Fa'ata'ita'iga o fesili i le fuafuaina o vaega vector

2 Faʻataʻitaʻiga o fesili i le fuafuaina o vaega vector

1. O le vector malosi F = 20 Newton e fausia ai se tulimanu e 30 ^o i le x-axis lelei. Fuafua vaega o le vector F i luga o le x-axis (F _x ) ma le y-axis (F _y ).

Talanoaga
F_x = F cos 30^o = (20)(cos 30^o) = (20)(0,5√3) = 10√3 Niutoni
F_y = F sin 30^o = (20)(sin 30^o) = (20)(0,5) = 10 Niutone

2. O le Vector F ₁ = 20 Newton e fausia se tulimanu e 30 ^o ma le y-axis lelei ma le F ₂ = 30 Newton e fausia se tulimanu e 60 ^o ma le x-axis leaga. Fuafua vaega o vectors F ₁ ma le F ₂ i luga o le x-axis ma luga o le y-axis.

Talanoaga
F_1x =F₁ cos 60^o = (20)(cos 60^o) = (20)(0,5) = -10 Newton (leaga auā o loʻo i le itu leaga x)
F_2x =F₂ cos 60^o = (30)(cos 60^o) = (30)(0,5) = -15 Newton (leaga auā o loʻo i le itu leaga x)
F_1y =F₁ agasala 60^o = (20)(sin 60^o) = (20)(0,5√3) = 10√3 Newton (lelei auā o loʻo i le itu lelei y)
F_2y =F₂ agasala 60^o = (30)(sin 60^o) = (30)(0,5√3) = -15√3 Newton (leaga auā o loʻo i le itu leaga y)

3. F ₁ = 2 N, F ₂ = 4 N, F ₃ = 6 N. Fuafua vaega o vectors F ₁ , F ₂ ma le F ₃ i luga o le x ma le y axes!

Talanoaga
F_1x =F₁ cos 60^o = (2)(cos 60^o) = (2)(0,5) = 1 Newton (lelei auā o loʻo i le itu lelei x)
F_2x =F₂ cos 30^o = (4)(cos 30^o) = (4)(0,5√3) = -2√3 Newton (leaga auā o loʻo i le itu leaga x)
F_3x =F₃ cos 60^o = (6)(cos 60^o) = (6)(0,5) = 3 Newton (lelei auā o loʻo i le itu lelei x)
F_1y =F₁ agasala 60^o = (2)(sin 60^o) = (2)(0,5√3) = √3 Newton (lelei auā o loʻo i le itu lelei y)
F_2y =F₂ agasala 30^o = (4)(sin 30^o) = (4)(0,5) = 2 Newton (lelei auā o loʻo i le itu lelei y)
F_3y =F₃ agasala 60^o = (6)(sin 60^o) = (6)(0,5√3) = -3√3 Newton (leaga auā o loʻo i le itu leaga y)

Fesili i le fuafuaina o vaega vector

1. O le vector malosi F = 8 Newton e fausia ai se tulimanu e 60^o i le x-axis lelei. Fuafua vaega o le vector F i luga o le x-axis (F_x) ma le y-axis (F_y).
2. Veketo F₁ = 8 Newtons e fausia ai se tulimanu e 45^o i le y-axis lelei ma le F₂ = 10 Newtons e fausia ai se tulimanu e 30^o i le itu-x leaga. Fuafua vaega o le vector F₁ ma le F₂ i luga o le x-axis ma luga o le y-axis.
3. F₁ = 4 N, F₂ = 8 N, F₃ = 12 N. Fuafua vaega o le vector F₁, F₂ ma le F₃ i luga o le x-axis ma le y-axis!

[Fa'aperetania: Foia o fa'afitauli o vectors – fuafuaina o vaega vectors ]