Go'aami qaybaha vektorka

Dhibaatooyinka la xalliyay ee ku jira vectors - go'aami qaybaha vector-ka

1. Xoogga 20 Newton wuxuu sameeyaa xagal 30 ^o ah oo leh dhidibka x. Soo hel labada qaybood ee x iyo y ee xoogga.

Solution

F _x = F cos 30 ^o = (20)(cos 30 ^o ) = (20)(0.5 √ 3 ) = 10 √ 3 Newtons

F _y = F dembi 30 ^o = (20) ( dembi 30 ^o ) = (20) (0.5) = 10 Newtons

[irp]

2. F ₁ = 20 Newton wuxuu sameeyaa xagal 30 ^o ah oo leh dhidibka y iyo F ₂ = 30 Newton wuxuu sameeyaa xagal 60 ^o ah oo leh dhidibka -x. Soo hel labada qaybood ee x iyo y ee F ₁ iyo F ₂.

Solution

F _1x = F ₁ cos 60 ^o = (20)(cos 60 ^o ) = (20)(0.5) = -10 Newtons (taban sababtoo ah waxay leedahay jiho la mid ah dhidibka -x)

F _2x = F ₂ cos 60 ^o = (30)(cos 60 ^o ) = (30)(0.5) = -15 Newtons (taban sababtoo ah waxay leedahay jiho la mid ah dhidibka -x)

F_1y =F₁ dembi 60^o = (20)(dembi 60^o) = (20)(0.5)√3= 10√3 Newton (togan sababtoo ah waxay leedahay jiha la mid ah dhidibka y)

F_2y =F₂ dembi 60^o = (30)(dembi 60^o) = (30)(0.5)√3) = -15√3 Newton (taban sababtoo ah waxay leedahay jiho la mid ah dhidibka -y)

[irp]

3. F ₁ = 2 N, F ₂ = 4 N, F ₃ = 6 N. Soo hel labada qaybood ee x iyo y ee F ₁ , F ₂ iyo F ₃!

Solution

F _1x = F ₁ cos 60 ^o = (2)(cos 60 ^o ) = (2)(0.5) = 1 Newtons (togan sababtoo ah waxay leedahay jiho isku mid ah oo leh dhidibka x)

F_2x =F₂ cos 30^o = (4)(koos 30)^o) = (4)(0.5)√3) = -2√3 Newton (taban sababtoo ah waxay leedahay jiho isku mid ah oo leh dhidibka -x)

F _3x = F ₃ cos 60 ^o = (6)(cos 60 ^o ) = (6)(0.5) = 3 Newtons (togan sababtoo ah waxay leedahay jiho isku mid ah oo leh dhidibka x)

F_1y =F₁ dembi 60^o = (2)(dembi 60^o) = (2)(0.5)√3) = √3 Newton (togan sababtoo ah waxay leedahay jiha la mid ah dhidibka y)

F _{2 y} = F ₂ sin 3 0 ^o = (4)(sin 30 ^o ) = (4)(0.5) = 2 Newtons (togan sababtoo ah waxay leedahay jiha isku mid ah oo leh dhidibka y)

F_3y =F₃ dembi 60^o = (6)(dembi 60^o) = (6)(0.5)√3) = -3√3 Newton (taban sababtoo ah waxay leedahay jiho isku mid ah oo leh dhidibka -y)

[irp]

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