Zvishandiso zveUnit - matambudziko nemhinduro

Zvishandiso zveUnit - matambudziko nemhinduro

1. Chinhu chinofamba nespeed ye v = (2i − 1.5j) m/s. Chii chinonzi displacement yechinhu mushure memasekonzi mana?

Zvinozivikanwa:

Chikamu chakatarwa chevelocity (v _x ) = 2 m/s

Chikamu chakamira chespeed (v _y ) = 1.5 m/s

Nguva yepakati (t) = masekondi gumi nemashanu

Kudiwa: Kudzingwa

Solution:

Mhedzisiro yekukurumidza (v):

Kutamiswa:

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

s = mamita gumi

2. Vekitori F ₁ = 14 N uye F ₂ = 10 N. Sarudza vhekitori inobuda kana yakataurwa muR = i + j.

Solution:

Zvikamu zvemavector:

F _1x = (F ₁ )(cos 60 ^o ) = (14)(0.5) = -7 N (Negative nekuti chikamu ichi chevector chinonongedza padivi pe x axis (kuruboshwe))

F _1y = (F ₁ )(sin 60 ^o ) = (14)(0.5√3) = 7√3 N (Yakanaka nekuti chikamu ichi chevector chinonongedza padivi pe positive y axis (kurudyi))

F _2x = 10 N

F _2y = 0

Zvikamu zvemavector anobuda:

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

Vekitari inobuda muyuniti vekitari:

R = 3 i + 7√3 j

1. Chii chinonzi unit vector? mhinduro: Vector yeyuniti ivhekitari ine hukuru hwe1. Inowanzo miririra gwara pasina kupa ruzivo nezvehukuru.
2. Sei mayuniti vectors akakosha muvector mathematics nefizikisi? mhinduro: Mavekitari eyuniti akakosha nekuti anopa nzira yakajairika yekutsanangura mafambiro. Anogona kuenzaniswa nehukuru kuti agadzire vekitari ine hurefu hwaunoda munzira yakatarwa.
3. Unowana sei vector yeyuniti kubva kune vector yakapihwa? mhinduro: Vekitari yeyuniti iri munzira yevekitari yakapihwa inogona kuwanikwa nekukamura vekitari nehukuru hwayo.
4. Ndeapi ma "standard unit vectors" ari mu "Cartesian coordinates", uye ndeapi ma "directions" azvo? mhinduro: Mavector eyuniti akajairwa muCartesian coordinates ndeaya i, j, uye k. i inonongedza kwakananga ku x-axis, j inonongedza kwakanangana ney-axis, uye k inonongedza kwakananga ku-z-axis.
5. Vekitari yeyuniti inogona kuva nezvimwe zvikamu zvisiri 1 kana -1 here? mhinduro: Ehe. Zvikamu zveyuniti vector zvinoenderana nekwainoenda. Mayuniti vector chete ndiwo anoenderana nema coordinate axes (senge i, j, k muCartesian coordinates) dzine zvikamu zve1, -1, kana 0.
6. Ko huwandu hwemayuniti maviri evectors iyuniti vhector here? mhinduroKwete. Huwandu hwemavekitari maviri eyuniti kazhinji hausi vekitari yeyuniti kunze kwekunge mavekitari maviri ari collinear uye akanongedzwa zvakapesana.
7. Vector yeyuniti inogona kuenzaniswa here kuti imiririre vector ine hukuru hwakasiyana asi iine divi rimwe chete? mhinduro: Ehe. Kuwedzera unit vector ne scalar kuchachinja hukuru hwayo ukuwo gwara rayo richiramba rakafanana.
8. Chii chinonzi hukuru hwechigadzirwa chemuchinjikwa chemayuniti maviri? mhinduro: Hukuru hwechigadzirwa chemuchinjikwa chemayuniti maviri mavector hwakaenzana nesine yekona iri pakati pawo. Kukosha kukuru i1 kana mavector ari akatarisana, uye hushoma i0 kana mavector ari akaenzana.
9. Sei zvichinzi dot product yemayuniti maviri vectors inopa cosine yekona iri pakati pavo? mhinduro: Fomura yechigadzirwa chedot yemavector maviri inopiwa nechibereko chehukuru hwawo uye cosine yekona iri pakati pawo. Kana mavector ese ari mavector eyuniti, hukuru hwawo i1, saka chigadzirwa chedot chinorerutsa cosine yekona chete.

10. Pfungwa yeyuniti vector inowedzerwa sei mu non-Cartesian coordinate systems? Mhinduro : Mu non-Cartesian coordinate systems, se spherical kana cylindrical coordinates, kune ma unit vectors akasiyana anoenderana ne coordinate direction yega yega. Semuenzaniso, mu spherical coordinates, ma unit vectors ndi r (radial direction), θ (polar angle direction), uye φ (azimuthal direction).