Kuwonjezera ma vector pogwiritsa ntchito zigawo - mavuto ndi mayankho

Kuwonjezera ma vector pogwiritsa ntchito zigawo - mavuto ndi mayankho

1. Ma vekitala atatu monga momwe zasonyezedwera pachithunzi chili pansipa.

V₁ = 30

V ₂ = 30

V ₃ = 40

Kodi ma vector otsatirawa ndi otani?

Zodziwika:

V ₁ = 30, ngodya pakati pa V ₁ ndi x axis = 30 ^o

V ₂ = 30, ngodya pakati pa V ₂ ndi x axis = 30 ^o

V ₃ = 40, ngodya pakati pa V ₃ ndi x axis = 0 ^o

Kufunidwa: Ma vector otsatira

Yankho:

Zigawo za ma vector :

V _1x = (V ₁ )(cos 30 ^o ) = (30)(0.5√3) = 15√3. Yabwino chifukwa chigawo ichi cha vekitala chimaloza motsatira mzere wa x wabwino (kumanja).

V _1y = (V ₁ )(sin 30 ^o ) = (30)(0.5) = 15. Yabwino chifukwa gawo la vekitala iyi limaloza motsatira mzere wabwino wa y (mmwamba).

V _2x = (V ₂ )(cos 30 ^o ) = (30)(0.5√3) = -15√3. Choyipa chifukwa chigawo ichi cha vekitala chimaloza motsatira mzere wa x woyipa (kumanzere).

V _2y = (V ₂ )(sin 30 ^o ) = (30)(0.5) = 15. Yabwino chifukwa gawo la vekitala iyi limaloza motsatira mzere wabwino wa y (mmwamba).

V _3x = (V ₃ )(cos 0 ^o ) = (40)(1) = 40. Yabwino chifukwa gawo la vekitala ili limaloza motsatira mzere wa x wabwino (kumanja).

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

Zigawo za ma vector otsatira:

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

Vekitala yotsatira :

2. Mphamvu ziwiri zolunjika, F ₁ = 12 N ndi F ₂ = 5 N. Kodi zotsatira za mphamvu zonse ziwiri ndi ziti?

Zodziwika:

Mphamvu 1 (F ₁ ) = 12 Newton

Mphamvu 2 (F ₂ ) = 5 Newton

Kufunidwa: Ma vector otsatira ( ΣF)

Yankho:

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

ΣF = √ 169 = 13 Newton

3. Ma vector atatu,

V₁ = 30

V ₂ = 30

V ₃ = 40

Dziwani ma vector omwe akubwera.

Zodziwika:

v ₁ = 30, imapanga 30 ^o pafupifupi mzere wa x woyipa

v ₂ = 30, imapanga 30 ^o pafupifupi mzere wa x wabwino

v ₃ = 40, imapanga 0 ^o pafupifupi mzere wa x wabwino

Kufunidwa: Ma vector otsatira

Yankho:

Zigawo za ma vector:

v _1x = v ₁ cos 30 ^o = (30)(0.5 √ 3) = -15 √ 3 ( Negative chifukwa gawo la vector ili limaloza motsatira mzere wa x wotsutsa (kumanzere) )

v _1y = v ₁ sin 30 ^o = (30)(0.5) = 15 ( Yabwino chifukwa gawo la vekitala iyi limaloza motsatira mzere wabwino wa y (mmwamba) )

v _2x = v ₂ cos 30 ^o = (30)(0.5 √ 3) = 15 √ 3 ( Yabwino chifukwa gawo la vekitala iyi limaloza motsatira mzere wa x wabwino (kumanja ) )

v _2y = v ₂ sin 30 ^o = (30)(0.5) = 15 ( Yabwino chifukwa gawo la vekitala iyi limaloza motsatira mzere wabwino wa y (mmwamba). )

v _3x = v ₃ cos 0 ^o = (40)(1) = 40 ( Yabwino chifukwa gawo la vekitala iyi limaloza motsatira mzere wa x wabwino (kumanja). )

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

Zigawo za ma vector otsatira:

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

Vekitala yotsatira:

4. Kodi zotsatira za ma vector atatu ndi ziti monga momwe zasonyezedwera pachithunzi pansipa :

Zodziwika:

F₁ = 3 Newtons, kumathandiza 60^o za mzere wabwino wa x

F ₂ = 3 Newtons, imapanga 0 ^o pafupifupi mzere wa x woyipa

F ₃ = 6 Newtons , imapanga 60 ^o pafupifupi mzere woyipa wa y

Kufunidwa: Chotsatira cha zotsatira

Yankho:

Zigawo za ma vector:

F _1x = F ₁ cos 60 ^o = (3)(0.5) = 1.5 N ( Yabwino chifukwa gawo la vekitala iyi limaloza motsatira mzere wa x wabwino (kumanja ) )

F _1y = F ₁ sin 60 ^o = (3)(0.5√3) = 1.5√3 N ( Yabwino chifukwa gawo la vekitala iyi limaloza motsatira mzere wabwino wa y (mmwamba) )

F _2x = F ₂ cos 0 ^o = (3)(1) = -3 N ( Negative chifukwa gawo la vector ili limaloza motsatira mzere wa x woyipa (kumanzere) )

F _2y = F ₂ tchimo 0 ^o = (3) (0) = 0

F _3x = F ₃ cos 60 ^o = (6)(0.5) = 3 N ( Yabwino chifukwa gawo la vekitala iyi limaloza motsatira mzere wa x wabwino (kumanja ) )

F _3y = F ₃ sin 60 ^o = (6)(0.5√3) = -3√3 N ( Negative chifukwa gawo la vector ili limaloza motsatira mzere woyipa wa y ( pansi ) )

Zigawo za ma vector otsatira:

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

Vekitala yotsatira:

5. Mphamvu ziwiri, F ₁ = 15 N ndi F 2 ₌ 9 N. Ngodya pakati pa mavekitala onse awiri ndi 60°. Kodi zotsatira za mavekitala ndi ziti?

Akufuna:

Mphamvu 1 (F ₁ ) = 15 Newton

Mphamvu 2 (F ₂ ) = 9 Newton

Ngodya ( θ) = 60 ^o

Kufunidwa: Chotsatira cha zotsatira

Yankho:

6. Kodi zotsatira za mavekitala atatu ndi ziti monga momwe zasonyezedwera pachithunzi chili pansipa?

Zodziwika:

F₁ = 20 Newton, ngodya pakati pa F₁ ndi x axis = 0

F ₂ = 20 Newtons, ngodya pakati pa F ₂ ndi x axis = 60

F ₃ = 24 Newtons, ngodya pakati pa F ₃ ndi x axis = 60

Kufunidwa: Chotsatira cha zotsatira

Yankho:

Zigawo za ma vector:

F _1x = (F ₁ )(cos 0) = (20)(1) = 20. Yabwino chifukwa gawo la vekitala iyi limaloza motsatira mzere wa x wabwino (kumanja )

F _1y = (F ₁ )(tchimo 0) = (20)(0) = 0

F _2x = (F ₂ )(cos 60) = (20)(0.5) = -10. Negative chifukwa gawo la vector ili limaloza motsatira mzere wa x wotsutsa (kumanzere)

F _2y = (F ₂ )(sin 60) = (20)(0.5√3) = 10√3. Yabwino chifukwa chigawo ichi cha vekitala chimaloza motsatira mzere wabwino wa y (mmwamba)

F _3x = (F ₃ )(cos 60) = (24)(0.5) = -12. Negative chifukwa gawo la vector ili limaloza motsatira mzere wa x wotsutsa (kumanzere)

F _3y = (F ₃ )(sin 60) = (24)(0.5√3) = -12√3. N negative chifukwa gawo la vector ili limaloza ku mzere woyipa wa y ( pansi )

Zigawo za ma vector otsatira:

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

Vekitala yotsatira: