Ma vector a unit - mavuto ndi mayankho

Ma vector a unit - mavuto ndi mayankho

1. Chinthu chimayenda pa liwiro la v = (2i − 1.5j) m/s. Kodi kusuntha kwa chinthucho pambuyo pa masekondi anayi ndi kotani?

Zodziwika:

Gawo lopingasa la liwiro (v _x ) = 2 m/s

Gawo loyima la liwiro (v _y ) = 1.5 m/s

Nthawi yopuma (t) = masekondi 4

Kufunidwa: Kusamutsidwa

Yankho:

Zotsatira za liwiro (v):

Kusamutsidwa:

s = vt = (2.5 m/s)(masekondi 4)

s = mamita 10

2. Vekitala F ₁ = 14 N ndi F ₂ = 10 N. Dziwani vekitala yotsatira ngati yatchulidwa mu R = i + j.

Yankho:

Zigawo za ma vector:

F _1x = (F ₁ )(cos 60 ^o ) = (14)(0.5) = -7 N (Negative chifukwa gawo la vector ili limaloza motsatira mzere wa x wotsutsa (kumanzere))

F _1y = (F ₁ )(sin 60 ^o ) = (14)(0.5√3) = 7√3 N (Yabwino chifukwa gawo la vekitala iyi limaloza motsatira mzere wabwino wa y (kumanja))

F _2x = 10 N

F _2y = 0

Zigawo za ma vector otsatira:

F _x = F _1x + F _2x + F _3x = -7 + 10 = 3 N

F _y = F _1y + F _2y + F _3y = 7√3 + 0 = 7√3 N

Chotsatira cha vekitala mu vekitala ya unit:

R = 3 i + 7√3 j

1. Kodi vekitala ya unit ndi chiyani? yankho: Vekitala ya unit ndi vekitala yomwe ili ndi kukula kwa 1. Nthawi zambiri imayimira njira popanda kupereka chidziwitso chilichonse chokhudza kukula.
2. Nchifukwa chiyani ma vector a unit ndi ofunikira mu masamu a vector ndi physics? yankho: Ma vekitala a unit ndi ofunikira chifukwa amapereka njira yokhazikika yofotokozera malangizo. Amatha kukulitsidwa ndi kukula kuti apange vekitala yokhala ndi kutalika komwe mukufuna mbali inayake.
3. Kodi mumapeza bwanji vekitala ya unit kuchokera ku vekitala yoperekedwa? yankho: Vekitala ya unit yomwe ili kutsogolo kwa vekitala yoperekedwa ingapezeke mwa kugawa vekitala ndi kukula kwake.
4. Kodi ma vector a standard unit mu Cartesian coordinates ndi ati, ndipo malangizo awo ndi otani? yankhoMa vector a mayunitsi wamba mu ma coordinates a Cartesian ndi i, jndipo k. i mfundo zomwe zikupita ku x-axis, j mfundo zomwe zimayang'ana mbali ya y-axis, ndipo k mfundo zomwe zikupita ku z-axis.
5. Kodi vekitala ya unit ingakhale ndi zigawo zina kupatula 1 kapena -1? yankhoInde. Zigawo za vekitala ya unit zimadalira komwe ikupita. Ma vekitala a unit okha ndi omwe amalumikizidwa ndi ma coordinate axes (monga i, j, k mu ma coordinates a Cartesian) adzakhala ndi zigawo za 1, -1, kapena 0.
6. Kodi kuchuluka kwa ma vector awiri a mayunitsi ndi vector ya mayunitsi? yankhoAyi. Chiwerengero cha mavekitala awiri nthawi zambiri sichimakhala vekitala ya unit pokhapokha mavekitala awiriwa ali ndi collinear komanso olunjika mosiyana.
7. Kodi vekitala ya unit ingathe kuyesedwa kuti iimire vekitala yokhala ndi kukula kosiyana koma mbali yomweyo? yankhoInde. Kuchulukitsa vekitala ya unit ndi scalar kudzasintha kukula kwake pamene kukupitirizabe kuyang'ana komwe kumayang'ana.
8. Kodi kukula kwa chogulitsa chophatikizana cha ma vector awiri a mayunitsi ndi kotani? yankho: Kukula kwa zotsatira zophatikizika za ma vector awiri a unit ndi kofanana ndi sine ya ngodya pakati pawo. Mtengo wapamwamba ndi 1 pamene ma vector ali opingasa, ndipo wotsika ndi 0 pamene ma vector ali ofanana.
9. Nchifukwa chiyani zotsatira za dot za ma vector awiri zimapereka cosine ya ngodya pakati pawo? yankho: Fomula ya dot product ya mavekitala awiri imaperekedwa ndi zotsatira za kukula kwawo ndi cosine ya ngodya pakati pawo. Pamene mavekitala onse awiri ali mavekitala a unit, kukula kwawo ndi 1, kotero dot product imangopangitsa kuti cosine ya ngodya ikhale yosavuta.

10. Kodi lingaliro la vekitala ya unit limakulitsidwa bwanji mu machitidwe osakhala a Cartesian coordinate? Yankho : Mu machitidwe osakhala a Cartesian coordinate, monga ma coordinate ozungulira kapena ozungulira, pali ma vekitala osiyanasiyana a unit ofanana ndi njira iliyonse yolumikizirana. Mwachitsanzo, mu ma coordinate ozungulira, ma vekitala a unit ndi r (radial direction), θ (polar angle direction), ndi φ (azimuthal direction).