Ku darista vectors iyadoo la adeegsanayo qaybaha - dhibaatooyinka iyo xalalka
1. Saddex fallaadho sida ku cad sawirka hoose.
V1 = 30
V 2 = 30
V 3 = 40
Waa maxay vector- yada ka dhasha.
La yaqaan:
V 1 = 30, xagal u dhexeeya dhidibka V 1 iyo x = 30 o
V 2 = 30, xagal u dhexeeya dhidibka V 2 iyo x = 30 o
V 3 = 40, xagal u dhexeeya V 3 iyo dhidibka x = 0 o
La Doonayo: Vectors-ka natiijada leh
Xalka:
V 1x = (V 1 )(cos 30 o ) = (30)(0.5√3) = 15√3. Togan sababtoo ah qaybtan vector-ka waxay tilmaamaysaa dhidibka x ee togan (midigta).
V 1y = (V 1 )(sin 30 o ) = (30)(0.5) = 15. Togan sababtoo ah qaybtan vector-ka waxay tilmaamaysaa dhidibka y ee togan (kor).
V 2x = (V 2 )(cos 30 o ) = (30)(0.5√3) = -15√3. Taban sababtoo ah qaybtan vector-ka waxay tilmaamaysaa dhidibka x ee taban (bidix).
V 2y = (V 2 )(sin 30 o ) = (30)(0.5) = 15. Togan sababtoo ah qaybtan vector-ka waxay tilmaamaysaa dhidibka y ee togan (kor).
V 3x = (V 3 )(cos 0 o ) = (40)(1) = 40. Togan sababtoo ah qaybtan vector-ka waxay tilmaamaysaa dhidibka x ee togan (midigta).
V 3y = (V 3 ) ( dembi 0 o ) = (40) (0) = 0
Qaybaha ka mid ah fallaadhaha natiijada:
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
Vektor-ka natiijada ka soo baxday :
2. Laba awoodood oo is dul saaran, F 1 = 12 N iyo F 2 = 5 N. Waa maxay natiijada labada awoodood.
La yaqaan:
Xoogga 1 (F 1 ) = 12 Newton
Xoogga 2 (F 2 ) = 5 Newton
La Doonayo: Vectors-ka natiijada leh ( ΣF)
Xalka:
ΣF 2 = F 1 2 + F 2 2 = 12 2 + 5 2 = 144 + 25 = 169
ΣF = √ 169 = 13 Newton
3. Saddex fallaadho,
V1 = 30
V 2 = 30
V 3 = 40
Go'aami fallaadhaha ka dhasha.
La yaqaan:
v 1 = 30, wuxuu ka dhigayaa 30 o oo ku saabsan dhidibka x ee taban
v 2 = 30, wuxuu ka dhigayaa 30 o oo ku saabsan dhidibka x ee togan
v 3 = 40, wuxuu ka dhigayaa 0 o oo ku saabsan dhidibka x ee togan
La Doonayo: Vectors-ka natiijada leh
Xalka:
Qaybaha vector-ka:
v 1x = v 1 cos 30 o = (30)(0.5 √ 3) = -15 √ 3 ( Taban sababtoo ah qaybtan vector waxay tilmaamaysaa dhidibka x ee taban (bidix) )
v 1y = v 1 sin 30 o = (30)(0.5) = 15 ( Togan sababtoo ah qaybtan vector-ka waxay tilmaamaysaa dhidibka y ee togan (kor) )
v 2x = v 2 cos 30 o = (30)(0.5 √ 3) = 15 √ 3 ( Togan sababtoo ah qaybtan vector waxay tilmaamaysaa dhidibka x ee togan (midigta ) )
v 2y = v 2 sin 30 o = (30)(0.5) = 15 ( Togan sababtoo ah qaybtan vector-ka waxay tilmaamaysaa dhidibka y ee togan (kor). )
v 3x = v 3 cos 0 o = (40)(1) = 40 ( Togan sababtoo ah qaybtan vector-ka waxay tilmaamaysaa dhidibka x ee togan (midigta). )
v 3y = v 3 dembi 0 o = (40) (0) = 0
Qaybaha ka mid ah fallaadhaha natiijada:
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
Vektor-ka natiijada ka soo baxday:
4. Waa maxay natiijada saddexda vector sida ka muuqata sawirka hoose :
La yaqaan:
F1 = 3 Newton, samaysyada 60o ku saabsan dhidibka x ee togan
F 2 = 3 Newtons, waxay ka dhigaysaa 0 o oo ku saabsan dhidibka x ee taban
F 3 = 6 Newtons , waxay ka dhigaysaa 60 o oo ku saabsan dhidibka y ee taban
La Raadinayo: Vector-ka natiijada keenay
Xalka:
Qaybaha vector-ka:
F 1x = F 1 cos 60 o = (3)(0.5) = 1.5 N ( Togan sababtoo ah qaybtan vector-ka waxay tilmaamaysaa dhidibka x ee togan (midigta ) )
F 1y = F 1 sin 60 o = (3)(0.5√3) = 1.5√3 N ( Togan sababtoo ah qaybtan vector-ka waxay tilmaamaysaa dhidibka y ee togan (kor) )
F 2x = F 2 cos 0 o = (3)(1) = -3 N ( Taban sababtoo ah qaybtan vector waxay tilmaamaysaa dhidibka x ee taban (bidix) )
F 2y = F 2 dembi 0 o = (3) (0) = 0
F 3x = F 3 cos 60 o = (6)(0.5) = 3 N ( Togan sababtoo ah qaybtan vector-ka waxay tilmaamaysaa dhidibka x ee togan (midigta ) )
F 3y = F 3 sin 60 o = (6)(0.5√3) = -3√3 N ( Taban sababtoo ah qaybtan vector-ka waxay tilmaamaysaa dhidibka y ee taban ( hoos u jeeda) )
Qaybaha ka mid ah fallaadhaha natiijada:
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
Vektor-ka natiijada ka soo baxday:
5. Laba xoog, F 1 = 15 N iyo F 2 = 9 N. Xaglaha u dhexeeya labada vector waa 60°. Waa maxay natiijada vectors-ka.
La doonayo:
Xoogga 1 (F 1 ) = 15 Newton
Xoogga 2 (F 2 ) = 9 Newton
Xagasha ( θ) = 60 o
La Raadinayo: Vector-ka natiijada keenay
Xalka:
6. Waa maxay natiijada saddexda vector sida ku cad sawirka hoose?
La yaqaan:
F1 = 20 Newton, xagal u dhexeeya F1 iyo dhidibka x = 0
F 2 = 20 Newtons, xagal u dhexeeya F 2 iyo x dhidibka = 60
F 3 = 24 Newtons, xagal u dhexeeya F 3 iyo x dhidibka = 60
La Raadinayo: Vector-ka natiijada keenay
Xalka:
Qaybaha vector-ka:
F 1x = (F 1 )(cos 0) = (20)(1) = 20. Togan sababtoo ah qaybtan vector-ka waxay tilmaamaysaa dhidibka x ee togan (midigta )
F 1y = (F 1 )( dembi 0) = (20) (0) = 0
F 2x = (F 2 )(cos 60) = (20)(0.5) = -10. Taban sababtoo ah qaybtan vector-ka waxay tilmaamaysaa dhidibka x ee taban (bidix)
F 2y = (F 2 )(sin 60) = (20)(0.5√3) = 10√3. Togan sababtoo ah qaybtan vector-ka waxay tilmaamaysaa dhidibka y ee togan (kor)
F 3x = (F 3 )(cos 60) = (24)(0.5) = -12. Taban sababtoo ah qaybtan vector-ka waxay tilmaamaysaa dhidibka x ee taban (bidix)
F 3y = (F 3 )(sin 60) = (24)(0.5√3) = -12√3. N taban sababtoo ah qaybtan vector-ka waxay tilmaamaysaa dhidibka y taban ( dhinaca hoose )
Qaybaha ka mid ah fallaadhaha natiijada:
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
Vektor-ka natiijada ka soo baxday:
