da kayan batu. Aikinsa da kuma rubuce-rubucen suna matukar muhimmanci da ga dukan bil'adama. Duk da haka, a cikin karshe, shi ya sa wani babba yawan kurakurai, kuma al'amarin shine cewa akwai wasu kurakurai da kuma kuskure. Works of Aristotle a lokacin zama sha'awar sauran masana kimiyya - Galileo Galilei. Daya daga cikin muhimman hakkokin theses sa a gaba ta hanyar Aristotle, karanta cewa jiki motsi faruwa ne kawai a yanayin saukan idan an amsa su wasu da karfi, m da tsanani da kuma shugabanci. Galileo ya tabbatar da cewa wannan shi ne kuskure. Force zai shafi gudun saitin, amma ba more. A Italiya ya nuna cewa karfi ne cikin hanyar da hanzari, kuma shi zai iya zama kawai yardatayya da shi. Galileo Galiley ma biya babba da hankali ga nazarin aiwatar da free fall, kawo dacewa dokokin. Kila kowa da kowa tuna, game da ya shahara gwaje-gwajen, wanda ya shafe a Hasumiyar Pisa. A cikin ayyukansu, da kayan yau da kullum kinematic mafita amfani da likita Ampere.

na farko Concepts

Kamar yadda aka ambata a baya, da kinematics na binciko hanyoyin da za a bayyana kudirin na idealized abubuwa. A yi, harsãshensa iya amfani ilmin lissafi analysis, talakawa aljabara da kuma lissafi. Amma abin da suke Concepts (wannan ra'ayi, kuma babu definition kuma parametric dabi'u) ne a zuciyar wannan karamin sashe na kimiyyar lissafi? Da farko, kowa da kowa ya kamata a fili gane cewa kinematics na translational motsi daga cikin kayan aya motsi la'akari ban da ikon yi. Wancan ne, don magance dacewa matsaloli, ba mu bukatar dabarbari da alaka da ikon. Yana ba a dauke kinematics, ko ta yaya yawa daga gare su akwai - daya, biyu, uku, ko da daruruwan dubbai. Duk da haka, kasancewar hanzari duk da haka bayar da. A wani yawan abu aya motsi kinematics matsaloli umurci ƙayyade hanzari darajar. Duk da haka, da Sanadin wannan sabon abu (ie, da kuma sojojin da yanayi) ba su dauke, kuma an tsallake.

rarrabuwa

Mun samu cewa kinematics bincika da kuma ya shafi hanyoyi don bayyana kudirin gawarwaki ba tare da game da sojojin aiki a kan su. Ba zato ba tsammani, wannan aiki da aka yi ga sauran sub-makanikai, da ake kira kuzarin kawo cikas. Riga akwai ake amfani da Newton dokokin, wanda damar a yi domin ayyana isasshen sigogi da kananan yawan da aka sani na farko data. Basic Concepts kinematics na kayan batu - shi ne sarari da kuma lokaci. Kuma dangane da ci gaban kimiyya a general kuma a cikin filin, akwai wata tambaya game da ya dace da irin wannan hade.

Daga farkon, akwai na gargajiya kinematics. Za mu iya cewa shi ne peculiar ba kawai gaban duka biyu na boko da na sarari gibba, amma suna zaman kanta da zabi wani musamman firam na reference. Af, za mu magana game da daga baya. Yanzu, kawai bayyana abin da shi ne game da. Sarari tazara a wannan harka za a dauke a matsayin kashi, lokaci - lokaci. Da alama cewa duk abin da ya kamata a bayyana a fili. Yanzu, wadannan gibba za a yi la'akari da na gargajiya kinematics cikakkar maras canjawa, a cikin wasu kalmomi, mai zaman kanta da mulki daga firam zuwa wani. Ko kasuwanci relativistic kinematics. Yana jinkiri a lokacin da ya sauya sheka tsakanin tunani Frames iya bambanta. Shi ne mai hikima to ko da cewa sun iya ba, kuma ya kamata, mai yiwuwa. Saboda wannan simultaneity na biyu bazuwar events kuma zama dangi da kuma shi ne batun musamman shawara. Saboda haka a cikin relativistic kinematics na biyu Concepts - sarari da kuma lokaci - ake hada a cikin daya.

Kinematics abu aya: gudun, hanzari, da kuma sauran dabi'u

Don a kalla kadan don fahimtar kimiyyar lissafi na wannan karamin sashe, dole ne ka kewaya mafi muhimmanci Concepts, san ma'anar da kuma wakiltar abin da ya ƙunshi a general sharuddan, da daya ko wasu darajar. Babu wani abu da rikitarwa game da shi sosai, yana da matukar sauki da kuma sauki. Ka yi la'akari da, watakila, a fara da asali Concepts amfani a cikin kinematics matsaloli.

motsi

Inji motsi, muka ɗauka a aiwatar a cikin abin da daya ko wani idealized abu ya canjãwa matsayinsu a sarari. A wannan yanayin, muna iya cewa canji ne dangane da sauran jikinsu. Wajibi ne a yi la'akari da cewa a lokaci guda daukan wuri da kuma kafa wani takamaiman lokaci tazara tsakanin abubuwa biyu. Alal misali, zai yiwu a ware wani tazara kafa domin lokacin elapsed tsakanin jiki zo daga wuri guda zuwa wani. Lura kuma cewa jiki da kuma ta haka za su iya hulɗa da juna, bisa ga dokokin general na makanikai. Wannan shi ne daidai abin da sau da yawa aiki kinematics da kayan batu. A reference tsarin - da wadannan ra'ayi, wanda aka inextricably nasaba da shi.

tsarawa

Su za a iya kira talakawa data cewa ƙyale mu mu sanin ko matsayi na jiki a kowace batu a lokacin. Tsarawa ake inextricably nasaba da manufar wani tunani tsarin da kuma tsara Grid. A mafi yawan lokuta ne mai hade da haruffa da lambobi.

radius vector

Daga cikin sunan shi ya zama a fili cewa shi ne. Duk da haka, bari mu magana game da shi. Idan wani batu motsa tare hanya, kuma mun san mafari ne na musamman firam na reference, yana yiwuwa ya rike mukamin vector a kowace lokaci. Ya za a shiga da farko matsayi na ma'ana da instantaneous ko guntun.

hanyar

Yana za a kira a ci gaba da layi wanda aka aza a sakamakon tashin wani barbashi a ba firam na reference.

Speed (duka mikakke kuma kusurwa)

Wannan darajar, wanda zai iya gaya yadda azumi jiki ke ta shiga wani lokaci na nesa.

Hanzari (da kusurwa da kuma mikakke)

Yana nuna a karkashin abin da dokar da kuma yadda maida canjãwa gudun saitin jiki.

Zai yiwu, a nan su ne - da babban abubuwa na kinematics da kayan batu. Ya kamata a lura cewa duka da gudu da hanzari ne vector yawa. Wannan yana nufin cewa ba su kawai da zanga-zanga sakamako, amma kuma wani shugabanci. Af, su za a iya directed a daya shugabanci da kuma a cikin m. A cikin farko idan, jikin za a kara a karo na biyu - to rage gudu.

A sauki ayyuka

Kinematics na wani abu nufi (gudu, hanzari da kuma nesa wanda shi ne kusan da muhimman hakkokin Concepts) yana ba har ma da cewa wata babbar lamba na matsaloli, da kuma da yawa daga cikinsu a daban-daban Categories. Bari mu yi kokarin warware wani sauki isa aiki domin sanin nesa tafiya ta jiki.

Zata da yanayin da muke da shi a hannunku, kamar yadda haka. The mota direba tsaye a kan farawa line. Mai aiki na samar da wani gani siginar flag da mota daukan kashe da cika fuska. Ƙayyade ko shi ne wani sabon rikodin a cikin gasar mahaya za su iya, idan nesa daidaita daya da ɗari mita, ya zarar shugaba a 7.8 seconds. Hanzari daga cikin abin hawa dauka daidai 3 mita, raba da square biyu.

Saboda haka, yadda za su magance wata matsala irin wannan? Yana da ban sha'awa, kamar yadda muka ana buƙatar ba to "bushe" da definition wasu sigogi. Ta haziqance up, kuma ya jũya a wasu halin da ake ciki da cewa diversifies aiwatar mafita da kuma search fihirisa. Amma abin da ya kamata mu shiryar da, da yadda za a tunkari aiki?

1. Kinematics na wani abu batu ya shafi yin amfani a yanayin saukan hanzari.

2. Yana aka zaci yanke shawara ta amfani da nesa dabara, domin shi ya bayyana a cikin na lamba darajar yanayi.

Mun warware matsalar a duk sauki. Don dauki wannan nesa dabara: S = VoT + (-) AT ^ 2/2. Mene ne ma'anar? Muna bukatar mu san yadda da yawa lokaci zai wuce racer kaddamarda nesa, sa'an nan kwatanta index tare da mai rikodin don gano zai doke shi ko ba. Don yin wannan, za mu ajiye lokaci domin shi ya samu da dabara: AT ^ 2 + 2VoT - 2s. Wannan bai zama ba fãce da quadratic lissafi. Amma da mota daukan kashe, yana nufin cewa da farko gudu ne daidai da 0. A lokacin da discriminant lissafi yanke shawara zai zama daidai da 2400 dole ne a cire ga tushen da search lokaci. Make up to na biyu gidan goma wuri: 48,98. Mun sami tushen lissafi: 48.98 / 6 = 8.16 seconds. Sai dai itace cewa da direba ba zai iya doke da data kasance rikodin.