Fa'aopoopoina o vectors e fa'aaoga ai vaega - fa'afitauli ma fofo

Fa'aopoopoina o vectors e fa'aaoga ai vaega - fa'afitauli ma fofo

1. Tolu vectors e pei ona faʻaalia i le ata o loʻo i lalo.

V₁ = 30

V2 = ₃₀

V3 = ₄₀

O a ni vectors e maua mai ai.

Ua iloa:

V ₁ = 30, tulimanu i le va o le V ₁ ma le x axis = 30 ^o

V ₂ = 30, tulimanu i le va o le V ₂ ma le x axis = 30 ^o

V ₃ = 40, tulimanu i le va o le V ₃ ma le x axis = 0 ^o

Mana'omia: O vectors e maua mai ai

Fofo:

O vaega o vectors :

V _1x = (V ₁ )(cos 30 ^o ) = (30)(0.5√3) = 15√3. Lelei auā o lenei vaega vector e faasino i luga o le x axis lelei (agai i le taumatau).

V _1y = (V ₁ )(sin 30 ^o ) = (30)(0.5) = 15. Lelei auā o lenei vaega vector e fa'asino i luga o le y axis lelei (aga'i i luga).

V _2x = (V ₂ )(cos 30 ^o ) = (30)(0.5√3) = -15√3. Leaga auā o lenei vaega veketi e faasino i luga o le au x leaga (agavale).

V _2y = (V ₂ )(sin 30 ^o ) = (30)(0.5) = 15. Lelei auā o lenei vaega vector e fa'asino i luga o le y axis lelei (aga'i i luga).

V _3x = (V ₃ )(cos 0 ^o ) = (40)(1) = 40. Lelei auā o lenei vaega vector e fa'asino i luga o le x axis lelei (aga'i taumatau).

V _3y = (V ₃ )(sala 0 ^o ) = (40)(0) = 0

O vaega o vectors e maua mai ai:

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

O le vector e mafua mai ai :

2. E lua malosiaga e fa'asaga sa'o le tasi i le isi, F ₁ = 12 N ma le F ₂ = 5 N. O le a le taunuuga o malosiaga uma e lua.

Ua iloa:

Malosiaga 1 (F ₁ ) = 12 Newton

Malosiaga 2 (F ₂ ) = 5 Newton

Mana'omia: O vectors e maua mai ai ( ΣF)

Fofo:

ΣF ² = F ₁ ² + F ₂ ² = 12 ² + 5 ² = 144 + 25 = 169

ΣF = √ 169 = 13 Newton

3. Tolu vectors,

V₁ = 30

V2 = ₃₀

V3 = ₄₀

Fuafua ia vectors e maua mai ai.

Ua iloa:

v ₁ = 30, e faia le 30 ^o i luga o le au x leaga

v ₂ = 30, e 30 ^{le o} i luga o le x axis lelei

v ₃ = 40, e 0 ^{le o} i luga o le x axis lelei

Mana'omia: O vectors e maua mai ai

Fofo:

O vaega o vectors:

v _1x = v ₁ cos 30 ^o = (30)(0.5 √ 3) = -15 √ 3 ( Leaga auā o lenei vaega veketi e faasino i luga o le x axis leaga (agavale) )

v _1y = v ₁ sin 30 ^o = (30)(0.5) = 15 ( Lelei auā o lenei vaega vector e faasino i luga o le y axis lelei (agai i luga) )

v _2x = v ₂ cos 30 ^o = (30)(0.5 √ 3) = 15 √ 3 ( Lelei auā o lenei vaega vector e faasino i luga o le x axis lelei (agai i le taumatau ) )

v _2y = v ₂ sin 30 ^o = (30)(0.5) = 15 ( Lelei auā o lenei vaega vector e fa'asino i luga o le y axis lelei (aga'i i luga). )

v _3x = v ₃ cos 0 ^o = (40)(1) = 40 ( E lelei auā o lenei vaega vector e faasino i luga o le x axis lelei (agai i le taumatau). )

v _3y = v ₃ agasala 0 ^o = (40)(0) = 0

O vaega o vectors e maua mai ai:

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

O le vector e mafua mai ai:

4. O le a le taunuuga o vectors e tolu e pei ona faaalia i le ata o loo i lalo :

Ua iloa:

F₁ = 3 Newtoni, faia 60^o e uiga i le x axis lelei

F ₂ = 3 Newtons, e 0 ^o i luga o le x axis leaga

F ₃ = 6 Newtons , e faia le 60 ^o i luga o le axis y leaga

Manaomia: O le vector e maua mai ai

Fofo:

O vaega o vectors:

F _1x = F ₁ cos 60 ^o = (3)(0.5) = 1.5 N ( Lelei auā o lenei vaega vector e fa'asino i luga o le x axis lelei (aga'i taumatau ) )

F _1y = F ₁ sin 60 ^o = (3)(0.5√3) = 1.5√3 N ( Lelei auā o lenei vaega vector e faasino i luga o le y axis lelei (agai i luga) )

F _2x = F ₂ cos 0 ^o = (3)(1) = -3 N ( Leaga auā o lenei vaega veketi e faasino i le itu leaga x (agavale) )

F _2y = F ₂ agasala 0 ^o = (3)(0) = 0

F _3x = F ₃ cos 60 ^o = (6)(0.5) = 3 N ( Lelei auā o lenei vaega vector e fa'asino i luga o le x axis lelei (aga'i taumatau ) )

F _3y = F ₃ sin 60 ^o = (6)(0.5√3) = -3√3 N ( Leaga auā o lenei vaega veketi e fa'asino i le itu leaga y ( i lalo ) )

O vaega o vectors e maua mai ai:

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

O le vector e mafua mai ai:

5. Malosiaga e lua, F ₁ = 15 N ma le F 2 ₌ 9 N. O le tulimanu i le va o vectors uma e lua e 60°. O le a le taunuuga o vectors.

Mana'omia:

Malosiaga 1 (F ₁ ) = 15 Newton

Malosiaga 2 (F ₂ ) = 9 Newton

Tulimanu ( θ) = 60 ^o

Manaomia: O le vector e maua mai ai

Fofo:

6. O le a le taunuuga o vectors e tolu e pei ona faaalia i le ata o loo i lalo?

Ua iloa:

F₁ = 20 Newton, tulimanu i le va o le F₁ ma le x axis = 0

F ₂ = 20 Newtons, tulimanu i le va o le F ₂ ma le x axis = 60

F ₃ = 24 Newtons, tulimanu i le va o le F ₃ ma le x axis = 60

Manaomia: O le vector e maua mai ai

Fofo:

O vaega o vectors:

F _1x = (F ₁ )(cos 0) = (20)(1) = 20. Lelei auā o lenei vaega vector e faasino i luga o le x axis lelei (agai i le taumatau )

F _1y = (F ₁ )(sala 0) = (20)(0) = 0

F _2x = (F ₂ )(cos 60) = (20)(0.5) = -10. Leaga auā o lenei vaega veketi e faasino i luga o le x axis leaga (agavale)

F _2y = (F ₂ )(sin 60) = (20)(0.5√3) = 10√3. Lelei auā o lenei vaega vector e faasino i luga o le y axis lelei (agai i luga)

F _3x = (F ₃ )(cos 60) = (24)(0.5) = -12. Leaga auā o lenei vaega veketi e faasino i luga o le x axis leaga (agavale)

F _3y = (F ₃ )(sin 60) = (24)(0.5√3) = -12√3. N leaga auā o lenei vaega vector e faasino i luga o le y axis leaga ( i lalo )

O vaega o vectors e maua mai ai:

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

O le vector e mafua mai ai: