Ukwengeza ama-vector usebenzisa izingxenye - izinkinga nezixazululo

Ukwengeza ama-vector usebenzisa izingxenye - izinkinga nezixazululo

1. Amavektha amathathu njengoba kuboniswe esithombeni esingezansi.

V₁ = 30

V ₂ = 30

V ₃ = 40

Iyini imiphumela ye- vectors.

Kwaziwa:

V ₁ = 30, i-engeli ephakathi kwe-V ₁ kanye ne-x axis = 30 ^o

V ₂ = 30, i-engeli ephakathi kwe-V ₂ kanye ne-x axis = 30 ^o

V ₃ = 40, i-engeli ephakathi kwe-V ₃ kanye ne-x axis = 0 ^o

Okufunwayo: Ama-vector aphumelayo

Isixazululo:

Izingxenye zama-vector :

V _1x = (V ₁ )(cos 30 ^o ) = (30)(0.5√3) = 15√3. Okuhle ngoba le ngxenye yevektha ikhomba eceleni kwe-x axis enhle (ngakwesokudla).

V _1y = (V ₁ )(sin 30 ^o ) = (30)(0.5) = 15. Okuhle ngoba le ngxenye yevektha ikhomba eceleni kwe-axis ehle ka-y (phezulu).

V _2x = (V ₂ )(cos 30 ^o ) = (30)(0.5√3) = -15√3. Okubi ngoba le ngxenye yevektha ikhomba eceleni kwe-axis x engebi (ngakwesobunxele).

V _2y = (V ₂ )(sin 30 ^o ) = (30)(0.5) = 15. Okuhle ngoba le ngxenye yevektha ikhomba eceleni kwe-axis ehle ka-y (phezulu).

V _3x = (V ₃ )(cos 0 ^o ) = (40)(1) = 40. Okuhle ngoba le ngxenye yevektha ikhomba eceleni kwe-x axis enhle (ngakwesokudla).

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

Izingxenye zamavektha aphumelayo:

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

Ivektha ephumela :

2. Amandla amabili aqonde komunye nomunye, F ₁ = 12 N kanye F ₂ = 5 N. Uyini umphumela wamandla womabili?

Kwaziwa:

Amandla 1 (F ₁ ) = 12 Newton

Amandla 2 (F ₂ ) = 5 Newton

Okufunwayo: Ama-vector aphumelayo ( ΣF)

Isixazululo:

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

ΣF = √ 169 = 13 Newton

3. Amavekhtha amathathu,

V₁ = 30

V ₂ = 30

V ₃ = 40

Nquma ama-vector aphumela.

Kwaziwa:

v ₁ = 30, kwenza u-30 ^o cishe i-axis x engemihle

v ₂ = 30, kwenza u-30 ^o cishe nge-axis x enhle

v ₃ = 40, kwenza u-0 ^o cishe nge-axis x enhle

Okufunwayo: Ama-vector aphumelayo

Isixazululo:

Izingxenye zama-vector:

v _1x = v ₁ cos 30 ^o = (30)(0.5 √ 3) = -15 √ 3 ( Okubi ngoba le ngxenye yevektha ikhomba eceleni kwe-axis x engembi (ngakwesobunxele) )

v _1y = v ₁ sin 30 ^o = (30)(0.5) = 15 ( Okuhle ngoba le ngxenye yevektha ikhomba eceleni kwe-axis enhle y (phezulu) )

v _2x = v ₂ cos 30 ^o = (30)(0.5 √ 3) = 15 √ 3 ( Okuhle ngoba le ngxenye yevektha ikhomba eceleni kwe-x axis enhle (ngakwesokudla ) )

v _2y = v ₂ sin 30 ^o = (30)(0.5) = 15 ( Okuhle ngoba le ngxenye yevektha ikhomba eceleni kwe-axis enhle y (phezulu). )

v _3x = v ₃ cos 0 ^o = (40)(1) = 40 ( Okuhle ngoba le ngxenye yevektha ikhomba eceleni kwe-x axis enhle (ngakwesokudla). )

v _3y = v ₃ isono 0 ^o = (40)(0) = 0

Izingxenye zamavektha aphumelayo:

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

Ivektha ephumela:

4. Uyini umphumela wamavektha amathathu njengoba kuboniswe esithombeni esingezansi :

Kwaziwa:

F₁ = AmaNewton ayi-3, kwenza 60^o mayelana ne-axis x enhle

F ₂ = 3 Newtons, kwenza u-0 ^o mayelana ne-axis x engemihle

F ₃ = 6 Newtons , kwenza u-60 ^o mayelana ne-axis engemihle ka-y

Kufunwa: Ivektha ephumela

Isixazululo:

Izingxenye zama-vector:

F _1x = F ₁ cos 60 ^o = (3)(0.5) = 1.5 N ( Okuhle ngoba le ngxenye yevektha ikhomba eceleni kwe-x axis enhle (ngakwesokudla ) )

F _1y = F ₁ sin 60 ^o = (3)(0.5√3) = 1.5√3 N ( Okuhle ngoba le ngxenye yevektha ikhomba eceleni kwe-axis enhle y (phezulu) )

F _2x = F ₂ cos 0 ^o = (3)(1) = -3 N ( Okubi ngoba le ngxenye yevektha ikhomba eceleni kwe-axis x engembi (ngakwesobunxele) )

F _2y = F ₂ isono 0 ^o = (3)(0) = 0

F _3x = F ₃ cos 60 ^o = (6)(0.5) = 3 N ( Okuhle ngoba le ngxenye yevektha ikhomba eceleni kwe-x axis enhle (ngakwesokudla ) )

F _3y = F ₃ sin 60 ^o = (6)(0.5√3) = -3√3 N ( Okubi ngoba le ngxenye yevektha ikhomba eceleni kwe- axis ka-y engemihle ( iwadi ezansi ) )

Izingxenye zamavektha aphumelayo:

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

Ivektha ephumela:

5. Amandla amabili, F ₁ = 15 N kanye F _{2 = 9 N. I} - engeli phakathi kwala mavektha womabili ingu-60°. Iyini imiphumela yamavektha.

Kufunwa:

Amandla 1 (F ₁ ) = 15 Newton

Amandla 2 (F ₂ ) = 9 Newton

I-engeli ( θ) = 60 ^o

Kufunwa: Ivektha ephumelayo

Isixazululo:

6. Uyini umphumela wamavektha amathathu njengoba kuboniswe esithombeni esingezansi?

Kwaziwa:

F₁ = 20 Newton, i-engeli ephakathi kuka-F₁ kanye ne-x axis = 0

F ₂ = 20 Newtons, i-engeli ephakathi kwe-F ₂ kanye ne-x axis = 60

F ₃ = 24 Newtons, i-engeli ephakathi kwe-F ₃ kanye ne-x axis = 60

Kufunwa: Ivektha ephumela

Isixazululo:

Izingxenye zama-vector:

F _1x = (F ₁ )(cos 0) = (20)(1) = 20. Okuhle ngoba le ngxenye yevektha ikhomba eceleni kwe-x axis enhle (ngakwesokudla )

F _1y = (F ₁ )(isono 0) = (20)(0) = 0

F _2x = (F ₂ )(cos 60) = (20)(0.5) = -10. Okubi ngoba le ngxenye yevektha ikhomba eceleni kwe-axis x engembi (ngakwesobunxele)

F _2y = (F ₂ )(sin 60) = (20)(0.5√3) = 10√3. Okuhle ngoba le ngxenye yevektha ikhomba eceleni kwe-axis ehle ka-y (phezulu)

F _3x = (F ₃ )(cos 60) = (24)(0.5) = -12. Okubi ngoba le ngxenye yevektha ikhomba eceleni kwe-axis x engembi (ngakwesobunxele)

F _3y = (F ₃ )(isono 60) = (24)(0.5√3) = -12√3. N negative ngoba le ngxenye yevektha ikhomba eceleni kwe- axis ye-y engemihle ( iwadi ephansi )

Izingxenye zamavektha aphumelayo:

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

Ivektha ephumela: