Vector - nā pilikia a me nā hoʻonā
Vector a me Scalar
1. Ma waena o nā koho aʻe, ʻo ia hoʻi nā hui scalar-vector…
A. Ikaika - hoʻolalelale
B. Kaomi - ikaika
C. Ka neʻe ʻana - ka wikiwiki
D. Ke au uila - kaomi
Lōlā:
Ikaika = vector, wikiwiki = vector
Kaomi = scalar, ikaika = vector
Ka neʻe ʻana = vector, ka wikiwiki = scalar
Au uila = scalar, kaomi = scalar
ʻO ka pane pololei ʻo B.
2.
Hōʻike ʻia ka pane pololei e ka helu…
A. 1 a me 4
B. 1 a me 2
C. 2 a me 3
D. 3 a me 4
Lōlā:
Māmā = scalar
Ka neʻe ʻana = vector
Kaumaha = vector
Hoʻolalelale = vector
ʻO ka pane pololei ʻo C.
Nā ʻāpana o nā vectors
3. ʻElua mau vectors, ʻo F 1 = 20 N a me F 2 = 30 N, he kuhikuhi ko lākou e like me ka mea i hōʻike ʻia ma ke kiʻi ma lalo nei. E hoʻoholo i ka hopena o nā ʻāpana o nā vectors ma ka axis-x a me ka axis-y.
A. 5√3 N a me -25 N
B. -5√3 N a me 25 N
C. 25 N a me 5√3 N
D. 30 N a me 25√3 N
ʻIke ʻia:
F1 = 20 Newtons
Ke kihi ma waena o F 1 a me ke axis x = 30 o
F2 = 30 Newtons
Ke kihi ma waena o F 2 a me ke axis x =30 o
Makemake ʻia: F x a me F y
Lōlā:
F 1x = F 1 cos 30 o = (20)(0.5√3) = 10√3 Newton (hōʻailona hoʻohui no ka mea e kuhikuhi ana i ka axis +x)
F 1y = F 1 sin 30 o = (20)(0.5) = 10 Newtons (hōʻailona hoʻohui no ka mea e kuhikuhi ana i ka axis +y)
F 2x = F 2 cos 30 o = (30)(0.5√3) = -15√3 Newton (hōʻailona minus no ka mea e kuhikuhi ana i ka axis -x)
F 2y = F 2 sin 30 o = (30)(0.5) = 15 Newtons (hōʻailona hoʻohui no ka mea e kuhikuhi ana i ka axis +y)
ʻO ka hopena o ka ʻāpana x:
F x = F 1x + F 2x = 10√3 N – 15√3 N = -5√3 Newtons
ʻO ka hopena o ka ʻāpana y:
Fy = F 1y + F 2y = 10 N + 15 N = 25 Newtons
ʻO ka pane pololei ʻo B.
ʻO ka hopena o nā vectors ʻelua
4. ʻElua keiki ʻo A lāua ʻo B e paʻi i kahi poloka, inā e paʻi ʻo A i ka poloka i ka hema me ka ikaika o 400 N a i ka manawa like e paʻi ʻo B i ka poloka i ka hikina me ka ikaika o 300 N, a laila e hoʻoholo i ka hopena o ka ikaika A a me B.
A. 100 N hema
B. 100 N hikina
C. 500 N hikina hema
D. 700 N hikina hema
ʻIke ʻia:
ʻU = ʻākau, T = hikina, S = hema, B = komohana
TL = hikina ʻākau, TG = hikina hema, BD = komohana hema, BL = komohana ʻākau
A = 400 Newtons i ka hema
B = 300 Newtons ma ka hikina
Makemake ʻia: ka nui a me ke kuhikuhi o ka ikaika upena (R)
Lōlā:
ʻO ka pane pololei ʻo C.
ʻO ka hopena o ka vector o ka neʻe ʻana
5. Holo kekahi i ka mokokaikala mai ka home he 6 km a i ke kūkulu ʻākau a laila 8 km a i ka hikina. E hoʻoholo i ke kūlana hope loa o ke kanaka mai ke kūlana mua.
A. 14 km hikina ʻākau
B. 14 km komohana hema
C. 10 km hikina ʻākau
D. 10 km ma ke komohana ʻākau
ʻIke ʻia:
Makemake ʻia: ka nui a me ke kuhikuhi o ka neʻe ʻana o ka hopena
Lōlā:
ʻO ka pane pololei ʻo C.
6.
Ma muli o ke kiʻi ma luna, inā kū ka 1 kuea i 1 km, a laila he aha ka neʻe ʻana o ka huina.
Lōlā:
Ka mamao = A + B + C = 6 + 6 + 2 = 14 km
Ka neʻe ʻana = R = 12 km
7. Hele kekahi kaʻa mai A a i B ma ke ʻano he 30 km ma ka ʻākau, a laila 60 km ma ka hikina, a laila 110 km ma ka hema. E hoʻoholo i ka neʻe ʻana o ke kaʻa mai A a i D.
Lōlā:
ʻAA' = 60 km
A'D = 110 km – 30 km = 80 km
8. Hele kekahi kaʻa mai ke kūlanakauhale A a i ke kūlanakauhale B he 100 km ma ka ʻākau, a laila i ke kūlanakauhale C he 60 km ma ka hikina, a laila i ke kūlanakauhale D he 20 km ma ka hema. E hoʻoholo i ka neʻe ʻana o ke kaʻa.
Lōlā:
D'D = 60 km
AD' = 100 km – 20 km = 80 km
- He aha ka vector?
- pane mai: He nui ka vector nona ka nui (ka nui) a me ke kuhikuhi. ʻO nā hiʻohiʻona e komo pū me ka wikiwiki, ka ikaika, a me ka wikiwiki.
- Pehea ka ʻokoʻa o kahi vector mai kahi scalar?
- pane mai: ʻO ka nui wale nō ko ka scalar, ʻoiai ʻo ka vector he nui a me ke kuhikuhi. No ka laʻana, he scalar ka mahana no ka mea he waiwai kona akā ʻaʻohe kuhikuhi, ʻoiai ʻo ka velocity he vector no ka mea e hōʻike ana i ka wikiwiki (magnitude) ma kahi kuhikuhi kikoʻī.
- Pehea e hiki ai ke hōʻike ʻia kahi vector ma ke ʻano kiʻi?
- pane mai: Hiki ke hōʻike ʻia kahi vector ma ke ʻano kiʻi e kahi pua. Hōʻike ka lōʻihi o ka pua i ka nui o ka vector, a ʻo ke kuhikuhi o ka pua e hōʻike ana i ke kuhikuhi o ka vector.
- He aha ke koʻikoʻi o ka huelo a me ke poʻo o kahi vector?
- pane mai: ʻO ka huelo ke kiko hoʻomaka o ka vector, a ʻo ke poʻo (a i ʻole ka wēlau) ke kiko hopena. Ke hana nei i nā hana e like me ka hoʻohui vector, kau ʻia ka huelo o kekahi vector ma ke poʻo o kekahi.
- Pehea e hoʻohui ʻia ai nā vectors?
- pane mai: Hoʻohui ʻia nā vectors me ka hoʻohana ʻana i ke ʻano poʻo-a-huelo. Hoʻonoho ʻia ka huelo o ka lua o ka vector ma ke poʻo o ka mua. A laila huki ʻia ka vector hopena mai ka huelo o ka vector mua a i ke poʻo o ka lua o ka vector.
- He aha ka ʻokoʻa ma waena o kahi vector unit a me kahi vector null?
- pane mai: ʻO ka nui o ka vector unit he hoʻokahi a kuhikuhi i kahi kuhikuhi i kuhikuhi ʻia. Hoʻohana ʻia ia e hōʻike i ke kuhikuhi o kahi vector me ka nānā ʻole i kona nui. ʻAʻohe nui o ka vector null (a i ʻole zero) a ʻaʻohe kuhikuhi kikoʻī.
- Pehea e hiki ai ke hoʻonui ʻia kahi vector me kahi scalar?
- pane mai: ʻO ka hoʻonui ʻana i kahi vector me kahi scalar e hoʻololi i kona nui akā ʻaʻole kona kuhikuhi. Inā maikaʻi ka scalar, e mau ana ke kuhikuhi; inā maikaʻi ʻole, e hoʻohuli ʻia ke kuhikuhi.
- He aha ke ʻano o nā vectors ʻelua e orthogonal a perpendicular paha?
- pane mai: He orthogonal a perpendicular paha nā vectors ʻelua inā he 90 degere ke kihi ma waena o lākou. ʻO kā lākou huahana kiko he zero.
- Pehea e hoʻoholo ʻia ai ka hopena o nā vectors ʻelua?
- pane mai: ʻO ka hopena ka huina o nā vectors ʻelua. Ma ke ʻano kiʻi, ke hōʻike ʻia nā vectors ma ke ʻano he mau pua, hiki iā ʻoe ke loaʻa ka hopena ma ke kau ʻana i ka huelo o ka vector ʻelua ma ke poʻo o ka mua a me ke kaha kiʻi ʻana i kahi pua hou (ka hopena) mai ka huelo o ka vector mua a i ke poʻo o ka lua.
- Inā e kuhikuhi ana kahi vector i ka hikina me ka nui o 10 mau anakahi, pehea ʻoe e wehewehe ai i kona ʻaoʻao ʻē aʻe?
- pane mai: ʻO ke kū'ē o kēia vector e loaʻa ka nui like (10 mau ʻāpana) akā e kuhikuhi i ka ʻaoʻao ʻē aʻe, ʻo ia hoʻi, ma ke komohana.
