Cov lus nug piv txwv txog kev txiav txim siab txog cov khoom vector

2 Piv txwv ntawm cov lus nug txog kev txiav txim siab cov khoom vector

1. Lub zog vector F = 20 Newton tsim lub kaum sab xis ntawm 30 ^o rau qhov x-axis zoo. Txheeb xyuas cov khoom ntawm vector F ntawm x-axis (F _x ) thiab y-axis (F _y ).

Kev Sib Tham
F_x = F cos 30^o = (20)(cos 30^o) = (20)(0,5√3) = 10√3 Newtons
F_y = F txhaum 30^o = (20)(kev txhaum 30^o) = (20)(0,5) = 10 Newtons

2. Vector F ₁ = 20 Newton tsim lub kaum sab xis ntawm 30 ^o nrog rau qhov y-axis zoo thiab F ₂ = 30 Newton tsim lub kaum sab xis ntawm 60 ^o nrog rau qhov x-axis tsis zoo. Txheeb xyuas cov khoom ntawm vectors F ₁ thiab F ₂ ntawm x-axis thiab ntawm y-axis.

Kev Sib Tham
F_1x =F₁ coj 60^o = (20)(cos 60^o) = (20)(0,5) = -10 Newton (tsis zoo vim nws nyob rau hauv qhov kev taw qhia x tsis zoo)
F_2x =F₂ coj 60^o = (30)(cos 60^o) = (30)(0,5) = -15 Newton (tsis zoo vim nws nyob rau hauv qhov kev taw qhia x tsis zoo)
F_1y =F₁ kev txhaum 60^o = (20)(kev txhaum 60^o) = (20)(0,5√3) = 10√3 Newton (zoo vim nws nyob rau hauv qhov kev taw qhia y zoo)
F_2y =F₂ kev txhaum 60^o = (30)(kev txhaum 60^o) = (30)(0,5√3) = -15√3 Newton (tsis zoo vim nws nyob rau hauv qhov kev taw qhia y tsis zoo)

3. F ₁ = 2 N, F ₂ = 4 N, F ₃ = 6 N. Txheeb xyuas cov khoom ntawm cov vectors F ₁ , F ₂ thiab F ₃ ntawm x thiab y axes!

Kev Sib Tham
F_1x =F₁ coj 60^o = (2)(cos 60^o) = (2)(0,5) = 1 Newton (zoo vim nws nyob rau hauv qhov kev taw qhia x zoo)
F_2x =F₂ coj 30^o = (4)(cos 30^o) = (4)(0,5√3) = -2√3 Newton (tsis zoo vim nws nyob rau hauv qhov kev taw qhia x tsis zoo)
F_3x =F₃ coj 60^o = (6)(cos 60^o) = (6)(0,5) = 3 Newton (zoo vim nws nyob rau hauv qhov kev taw qhia x zoo)
F_1y =F₁ kev txhaum 60^o = (2)(kev txhaum 60^o) = (2)(0,5√3) = √3 Newton (zoo vim nws nyob rau hauv qhov kev taw qhia y zoo)
F_2y =F₂ kev txhaum 30^o = (4)(kev txhaum 30^o) = (4)(0,5) = 2 Newton (zoo vim nws nyob rau hauv qhov kev taw qhia y zoo)
F_3y =F₃ kev txhaum 60^o = (6)(kev txhaum 60^o) = (6)(0,5√3) = -3√3 Newton (tsis zoo vim nws nyob rau hauv qhov kev taw qhia y tsis zoo)

Cov lus nug txog kev txiav txim siab txog cov khoom vector

1. Lub zog vector F = 8 Newton tsim lub kaum sab xis ntawm 60^o rau qhov x-axis zoo. Txheeb xyuas cov khoom ntawm vector F ntawm x-axis (F_x) thiab y-axis (F_y).
2. Vector F₁ = 8 Newtons tsim ib lub kaum sab xis ntawm 45^o mus rau qhov y-axis zoo thiab F₂ = 10 Newtons tsim ib lub kaum sab xis ntawm 30^o rau qhov tsis zoo x-axis. Txheeb xyuas cov khoom ntawm vector F₁ thiab F₂ ntawm x-axis thiab ntawm y-axis.
3. F₁ = 4 N, F₂ = 8 N, F₃ = 12 N. Txheeb xyuas cov khoom ntawm lub vector F₁, F₂ thiab F₃ ntawm x-axis thiab y-axis!

[Lus Askiv: Kev daws cov teeb meem vectors - kev txiav txim siab txog cov khoom vector ]