Hoʻohui i nā vectors me ka hoʻohana ʻana i nā ʻāpana - nā pilikia a me nā hoʻonā
1. ʻEkolu mau vectors e like me ka mea i hōʻike ʻia ma ke kiʻi ma lalo nei.
V1 = 30
V 2 = 30
V 3 = 40
He aha nā vectors hopena?
ʻIke ʻia:
V 1 = 30, kihi ma waena o V 1 a me ke axis x = 30 o
V 2 = 30, kihi ma waena o V 2 a me ke axis x = 30 o
V 3 = 40, ke kihi ma waena o V 3 a me ke axis x = 0 o
Makemake ʻia: ʻO nā vectors hopena
Lōlā:
ʻO V 1x = (V 1 )(cos 30 o ) = (30)(0.5√3) = 15√3. Maikaʻi no ka mea, ke kuhikuhi nei kēia ʻāpana vector ma ke axis x maikaʻi (ʻākau).
ʻO V 1y = (V 1 )(sin 30 o ) = (30)(0.5) = 15. Maikaʻi no ka mea ke kuhikuhi nei kēia ʻāpana vector ma ke axis y maikaʻi (i luna).
ʻO V 2x = (V 2 )(cos 30 o ) = (30)(0.5√3) = -15√3. Maikaʻi ʻole no ka mea ke kuhikuhi nei kēia ʻāpana vector ma ke axis x maikaʻi ʻole (hema).
ʻO V 2y = (V 2 )(sin 30 o ) = (30)(0.5) = 15. Maikaʻi no ka mea ke kuhikuhi nei kēia ʻāpana vector ma ke axis y maikaʻi (i luna).
ʻO V 3x = (V 3 )(cos 0 o ) = (40)(1) = 40. Maikaʻi no ka mea, ke kuhikuhi nei kēia ʻāpana vector ma ke axis x maikaʻi (ʻākau).
V 3y = (V 3 )(sin 0 o ) = (40)(0) = 0
Nā ʻāpana o nā vectors hopena:
ʻO V x = V 1x – V 2x + V 3x = 15√3 – 15√3 + 40 = 40
V y = V 1y + V 2y + V 3y = 15 + 15 = 30
2. ʻElua mau mana e kū pono ana kekahi i kekahi, F 1 = 12 N a me F 2 = 5 N. He aha ka hopena o nā mana ʻelua.
ʻIke ʻia:
Ikaika 1 (F 1 ) = 12 Newton
Ikaika 2 (F 2 ) = 5 Newton
Makemake ʻia: ʻO nā vectors hopena ( ΣF)
Lōlā:
ΣF 2 = F 1 2 + F 2 2 = 12 2 + 5 2 = 144 + 25 = 169
ΣF = √ 169 = 13 Newton
3. ʻEkolu mau vectors,
V1 = 30
V 2 = 30
V 3 = 40
E hoʻoholo i nā vectors hopena.
ʻIke ʻia:
v 1 = 30, hana i 30 o e pili ana i ke axis x maikaʻi ʻole
ʻo v 2 = 30, hana iā 30 o e pili ana i ka axis x maikaʻi
ʻo v 3 = 40, hana iā 0 o e pili ana i ka axis x maikaʻi
Makemake ʻia: ʻO nā vectors hopena
Lōlā:
Nā ʻāpana o nā vectors:
v 1x = v 1 cos 30 o = (30)(0.5 √ 3) = -15 √ 3 ( Maikaʻi ʻole no ka mea ke kuhikuhi nei kēia ʻāpana vector ma ke axis x maikaʻi ʻole (hema) )
v 1y = v 1 sin 30 o = (30)(0.5) = 15 ( Maikaʻi no ka mea ke kuhikuhi nei kēia ʻāpana vector ma ke axis y maikaʻi (i luna) )
v 2x = v 2 cos 30 o = (30)(0.5 √ 3) = 15 √ 3 ( Maikaʻi no ka mea ke kuhikuhi nei kēia ʻāpana vector ma ke axis x maikaʻi (ʻākau ) )
v 2y = v 2 sin 30 o = (30)(0.5) = 15 ( Maikaʻi no ka mea, ke kuhikuhi nei kēia ʻāpana vector ma ke axis y maikaʻi (i luna). )
v 3x = v 3 cos 0 o = (40)(1) = 40 ( Maikaʻi no ka mea, kuhikuhi kēia ʻāpana vector ma ke axis x maikaʻi (ʻākau). )
v 3y = v 3 hewa 0 o = (40)(0) = 0
Nā ʻāpana o nā vectors hopena:
v x = – v 1x + v 2x + v 3x = -15 √ 3 + 15 √ 3 + 40 = 40
v y = v 1y + v 2y + v 3y = 15 + 15 = 30
ʻO ka vector hopena:
4. He aha ka hopena o nā vectors ʻekolu e like me ka mea i hōʻike ʻia ma ke kiʻi ma lalo nei :
ʻIke ʻia:
F1 = 3 Newton, noho a hoike 60o e pili ana i ke axis x maikaʻi
ʻO F 2 = 3 Newtons, hana i ka 0 o e pili ana i ka axis x maikaʻi ʻole
ʻO F 3 = 6 Newtons , hana i 60 o e pili ana i ka axis y maikaʻi ʻole
Makemake ʻia: ʻO ka vector hopena
Lōlā:
Nā ʻāpana o nā vectors:
F 1x = F 1 cos 60 o = (3)(0.5) = 1.5 N ( Maikaʻi no ka mea, ke kuhikuhi nei kēia ʻāpana vector ma ke axis x maikaʻi (ʻākau ) )
F 1y = F 1 sin 60 o = (3)(0.5√3) = 1.5√3 N ( Maikaʻi no ka mea, kuhikuhi kēia ʻāpana vector ma ke axis y maikaʻi (i luna) )
F 2x = F 2 cos 0 o = (3)(1) = -3 N ( Maikaʻi ʻole no ka mea ke kuhikuhi nei kēia ʻāpana vector ma ke axis x maikaʻi ʻole (hema) )
F 2y = F 2 hewa 0 o = (3)(0) = 0
F 3x = F 3 cos 60 o = (6)(0.5) = 3 N ( Maikaʻi no ka mea, ke kuhikuhi nei kēia ʻāpana vector ma ke axis x maikaʻi (ʻākau ) )
F 3y = F 3 sin 60 o = (6)(0.5√3) = -3√3 N ( Maikaʻi ʻole no ka mea ke kuhikuhi nei kēia ʻāpana vector ma ke axis y maikaʻi ʻole ( i lalo ) )
Nā ʻāpana o nā vectors hopena:
ΣF x = F 1x – F 2x + F 3x = 1.5 N – 3 N + 3 N = 1.5 N
ΣF y = F 1y + F 2y – F 3y = 1.5√3 N + 0 N – 3√3 N = -1.5√3 N
ʻO ka vector hopena:
5. ʻElua mau ikaika, ʻo F 1 = 15 N a me F 2 = 9 N. ʻO ke kihi ma waena o nā vectors ʻelua he 60°. He aha ka hopena o nā vectors.
Makemake ʻia:
Ikaika 1 (F 1 ) = 15 Newton
Ikaika 2 (F 2 ) = 9 Newton
Kihi ( θ) = 60 o
Makemake ʻia: ʻO ka vector hopena
Lōlā:
6. He aha ka hopena o nā vectors ʻekolu e like me ka mea i hōʻike ʻia ma ke kiʻi ma lalo nei?
ʻIke ʻia:
F1 = 20 Newton, kihi ma waena o F1 a me ke axis x = 0
F 2 = 20 Newtons, kihi ma waena o F 2 a me ke axis x = 60
F 3 = 24 Newtons, kihi ma waena o F 3 a me ke axis x = 60
Makemake ʻia: ʻO ka vector hopena
Lōlā:
Nā ʻāpana o nā vectors:
F 1x = (F 1 )(cos 0) = (20)(1) = 20. Maikaʻi no ka mea, kuhikuhi kēia ʻāpana vector ma ke axis x maikaʻi (ʻākau )
F 1y = (F 1 )(sin 0) = (20)(0) = 0
F 2x = (F 2 )(cos 60) = (20)(0.5) = -10. Maikaʻi ʻole no ka mea ke kuhikuhi nei kēia ʻāpana vector ma ke axis x maikaʻi ʻole (hema).
F 2y = (F 2 )(sin 60) = (20)(0.5√3) = 10√3. Maikaʻi no ka mea, kuhikuhi kēia ʻāpana vector ma ke axis y maikaʻi (i luna)
F 3x = (F 3 )(cos 60) = (24)(0.5) = -12. Maikaʻi ʻole no ka mea ke kuhikuhi nei kēia ʻāpana vector ma ke axis x maikaʻi ʻole (hema).
F 3y = (F 3 )(sin 60) = (24)(0.5√3) = -12√3. N maikaʻi ʻole no ka mea ke kuhikuhi nei kēia ʻāpana vector ma ke axis y maikaʻi ʻole ( i lalo )
Nā ʻāpana o nā vectors hopena:
ʻO F x = F 1x – F 2x – F 3x = 20 – 10 – 12 = -2
F y = F 1y + F 2y – F 3y = 0 + 10√3 – 12√3 = -2√3
ʻO ka vector hopena:
