A Vector uwandu mu wefizikisi. Mienzaniso vector zvakawanda

Physics uye masvomhu haagoni kuita pasina pfungwa "munhu vektori uwandu." Zvakakosha kuziva uye kudzidza, uye kuti vakwanise kushanda nayo. Izvi zvinofanira zvechokwadi kudzidza kudzivisa kuvhiringidzika uye kudzivisa zvikanganiso mapenzi.

Sei kusiyanisa scalar ukoshi kubva vector?

Wokutanga nguva dzose ane chete noruzhinji. Ichi nhamba yake. Most scalar zvakawanda zvinogona kuva zvose zvakanaka uye kunaka tsika. Mienzaniso yaro anogona kushumira somunhu zvemagetsi mutariri kana basa tembiricha. Asi pane scalars vasingagoni kuva akaipa, akadai urefu uye uremu.

A Vector uwandu, kunze Numeric kukosha kuti nguva dzose wabatwa mhedziso kukosha, kunoratidzwa zvakawanda uye kutungamirirwa. Saka, zvinogona kumiririrwa zvakajeka, kureva, muchimiro nomuseve, ane kureba akaenzana modulus tsika zvainanga mune imwe negwara.

Paainyorera mumwe Vector uwandu runotaurwa parutivi museve chiratidzo pamusoro tsamba. Kana totaura munhu Numeric kukosha, museve haana kunyorwa, kana rakundwa modulo.

Chii chimwe chinonyanya kwaiwanzoitwa pamwe vectors?

First - fananidzo. Vanogona kuva vakaenzana kana kwete. Kana dzakafanana modules okutanga. Asi ichi hachisi chete ezvinhu. Vanofanira pachine chete kana akatarisana mirayiridzo. Muchiitiko chokutanga, vanofanira kunzi vakaenzana vectors. Chechipiri, ndivo zvakasiyana. Kana asina kuzadziswa kunyange mumwe izvi zvinhu, ipapo vectors havana kuenzana.

Kwozouya kuwedzera. Kunogona kuitwa mitemo maviri: netriangle kana parallelogram. Wokutanga zvinoda Kumbomira Wokutanga Vector, uye kubva kumugumo wechipiri. VaGumbo mugumisiro uchava mumwe kuti unoda vabatisise wokutanga kuguma wechipiri.

Rule of parallelogram zvinogona kushandiswa kana zvakakodzera kuisa pasi Vector kwazvo muna wefizikisi. Kusiyana wokutanga ushe, ipapo zvinofanira kumbosiyiwa nomumwe pfungwa. Zvadaro kupedzisa navo kuti parallelogram. Mugumisiro chiito dzinofanira kuonekwa sezvo diagonal ari parallelogram wakavhomorwa kubva chete pfungwa.

Kana Vector iri subtracted nemamwe, vachakurumidza zvakare vambomira kubva imwe. zvakazoitika chete ari Vector, rinobatana kuti ari kunonoka rechipiri magumo wokutanga pakuguma.

Izvo vectors vari kudzidza wefizikisi?

Ivo sezvinongoitawo scalar. Unogona chete kurangarira kuti chero Vector kwazvo muna wefizikisi imomo. Kana kuziva zviratidzo nezvavakatadzisa inogona dzaona. Nokuti vaya vanosarudza kusarudza wokutanga, tafura iyi inobatsira. Inopa chikuru vektori panyama zvakawanda.

Symbol iri nzira	zita
V	havukavu
R	misha
uye	kumhanyisa
F	simba
R	tichimhanya
E	yemagetsi munda umbirimi
The	rinobva induction
M	nguva simba

Zvino zvishoma nezvevamwe tsika idzi.

ukoshi rokutanga - nokukurumidza

Sezvo zvakakodzera kutanga kupa mienzaniso vector zvakawanda. Izvi nokuti Kunyatsoziva pakati wokutanga.

Speed rinorondedzerwa so maitiro muviri kufamba muchadenga. Iye anopiwa kusanganiswa kukosha uye kutungamirirwa. Naizvozvo, kuti velocity ane vector uwandu. Uyezve, unogona kukamurwa mhuka. Chokutanga Linear velocity. It chinotarisirwa ari kufunga kuti rectilinear yunifomu inofamba. Zvisinei, pane kuti vave hama nzira zvaiyambuka nomuviri panguva kufamba.

Chete nzira unogamuchirwa kushandisa panguva non-rekuchikoro inofamba. Chete ipapo ichava avhareji. Uye nguva dzaunoda kusarudza, tinofanira kuva diki sezvinobvira. Uderedze razero nguva penguva velocity mutengo atova nguva imwe.

Kana tikaongorora ane zvemasanga kufamba, pane nguva dzose nokukurumidza - a vector uwandu. Handiti, zvakakodzera anoora kupinda zvinoriumba rinotungamirirwa pamwe neimwe Vector aitungamirira batanidza mitsetse. Uyezve, kunorondedzerwa se rinobva pakati nharaunda Vector, vatora nguva.

ukoshi wechipiri - simba

It anosarudza nechiyero kusimba matambudziko anokonzerwa pamusoro muviri nedzimwe miviri kana minda. Sezvo simba - a Vector uwandu, inofanira kuva kunokosha zvikuru uye mirayiridzo. Sezvo chiito muviri, zvakakosha vanotaurawo kuti simba rikashandiswa. Kuti tiwane kutarisana kumiririrwa simba vectors, unogona kureva zvinotevera tafura.

simba	Pfungwa chikumbiro	divi
nekuomarara	muviri centre	kuna Center of Earth
rinokwevera zvinhu pasi	muviri centre	kuti nzvimbo imwe muviri
elasticity	nzvimbo kubatana zviri kuwirirana mitumbi	pamusoro zvekunze zvinofurira
kukweshera	pakati kunyorera hukawanika	nenzira pakatarisana sangano

Uyewo ane Vector yakawanda ari mambure simba. Inonzi Verengai vanhu vose kuita pamusoro muviri zvemaziso mauto. Kuti uone zvakafanira kuita kuwedzera nheyo yacho Triangle utongi. Chete vanoda kunonoka vectors panguva kubva kumugumo yaimbovapo. The Zvichaguma mumwe unobatanidza pakutanga rokutanga kusvika kumugumo yokupedzisira.

The ukoshi wechitatu - Kutama

Munguva kufamba muviri rinotsanangura imwe mutsetse. Inonzi trajectory. mutsetse uyu anogona kuva zvakasiyana. Zvakakosha kupfuura chitarisiko chawo, kutanga uye kuguma rwokufamba. Ivo zvakabatanidzwa chidimbu, unonzi sangano. Izvi zvakare vector uwandu. Uye nguva dzose rinotungamirirwa kubva pakutanga kufamba kusvikira apo sangano yave wakagumiswa. Kureva izvozvo kushandisa Latin tsamba r.

Pano, iwe mugamuchire zvinotevera mubvunzo: "Gwara - mumwe Vector uwandu?". Kazhinji, mashoko aya haasi echokwadi. Nzira wakaenzana nzira urefu uye asina kunyanya nhungamiro. An Kunze ndiko mamiriro ezvinhu apo vaiona twasu-mutsetse inofamba muna imwe chete. Zvino pamwero mukuru misha mutengo rinobatana gwara uye mirayiridzo rawo zvakafanana. Naizvozvo, kana tichifunga kufamba pamwe yakarurama mutsetse pasina kuchinja kutungamirirwa kufamba pamusoro nzira inogona vanobatanidzwa mienzaniso vector zvakawanda.

The ukoshi chechina - kumhanyisa

Zviri anozivikanwa nokukurumidza chinja nokukurumidza. Uyezve, kumhanyisa angava zvose zvakanaka nezvakaipa. In yakarurama kumhanya chinotungamirwa kune mukuru nokukurumidza. Kana sangano kunoitika pamwe munhu curved nzira, ipapo ayo kumhanyisa Vector uchiora kupinda zvinoriumba maviri, mumwe icho chinotungamirwa kurutivi musimboti curvature of nharaunda.

Govera avhareji uye nguva imwe kumhanyisa ukoshi. Wokutanga anofanira dzaona sezvo nhamba mwero shanduko kuti imwe nguva nenguva ino. Kana iwe vanoedza kufunga nguva penguva kuti razero anoratidza nguva imwe kumhanyisa.

ukoshi Wechishanu - kufamba kweropa

Mune imwe nzira inonzi tichimhanya. Pulse Vector mutengo uri nokuti zvakananga chokuita pakukurumidza uye simba kureva muviri. Vose vane gwara uye akakudza kufamba kweropa rake.

By tsanangudzo, yokupedzisira zvakagadzirwa muviri uremu pamusoro unodiwa. Kushandisa pfungwa tichimhanya ane muviri, zvinokwanisika mune imwe rekodhi-anozivikanwa mutemo Newton vake. Zvakaratidza kuti kuchinja kwacho zvakagadzirwa simba panguva penguva.

In wefizikisi, nebasa rinokosha iri kuchengetedza tichimhanya, iyo rinoti iri namahwindo hurongwa zvitunha yaro zvachose tichimhanya iri kugara.

Tiri zvishomanana chaizvo dzakanyorwa, iyo tsika (vector) akadzidza ari wefizikisi kosi.

Basa inelastic aaiitawo

Condition. On the njanji ndiyo mira papuratifomu. To motokari yake kusvika pane imwe nokumhanya 4 m / s. Misa Chikuva uye motokari - 10 uye 40 matani azvaitwa. The motokari paricharova pachikuva paine coupler. Zvakakodzera ngaaverenge nokumhanya wegadziriro, "ngoro" pashure matambudziko.

Decision. Chokutanga, notation inofanira akapinda: motokari kumhanya pamberi was - v _1, ngoro pamwe chikuva mushure setambo yokukwevesa - V, m mukanyiwa wenhumbi _1, kuchikuva - mamita _2. Maererano dambudziko kukosha velocity V vanoda kuziva.

Mitemo kugadzirisa mabasa akadaro vanoda schematic maitiro mifananidzo asati uye mushure kuita. The akabatana Nzombe musoro kutuma achitevedza njanji nenzira iyo iri kutofamba.

Under izvi mamiriro ezvinhu anogona kunzi ngoro yakavharwa. Izvi pakutsvaga ndechokuti nechitarisiko masimba anogona kuregeredzwa. Simba regiravhiti uye pasi maitiro akanaka uye kukweshera pamusoro njanji havasi kufungwa nezvazvo.

Maererano nomurayiro kuchengetedza tichimhanya, Vector kwavo kupfupikisa kubata mumotokari pachikuva kunoitika coupling pashure matambudziko. Chokutanga, kuchikuva haangatongozununguswi, saka kwayo kupomba ndiyo razero. Kutamira chete motokari, ayo tichimhanya - zvinobikwa m ₁ uye v _1.

Sezvo wavanozvisunga yakanga inelastic, kureva ngoro akaita mutsimba papuratifomu, uye ipapo akatanga kufamba munzira imwe chete mirayiridzo, kuti tichimhanya haana kushandura achitungamirirwa hurongwa. Asi zvarinoreva yakanga yakasiyana. Kureva, zvinobikwa Verengai mukanyiwa mumotokari pamwe chikuva uye yaidiwa nokukurumidza.

Tinogona kunyora mukana wokuti vanhu vanga ichi: m ₁ v ₁ * = (m ₁ + mamita ₂₎ * v. Zvichava kwechokwadi fungidziro ari tichimhanya Vector kune vakasarudzwa akabatana. Nokuti zviri nyore kuona mukana wokuti vanhu vanga iyo kunodiwa kuverenga kutsvakwa kumhanya: v = m ₁ * v ₁ / (m ₁ + mamita _2).

Maererano nemitemo anofanira zvaitambidzwa kukosha kurema iri matani uremu. Naizvozvo, kubudikidza dzinomiririra kuvapinza nzira inofanira kutanga ngazviwande kubudikidza anozivikanwa kwazvo muzana zviuru. Simple Masvomhu kupa nhamba 0.75 m / s.

Answer. ngoro pamwe kuchikuva nokukurumidza ndiyo 0.75 m / s.

Dambudziko chete weboka muzvikamu dzomuviri

Condition. Speed zvinobhururuka magirinedhi 20 m / s. Zvinonzi ipazwe zvimedu maviri. Misa 1,8 makirogiramu vokutanga. It anopfuurira kufamba mugwara umo girinedhi ichibhururuka ari kumhanya 50 m / s. The Chidimbu wechipiri ane uremu 1,2 makirogiramu. Chii chiri kumhanya?

Decision. Regai negurumwandira nezvimedu runotaurwa netsamba m ₁ uye mamita _2. Dzavo prices zvichaita azvaitwa v ₁ uye v _2. The kwokutanga mwero magirinedhi - v. Mune basa unofanira kuverenga ukoshi v _2.

Kuti uwane shard vakaramba kufamba nenzira iyoyo mirayiridzo sezvo vamwe mutamba, uye wechipiri kuti achibhururuka negwara. Kana wasarudza kutungamirirwa akabatana mumwe wakange kwokutanga tichimhanya, pashure nokuputsa hombe shard ichibhururuka kuburikidza akabatana, uye vaduku - pamusoro Sekaiichi.

Basa iri akabvumira kushandisa mutemo kuchengetedza tichimhanya nokuti kuti magirinedhi dzinopaza kunoitika panguva. Saka, pasinei nokuti girinedhi uye chikamu simba regiravhiti, iye haana nguva kuita uye kushandura vatungamirire tichimhanya Vector rayo ukoshi modulo.

Huwandu Vector kwazvo tichimhanya mushure girinedhi ndiye akauya pamberi pake. Kana tinonyora mutemo kuchengetedza tichimhanya ane muviri ari fungidziro iri nzombe akabatana, ipapo zvichava seizvi: (m ₁ + mamita ₂₎ * v = M * v _{1 1} - M ₂ * v _2. Pazviri nyore kutaura zvinodiwa nokukurumidza. Zvinonzi pakutsvaga nzira: v ₂ = ((m ₁ + mamita ₂₎ * V - m ₁ * v ₁₎ / m _2. Pashure kuzvitsinhanisa of kusanganiswa tsika yaunganidzwa Masvomhu, uye 25 m / s.

Answer. Kumhanya muchinyorwa ichi maduku 25 m / s.

Problem pamusoro bara angled

Condition. In mukanyiwa M yakaiswa chombo papuratifomu. Kubva mairi bara projectile vakawanda m. It paunobuda pa necheparutivi α kune chinjikira ane velocity V (apa hama pasi). Unoda kuziva kukosha pachikuva nokukurumidza pashure vachiridzira.

Decision. In basa iri, unogona kushandisa mutemo kuchengetedza tichimhanya ari fungidziro pamusoro akabatana mombe. Asi chete zvakaitika apo kwokunze maberere ose nomuuyo mauto ndiyo razero.

Pakutungamirira akabatana nzombe kusarudza mirayiridzo iyo projectile kuchabhururuka, uye kuenderana kune chinjikira mutsetse. Panyaya iyi, iyo fungidziro mauto regiravhiti uye pasi maitiro pana nzombe achava razero.

Dambudziko riri kugadziriswa vakawanda chimiro, sezvo pasina chaizvo mashoko kuti anozivikanwa kwazvo. Mhinduro iri nzira.

Pulse vachiridzira hurongwa kuva zero, sezvo pachikuva uye goko vaiva mira. Regai aida velocity pechikuva achapiwa ne tsamba Latin u. Zvadaro tichimhanya yayo mushure bara kunotemwa sezvo zvibereko zvakawanda uye velocity kuti fungidziro. Sezvo kuchikuva unoiswa shure (kuzorwa mombe akabatana mirayiridzo), kurova kwemwoyo mutengo akaipa.

projectile zvairatidza - zvinobikwa kwayo uremu uye fungidziro iri nzombe akabatana nokukurumidza. Nokuti chokuti velocity iri kutaurirwa necheparutivi kuti mujengachenga, ndiwo fungidziro pamusoro velocity kuwanda kubudikidza cosine ari pakona. In earufabheti kuenzana taitsvaka seizvi: 0 = - Mu + mv * Kosi α. Kwazviri nokuda nyore kuchinja nzira akawana mhinduro: U = (mv * Kosi α) / M.

Answer. Platform havukavu kunorondedzerwa nzira U = (mv * Kosi α) / M.

The dambudziko kuyambuka rwizi

Condition. Upamhi rwizi pamwe yaro yose kureba akafanana uye akaenzana L, kufambirana nerokuti dzarwo. It anozivikanwa kumhanya mvura murwizi v _1, uye muchihwande chikepe nokukurumidza v _2. 1). Pamharadzano mhino vematombo rinotungamirirwa kunoparirwa mhiri. How kure nayo tichariita S nomurwizi? 2). Ndeupi angled α zvakafanira kutuma igwa kuti mhuno, saka iye asvika mhiri ndekwokuda perpendicular kusvikira yekubva? zvikuru sei nguva t waida kuti kuchinjika yakadaro?

Decision. 1). Full chikepe havukavu ndiyo Vector uwandu zvakawanda maviri. Wokutanga nokuda rwizi, iyo chinotungamirwa pamwe mumhenderekedzo. Wechipiri - a private nokukurumidza chikepe perpendicular kugungwa. zvokuridza maviri zvakafanana nhamba inotengwa. Origin akaumba rwizi upamhi uye daro kuti aricheke zvibhakera. Wechipiri - the velocity vector.

Anoratidza kumbozviita: s / l = vs. ₁ / v _2. Mushure kutendeuka, kuti nzira nokuda asingazivikanwi tsika: s = L * (v ₁ / v _2).

2). In shanduro iri dambudziko akurumidze Vector ndiyo perpendicular kugungwa. Zviri akaenzana Vector Verengai v ₁ uye v _2. Sine of pakona uko Vector anofanira tsauka pachako akurumidze, akaenzana reshiyo modules v ₁ uye v _2. Kuverenga nguva kufamba kunodiwa kugovera upamhi kuverengerwa panguva akurumidze erwizi. Kukosha yokupedzisira rinowanikwa maererano Pythagorean theorem no.

v = √ (v _{² February} - v ₁ ^{of 2),} kana T = l / (√ (ndima _{February ²} - v ₁ ^{of 2)).}

Answer. 1). S = k * (v ₁ / v ₂₎ 2). chivi α = v ₁ / v _2, t = l / (√ ( vs. ₂ ² - v ₁ ^2)).