A Vector ubuningi physics. Izibonelo Vector nenani

Physics kanye mathematics ngeke akwenze ngaphandle welithi "eliningi vector." Kuyadingeka ukuba bazi futhi bafunde, futhi bakwazi isebenze ngayo. Lokhu kufanele nakanjani sizofunda ukuthi singazigwema kanjani ukudideka futhi ukugwema amaphutha oyisiphukuphuku.

Indlela ukuhlukanisa value scalar kusuka Vector?

Eyokuqala njalo has isici esisodwa kuphela. Lena inombolo yakhe. izinto eziningi kakhulu scalar kungaba amanani okuhle nokubi. Izibonelo zazo zingaba i icala kagesi noma umsebenzi lokushisa. Kodwa kukhona scalars ukuthi ngeke likwazi ukuthi limbi, ezifana ubude nesisindo.

A Vector ubuningi, ngaphandle inani lenombolo ukuthi njalo ezithathwe inani eliphelele, libhekene kanye nokuqonda. Ngakho-ke, kungashiwo emelelwa imidwebo, okungukuthi, ngesimo umcibisholo, ogama ubude ilingana amanani wemfihlo okuhloswe indlela ethile.

Lapho ebhalela Vector ubuningi ngamunye luchazwa ngegama uphawu umcibisholo incwadi. Uma kuziwa yinani lenombolo, umcibisholo Akulotshiwe yini ukuthi, noma uphuzwe modulo.

Isiphi isinyathelo uvame kwenziwe nge zithwala?

Okokuqala - sifaniso. Zingase alingane noma cha. Esimweni sokuqala modules ezifanayo. Kodwa lokhu akulona isimo kuphela. Kufanele usazoba iziqondiso ezifanayo noma okuphambene. Esimweni sokuqala, kufanele ngokuthi zithwala alinganayo. Okwesibili, kukhona okuphambene. Uma kungenjalo wagcwalisa ngisho eyodwa nale mibandela, khona-ke zithwala are lingana.

Bese kufika kwalokho. It kungenziwa ngu izimiso ezimbili: unxantathu noma parallelogram. Eyokuqala kudinga ekuhlehlisweni esokuqala vector, bese kusuka ekupheleni lesibili. unezela umphumela uyoba umuntu ofuna ukuba abambelele ukuphela lokuqala yesibili.

Umthetho lo parallelogram engasetshenziswa uma kubalulekile walala Vector ubuningi physics. Ngokungafani umthetho wokuqala, lapho kufanele zihlehlise ngomunye iphuzu. Khona-ke uziqede a parallelogram. Waba yini umphumela wesibindi isenzo kumelwe zibhekwe njengezindawo okungamelwe diagonal we parallelogram sisuselwa iphuzu elifanayo.

Uma vector is sisuswe nezinye, zizophinde lihlehlisiwe kusuka kwelinye iphuzu. Kuphela umphumela uba vector, okuyinto ezokwenzeka ukuthi we imisiwe ekupheleni lesibili kuze kube sekupheleni kuqala.

Yikuphi zithwala basafunda physics?

Ziyakwazi ngokufana nomtwana scalar. Ungakwazi nje khumbula ukuthi iyiphi nenani Vector-physics khona. Noma ukwazi izimpawu ngazo ingabalwa. Kulabo abakhetha ukhetho lokuqala, leli thebula ziwusizo. Linikeza Vector eziyisisekelo lucobo.

Symbol ku-formula	igama
v	isivinini
r	ukufuduka
futhi	ukusheshisa
F	amandla
r	umfutho
E	kagesi emkhakheni umfutho
I	lokungeniswa kazibuthe
M	mzuzu amandla

Manje okuncane mayelana ezinye zalezi amagugu.

Inani lokuqala - ijubane

Njengoba kubalulekile ukuqala ukunikeza izibonelo Vector kobukhulu. Lokhu kungenxa yokuthi kuba ezijwayele ngaphezulu phakathi kuqala.

Speed lichazwa ngokuthi isici komzimba emkhathini. Yena unikezwa value kwamanani futhi beqondiswa nguye. Ngakho-ke, the velocity kuyinto ubuningi vector. Ngaphezu kwalokho, kungenziwa ihlukaniswe zilwane. Esokuqala Isivinini komugqa. It is yaphathwa ukucabangela of rectilinear iyunifomu ezinyakazayo. Nokho, kuvela ukuthi indlela isihlobo siwela umzimba ngesikhathi ukunyakaza.

Ifomula efanayo kwamukelekile isebenziseke ezinyakazayo non-iyunifomu. Kuphela ngaleso sikhathi kuyoba isilinganiso. Futhi nenani lesikhathi ofuna ukhethe, kumele kube njengoba encane ngangokunokwenzeka. Sivame zero isikhathi Isivinini isikhawu inani lingu leso kakade.

Uma sicabanga ukuhamba kabi amandla akhe, kukhona njalo ijubane - eliningi vector. Phela, kubalulekile ukubola ku izingxenye iqondiswe kanye Vector ngamunye ukuqondisa Ukudidiyela imigqa. Ngaphezu kwalokho, lokhu kubizwa ngokusentshenziswa a esuselwe vector engaba, uthethe isikhathi.

Eyesibili value - amandla

Ithola elithile ukushuba umthelela bafakela umzimba ngamanye imizimba noma amasimu. Njengoba amandla - eliningi vector, kufanele ngentengo yaso nokubaluleka isiqondiso. Njengoba enza umzimba, kubalulekile futhi ukhombe okwakukhona kuzo amandla sisetshenziswa. Ukuze uthole kuvumelana kwetinhlavu amandla zithwala, ungakwazi ubheke Ithebula elilandelayo.

amandla	Iphuzu lokusebenza	isiqondiso
kobukhulu	umzimba isikhungo	iSikhungo Zomhlaba
adonsela phansi jikelele	umzimba isikhungo	enkabeni komunye umzimba
kuyaqina	indawo yokuxhumana yemizimba uxhumana	ukuze simelane namathonya zangaphandle
friction	phakathi evele ixhumana	kolunye uhlangothi ukunyakaza

Ubuye eliningi Vector ungamandla net. Lokhu kubizwa ngokusentshenziswa sakho konke esebenza emzimbeni amabutho lokukhanda. Ukuze ubone ukuthi kubalulekile ukwenza ukwengeza isimiso kokubusa unxantathu. Badinga kuphela uyephuza zithwala ngesikhathi kusuka ekupheleni kwalowo odlule. Umphumela walokhu uyoba umuntu exhumanisa ekuqaleni lokuqala kuze kube sekupheleni lakamuva.

Esesithathu value - yisa

Phakathi ukunyakaza komzimba uchaza umugqa ezithile. Ibizwa ngokuthi trajectory. Lo mugqa kungaba zihluke kakhulu. Kubalulekile kokuthile okungaphezu nje kokubukeka yayo, futhi ekuqaleni nasekupheleni kwale nhlangano. Basuke exhunywe ingxenye, okuthiwa ukunyakaza. Lokhu kubuye eliningi vector. Futhi njalo iqondiswe kusukela ekuqaleni ukunyakaza ukuze afinyelele eqophelweni lapho ukunyakaza inqanyuliwe. Lumelela ke lasemukela lesi Latin incwadi r.

Lapha, ungathola umbuzo olandelayo: "Indlela - eliningi Vector?". Ngokuvamile, le nkulumo ayilona iqiniso. Indlela alinganayo endleleni obuphelele futhi ayinaso isiqondiso esithile. Okungabalulwa isimo uma zibhekwa yomugqa oqondile ezinyakazayo kwelinye direction. Khona-ke ubukhulu ukubaluleka ukufuduka kuvumelana indlela kanye isiqondiso wabo ezifanayo. Ngakho, lapho ucabanga ukunyakaza kanye umugqa oqondile ngaphandle kokushintsha kokuqondisa yezokuvakasha endleleni kungafakwa izibonelo Vector kobukhulu.

Eyesine value - ukusheshisa

Kuyinto isici isivinini ushintsho ijubane. Ngaphezu kwalokho, ukushesha kungenzeka kokubili emihle nemibi. Esikhathini ukugijima ngqo kuqondiswe isivinini okukhulu. Uma ukuhamba senzeka endleleni lwalugobile ke ukusheshisa yayo vector ubola ku izingxenye ezimbili, enye yazo kuqondiswe maphakathi ugobile engaba.

Ukwabela isilinganiso futhi leso ukusheshisa value. Eyokuqala kufanele ibalwe njengoba isilinganiso ngesilinganiso Ukushintshwa isikhathi esithile ukuba lesi sikhathi. Uma ukuzama cabanga isikhawu zero abonisa ukusheshisa ngokuphazima kweso.

Inani wesihlanu - ishayela

Kwenye indlela ibizwa ngokuthi umfutho. Pulse Vector ukubaluleka kungenxa yokuthi okuhlobana ngokuqondile ijubane futhi amandla isetshenziswa emzimbeni. Bobabili babe isiqondiso bese usetha inhliziyo yakhe yaqala ukushaya.

Ngu definition, lona wamuva iwumkhiqizo esisindo ku izinga. Ukusebenzisa umqondo we umfutho semtimba, kungenzeka kwenye irekhodi elaziwayo umthetho Newton. It kuvela ukuthi ushintsho umfutho iwumkhiqizo amandla ngesikhathi sokuphumula.

Ngo-physics, indima ebalulekile kuyinto nokongiwa umfutho, okubonisa ukuthi irherho le-closed zemizimba umfutho walo Imininingwane kuyinto njalo.

Thina ahlelwe kancane, lapho izindinganiso (vector) bafundelwa Yiqiniso physics.

Umsebenzi umthelela inelastic

Isimo. On the komzila kuyinto platform umile. Ukuze imoto yakhe esondela ngesivinini 4 m / s. platform IMisa nemoto - 10 no-40 amathani ngokulandelana. Imoto hits platform kukhona coupler. Kuyadingeka ukuba abale ngesivinini uhlelo, "inqola" emva umthelela.

Isinqumo. Okokuqala, notation kufanele ifakwe: isivinini semoto phambi umthelela - v _1, le nqola yesikhulumi emva donsa - v, m nenqwaba ukuthutha _1, yesikhulumi - m _2. Ngokusho inkinga ukubaluleka the velocity v sokwazi.

Imithetho ukuxazulula imisebenzi enjalo adinga kwendikimba uhlelo izithombe ngaphambi nangemva ukuphendula. I OX-eksisi kunengqondo ukuthumela eduze komzila e isiqondiso lapho imoto ihamba.

Ngaphansi kwalezi zimo uhlelo angabhekwa izinqola ivaliwe. Lokhu kunqunywa yokuthi amabutho angaphandle kungenziwa dengwane. Amandla adonsela phansi futhi phansi ukuphendula olinganiselayo nokungqubuzana ngokumelene komzila kungukuthi kunakwe.

Ngokomthetho ukulondolozwa umfutho, Vector yabo afingqa nokuxhumana semoto yesikhulumi okuvamile elihlangana emva umthelela. Okokuqala, endaweni yesikhulumi ongahlabeki umxhwele, ngakho ishayela yayo zero. Ukuhambisa kuphela imoto, umfutho walo - umkhiqizo m ₁ kanye v _1.

Njengoba isiteleka inelastic, okusho inqola wabambana emsamo, bese eqala Roll kanye luhamba luye ohlangothini olulodwa, umfutho awushintshanga isiqondiso uhlelo. Kodwa incazelo yalo wayehlukile. Okungukuthi, umkhiqizo yesamba nenqwaba imoto yesikhulumi futhi ijubane edingekayo.

Asikwazi nokubhala lokhu kwesibalo: m ₁ v ₁ * = (m ₁ + m ₂₎ * v. Ke kuyoba yiqiniso ngoba projection we-vector umfutho kuya axis ekhethiwe. Ngoba kulula baphethe kwesibalo esidingeka ukubala ijubane oyifunayo: v = m ₁ * v ₁ / (m ₁ + m _2).

Ngokusho imithetho kufanele idluliselwe ukubaluleka isisindo e amathani isisindo. Ngakho-ke, ukuze kufakwe esikhundleni wabayisa ifomula kufanele kuqala iphindwe nenani eyaziwa ayizinkulungwane ngayinye. izibalo ezilula ukunikeza inani 0.75 m / s.

Impendulo. inqola ngesivinini yesikhulumi 0.75 m / s.

Inkinga nge division zibe izingxenye zomzimba

Isimo. Speed ezindizayo amabhomu 20 m / s. It is igqekezwe kuzicucu ezimbili. IMisa lokuqala 1.8 kg. It uqhubekela ohlangothini lapho amabhomu flying ngesivinini 50 m / s. Lesi siqeshana yesibili has a isisindo 1.2 kg. Kuyini ijubane layo uma igijima?

Isinqumo. Ake ubungako izingcezwana okhonjiswe izinhlamvu m ₁ m _2. rates abo ngeke ngokulandelana v ₁ kanye v _2. Izinga kokuqala amabhomu - v. Esikhathini umsebenzi udinga ukubala inani v _2.

Ukuze shard nakakhulu yaqhubeka ukuhambisa luhamba luye ohlangothini olulodwa njengoba lonke emhlophe, kanti eyesibili ezindiza kolunye uhlangothi. Uma ukhetha isiqondiso ahlangene leyo eyayiphethe umfutho kokuqala, futhi ngemva kokuhlephula a shard esikhulu endiza eksisi, nabancane - ngokumelene Axis.

Lo msebenzi kuvunyelwe ukusebenzisa umthetho ukulondolozwa umfutho ngenxa yokuthi ukuthi amabhomu aphule kwenzeka ngokuphazima kweso. Ngakho-ke, naphezu kweqiniso lokuthi le amabhomu kanye ingxenye amandla adonsela phansi, akanayo yisikhathi sokuthatha isinyathelo futhi ushintshe isiqondiso Vector umfutho libe modulo.

Inani Vector nenani umfutho ngemva isiqhumane nguye beza phambi kwakhe. Uma sibhala umthetho ukulondolozwa umfutho sehlangano e projection ku OX-eksisi, khona-ke izobukeka kanje: (m ₁ + m ₂₎ * v = m * v _{1 1} - m ₂ * v _2. Kusukela kube lula ukuveza ijubane oyifunayo. Okunqumayo ifomula: v ₂ = ((m ₁ + m ₂₎ * v - m ₁ * v ₁₎ / m _2. Ngemva esikhundleni lamanani zezinombolo etholwe izibalo, futhi 25 m / s.

Impendulo. Ijubane isinqamu elincane 25 m / s.

Inkinga mayelana engela shot

Isimo. Esikhathini mass M isethwe platform isikhali. Kulo shot projectile mass m. Isuka i-α-engeli enezingqimba nge v Isivinini (unikezwa isihlobo emhlabathini). Ufuna ukwazi ukubaluleka ijubane platform emva kokudubula.

Isinqumo. Kulesi msebenzi, ungasebenzisa umthetho ukulondolozwa nomfutho projection phezu OX axis. Kodwa kuphela esimweni lapho projection sangaphandle amabutho nomphumela zero.

Wokuqondisa OX-eksisi ukukhetha isiqondiso lapho projectile fly, futhi zifana kuya umugqa ovundlile. Kulokhu, projection amabutho-gravity kanye nokuphenyisisa ukusabela floor OX kuyoba zero.

Inkinga isixazululekile ngefomu jikelele, njengoba engekho idatha ethize nenani ezaziwayo. Impendulo kuba ifomula.

Pulse labadubuli izinhlelo ukuba zero, njengoba yesikhulumi kanye igobolondo babe izimele. Vumela Isivinini oyifunayo yesikhulumi zizomakwa incwadi Latin u. Khona-ke umfutho wayo ngemva shot inqunywa ngokuthi umkhiqizo mass velocity of lelivakalako. Kusukela platform isethwe emuva (ngokumelene OX-eksisi isiqondiso), ukubaluleka ishayela alivumi.

ngokubhuduzela projectile - umkhiqizo isisindo salo kanye lelivakalako ngesivinini OX axis. Ngenxa yokuthi i-Isivinini iqondiswa engela emkhathizwe, kuba projection we velocity iphindwe cosine ye-engeli. Ngo ukulingana kwama-alfabhethi zaziyoba ibukeke lokhu: 0 = - Mu + mv * cos α. Therefrom ngu elula ukuguqulwa ifomula impendulo etholwe: u = (mv * cos α) / M.

Impendulo. isivinini Ipulatifomu kuchazwe ifomula u = (mv * cos α) / M.

Inkinga yokweqa emfuleni

Isimo. Ububanzi emfuleni kanye ubude bayo yonke efanayo futhi ilingana l, parallel wachichima. Kuyaziwa for ijubane kwamanzi e-v emfuleni _1, kanye nesivinini v ₂ isikebhe _yangasese. 1). Ngesikhathi bezihlahla Ukunqamula ekhaleni iqondiswe ngokuqinile ogwini olungaphesheya. kude kanjani uyothwala s esezansi? 2). Yikuphi α engela kuyadingeka ukuthumela ekhaleni isikebhe, ukuze sifike ogwini olungaphesheya esokuba perpendicular iphuzu ngokumuka? Singakanani isikhathi t adingekayo inezimpabano enjalo?

Isinqumo. 1). isivinini isikebhe Full vector isamba ngobuningi ezimbili. Eyokuqala i emfuleni, okuyinto iqondiswa ogwini. Esesibili - isivinini isikebhe yangasese perpendicular ogwini. onxantathu ezimbili ezifanayo sibalo eyatholakala. Umsuka kwakhiwa emfuleni ububanzi ibanga ukuthi amagalelo umsiki. Esesibili - vector velocity.

Asikisela Ngokucabangela umbhalo onjalo: s / l = v ₁ / v _2. Ngemva kokuguquka, ifomula wokulandisa engaziwa: s = l * (v ₁ / v _2).

2). Kulesi nguqulo ye-vector inkinga isivinini obugcwele perpendicular ogwini. Kuyinto ilingane v Vector sum ₁ kanye v _2. Sine ye-engeli lapho Vector kumelwe hlanhlatha isivinini siqu, ilingana amamojuli isilinganiso v ₁ kanye v _2. Ukubala isikhathi sokuhamba edingekayo ukwehlukana ububanzi abalwa ngejubane egcwele emfuleni. Inani wale mithandazo ibalwe theorem kaPythagoras.

v = √ (v ₂ ² - v ₁ ^2), khona-ke t = l / (√ (v ₂ ² - v ₁ ^2)).

Impendulo. 1). s = l * (v ₁ / v ₂₎ 2). isono α = v ₁ / v _2, t = l / (√ ( v ₂ ² - v ₁ ^2)).