Ama-vector eyunithi - izinkinga nezixazululo

Ama-vector eyunithi - izinkinga nezixazululo

1. Into ihamba ngesivinini esingu -v = (2i − 1.5j) m/s. Iyini i- displacement yento ngemva kwemizuzwana emi-4?

Kwaziwa:

Ingxenye evundlile yejubane (v _x ) = 2 m/s

Ingxenye eqondile yejubane (v _y ) = 1.5 m/s

Isikhawu sesikhathi (t) = imizuzwana eyi-4

Okufunwayo: Ukufuduka

Isixazululo:

Umphumela wejubane (v):

Ukufuduka:

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

s = amamitha ayi-10

2. Ivektha F ₁ = 14 N kanye no-F ₂ = 10 N. Thola ivektha ephumela uma ishiwo ku-R = i + j.

Isixazululo:

Izingxenye zama-vector:

F _1x = (F ₁ )(cos 60 ^o ) = (14)(0.5) = -7 N (Okungekuhle ngoba le ngxenye yevektha ikhomba eceleni kwe-axis x engekuhle (ngakwesobunxele))

F _1y = (F ₁ )(sin 60 ^o ) = (14)(0.5√3) = 7√3 N (Kuhle ngoba le ngxenye yevektha ikhomba eceleni kwe-axis ka-y enhle (ngakwesokudla))

F _2x = 10 N

F _2y = 0

Izingxenye zamavektha aphumelayo:

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

Ivektha ephumela ku-vektha yeyunithi:

R = 3 i + 7√3 j

1. Iyini i-vector yeyunithi? Impendulo: I-vector yeyunithi iyi-vector enobukhulu obungu-1. Ngokuvamile imelela isiqondiso ngaphandle kokudlulisela noma yiluphi ulwazi mayelana nobukhulu.
2. Kungani ama-unit vectors ebalulekile kuzibalo ze-vector kanye ne-physics? Impendulo: Ama-vector eyunithi abalulekile ngoba ahlinzeka ngendlela ejwayelekile yokuchaza iziqondiso. Angalinganiswa ngobukhulu ukuze akhiqize i-vector enobude obufunwayo ohlangothini oluthile.
3. Uyithola kanjani i-vector yeyunithi kusuka ku-vector enikeziwe? Impendulo: I-vector yeyunithi ebheke ku-vector ethile ingatholakala ngokuhlukanisa i-vector ngobukhulu bayo.
4. Ziyini izivektha zeyunithi ezijwayelekile ku-Cartesian coordinates, futhi ziyini iziqondiso zazo? Impendulo: Ama-vector amayunithi ajwayelekile kuma-coordinate e-Cartesian ango i, j, Futhi k. i amaphuzu aqonde ohlangothini lwe-x-axis, j amaphuzu abheke ohlangothini lwe-y-axis, kanye k amaphuzu abheke ohlangothini lwe-z-axis.
5. Ingabe i-vector yeyunithi ingaba nezingxenye ngaphandle kuka-1 noma u--1? Impendulo: Yebo. Izingxenye zevektha yeyunithi zincike ekuqondeni kwayo. Amavektha eyunithi kuphela ahambisana nama-axes e-coordinate (njenge i, j, k ku-Cartesian coordinates) kuzoba nezingxenye ezingu-1, -1, noma u-0.
6. Ingabe isamba samavekhtha amabili eyunithi siyivekhtha yeyunithi ngempela? Impendulo: Cha. Isamba samavekhtha amabili amayunithi ngokuvamile asiyona ivekhtha yeyunithi ngaphandle kokuthi amavekhtha amabili aqondiswe ngokuphambene futhi aqondile.
7. Ingabe i-vector yeyunithi ingalinganiswa ukuze imele i-vector enobukhulu obuhlukile kodwa ohlangothini olufanayo? Impendulo: Yebo. Ukuphindaphinda i-unit vector nge-scalar kuzoshintsha ubukhulu bayo ngenkathi kugcina isiqondiso sayo sifana.
8. Ungakanani ubukhulu bomkhiqizo ohlanganisiwe wamavektha amabili? Impendulo: Ubukhulu bomkhiqizo ohlanganisiwe wamavekhtha amabili eyunithi bulingana ne-sine ye-engeli ephakathi kwawo. Inani eliphakeme lingu-1 uma amavekhtha eqondile, kanti inani eliphansi lingu-0 uma amavekhtha ehambisana.
9. Kungani umkhiqizo wamachashazi wamavektha amabili unikeza i-cosine ye-engeli ephakathi kwawo? Impendulo: Ifomula yomkhiqizo wechashazi lamavekhtha amabili inikezwa ngumkhiqizo wobukhulu bawo kanye ne-cosine ye-engeli ephakathi kwawo. Uma womabili amavekhtha e-unit vectors, ubukhulu bawo bungu-1, ngakho umkhiqizo wechashazi wenza kube lula i-cosine ye-engeli kuphela.

10. Umqondo we-unit vector welulwa kanjani ezinhlelweni ze-non-Cartesian coordinate? Impendulo : Ezinhlelweni ze-non-Cartesian coordinate, njenge-spherical noma cylindrical coordinates, kune-unit vectors ezahlukene ezihambisana ne-coordinate direction ngayinye. Isibonelo, ku-spherical coordinates, i-unit vectors yi- r (radial direction), i-θ (polar angle direction), kanye ne -φ (azimuthal direction).