Ƙayyade abubuwan da aka haɗa na vector

An warware matsalolin vectors - ƙayyade abubuwan vector

1. Ƙarfin Newton mai lamba 20 yana yin kusurwar 30 ^o tare da axis ɗin x. Nemo ɓangarorin x da y na ƙarfin.

Magani

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

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

[irp]

2. F ₁ = 20 Newton yana yin kusurwar 30 ^o tare da axis y kuma F ₂ = 30 Newton yana yin kusurwar 60 ^o tare da axis -x. Nemo sassan x da y na F ₁ da F ₂.

Magani

F _1x = F ₁ cos 60 ^o = (20)(cos 60 ^o ) = (20)(0.5) = -10 Newtons (mara kyau saboda yana da alkibla iri ɗaya da axis -x)

F _2x = F ₂ cos 60 ^o = (30)(cos 60 ^o ) = (30)(0.5) = -15 Newtons (mara kyau saboda yana da alkibla iri ɗaya da axis -x)

F_1y = F₁ zunubi 60^o = (20)(zunubi 60^o) = (20)(0.5)√3) = 10√3 Newton (alama ce mai kyau saboda tana da alkibla iri ɗaya da axis ɗin y)

F_2y = F₂ zunubi 60^o = (30)(zunubi 60^o) = (30)(0.5)√3) = -15√3 Newton (mara kyau saboda yana da alkibla iri ɗaya da axis -y)

[irp]

3. F ₁ = 2 N, F ₂ = 4 N, F ₃ = 6 N. Nemo sassan x da y na F ₁ , F ₂ da F ₃!

Magani

F _1x = F ₁ cos 60 ^o = (2)(cos 60 ^o ) = (2)(0.5) = Newtons 1 (tabbatacce saboda yana da alkibla iri ɗaya da axis x)

F_2x = F₂ cos 30^o = (4)(kwas 30)^o) = (4)(0.5)√3) = -2√3 Newton (mara kyau saboda yana da alkibla iri ɗaya da axis -x)

F _3x = F ₃ cos 60 ^o = (6)(cos 60 ^o ) = (6)(0.5) = Newtons 3 (tabbatacce saboda yana da alkibla iri ɗaya da axis x)

F_1y = F₁ zunubi 60^o = (2)(zunubi 60^o) = (2)(0.5)√3) = √3 Newton (alama ce mai kyau saboda tana da alkibla iri ɗaya da axis ɗin y)

F _{2 y} = F ₂ zunubi 3 0 ^o = (4)(zunubi 30 ^o ) = (4)(0.5) = 2 Newtons (tabbatacce saboda yana da alkibla iri ɗaya da axis y)

F_3y = F₃ zunubi 60^o = (6)(zunubi 60^o) = (6)(0.5)√3) = -3√3 Newton (mara kyau saboda yana da alkibla iri ɗaya da axis -y)

[irp]

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1. Ƙayyade sakamakon a cikin vector na layi
2. Ƙayyade abubuwan da aka haɗa na vector
3. Ta hanyar amfani da ka'idar Pythagorean, ƙayyade sakamakon vectors guda biyu.
4. Ƙayyade sakamakon vectors guda biyu ta amfani da lissafin cosines
5. Ƙayyade sakamakon vectors guda biyu ta amfani da abubuwan da ke cikin vectors