Nā vectors unit - nā pilikia a me nā hoʻonā

Nā vectors unit - nā pilikia a me nā hoʻonā

1. Neʻe kekahi mea ma ka wikiwiki o v = (2i − 1.5j) m/s. He aha ka neʻe ʻana o ka mea ma hope o 4 kekona?

ʻIke ʻia:

ʻO ka ʻāpana pae o ka wikiwiki (v _x ) = 2 m/s

ʻO ka ʻāpana kū pololei o ka wikiwiki (v _y ) = 1.5 m/s

Ka manawa (t) = 4 kekona

Makemake ʻia: Hoʻoneʻe ʻana

Lōlā:

ʻO ka hopena o ka wikiwiki (v):

Ka hoʻoneʻe ʻana:

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

s = 10 mika

2. Vector F ₁ = 14 N a me F ₂ = 10 N. E hoʻoholo i ka vector hopena inā i ʻōlelo ʻia ma R = i + j.

Lōlā:

Nā ʻāpana o nā vectors:

F _1x = (F ₁ )(cos 60 ^o ) = (14)(0.5) = -7 N (Mai maikaʻi ʻole no ka mea ke kuhikuhi nei kēia ʻāpana vector ma ke axis x maikaʻi ʻole (hema))

F _1y = (F ₁ )(sin 60 ^o ) = (14)(0.5√3) = 7√3 N (Maikaʻi no ka mea, ke kuhikuhi nei kēia ʻāpana vector ma ke axis y maikaʻi (ʻākau))

F _2x = 10 N

F _2y = 0

Nā ʻāpana o nā vectors hopena:

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

ʻO ka vector hopena ma ka vector unit:

R = 3 i + 7√3 j

1. He aha ka vector unit? paneʻO ka vector unit he vector nona ka nui o 1. Hōʻike pinepine ia i ke kuhikuhi me ka ʻole o ka hōʻike ʻana i kekahi ʻike e pili ana i ka nui.
2. No ke aha he mea nui nā vectors unit i ka makemakika vector a me ka physics? paneHe mea nui nā vectors unit no ka mea hāʻawi lākou i kahi ala maʻamau e wehewehe i nā kuhikuhi. Hiki ke hoʻonui ʻia lākou e ka nui e hana i kahi vector me ka lōʻihi i makemake ʻia ma kahi kuhikuhi kikoʻī.
3. Pehea ʻoe e loaʻa ai kahi vector unit mai kahi vector i hāʻawi ʻia? paneHiki ke loaʻa kahi vector unit ma ke kuhikuhi o kahi vector i hāʻawi ʻia ma ka puʻunaue ʻana i ka vector me kona nui.
4. He aha nā vectors anakahi maʻamau ma nā hoʻonohonoho Cartesian, a he aha ko lākou mau kuhikuhi? paneʻO nā vectors anakahi maʻamau ma nā hoʻonohonoho Cartesian i, j, a k. i nā kiko ma ke kuhikuhi o ke axis-x, j nā kiko ma ke kuhikuhi o ka axis-y, a k nā kiko ma ke kuhikuhi o ka axis-z.
5. Hiki i kahi vector unit ke loaʻa nā ʻāpana ʻē aʻe ma mua o 1 a i ʻole -1? paneʻAe. Pili nā ʻāpana o kahi vector unit i kona kuhikuhi. ʻO nā vector unit wale nō i hoʻohālikelike ʻia me nā axis coordinate (e like me i, j, k ma nā hoʻonohonoho Cartesian) e loaʻa iā ia nā ʻāpana o 1, -1, a i ʻole 0.
6. He vector unit anei ka huina o nā vectors unit ʻelua? paneʻAʻole. ʻAʻole maʻamau he vector unit ka huina o ʻelua mau vectors unit ke ʻole he collinear a kuhikuhi ʻē nā vectors ʻelua.
7. Hiki ke hoʻonui ʻia kahi vector unit e hōʻike i kahi vector me ka nui ʻokoʻa akā ke kuhikuhi like? paneʻAe. ʻO ka hoʻonui ʻana i kahi vector unit me kahi scalar e hoʻololi i kona nui me ka mālama ʻana i kona kuhikuhi like.
8. He aha ka nui o ka huahana kea o nā vectors unit ʻelua? paneʻO ka nui o ka huahana kea o ʻelua mau vectors unit ua like ia me ka sine o ke kihi ma waena o lāua. ʻO ka waiwai kiʻekiʻe loa he 1 ke kū pololei nā vectors, a ʻo ka palena iki he 0 ke kūlike nā vectors.
9. No ke aha i hāʻawi ai ka huahana kiko o nā vectors unit ʻelua i ke cosine o ke kihi ma waena o lāua? paneʻO ke ʻano huahana kiko no nā vectors ʻelua i hāʻawi ʻia e ka huahana o ko lākou nui a me ke cosine o ke kihi ma waena o lākou. Ke lilo nā vectors ʻelua i mau vectors unit, ʻo ko lākou nui he 1, no laila e hoʻomaʻalahi ka huahana kiko i ke cosine o ke kihi wale nō.

10. Pehea e hoʻonui ʻia ai ke kumumanaʻo o kahi vector unit i nā ʻōnaehana hoʻonohonoho ʻaʻole Cartesian? Pane : Ma nā ʻōnaehana hoʻonohonoho ʻaʻole Cartesian, e like me nā hoʻonohonoho poepoe a cylindrical paha, aia nā vector unit like ʻole e pili ana i kēlā me kēia kuhikuhi hoʻonohonoho. No ka laʻana, ma nā hoʻonohonoho poepoe, ʻo nā vector unit he r (kuhikuhi radial), θ (kuhikuhi kihi polar), a me φ (kuhikuhi azimuthal).