Ntxiv cov vectors siv cov khoom sib xyaw - teeb meem thiab kev daws teeb meem

Ntxiv cov vectors siv cov khoom sib xyaw - teeb meem thiab kev daws teeb meem

1. Peb lub vectors raws li qhia hauv daim duab hauv qab no.

V₁ = 30

V₂ = 30

V₃ = 40

Qhov tshwm sim yog dab tsi cov duab.

Paub:

V₁ = 30, lub kaum sab xis ntawm V₁ thiab x axis = 30^o

V₂ = 30, lub kaum sab xis ntawm V₂ thiab x axis = 30^o

V₃ = 40, lub kaum sab xis ntawm V₃ thiab x axis = 0^o

Xav tau: Cov vectors tshwm sim

Tshuaj:

Cov khoom ntawm vectors :

V_1x = (V)₁)(cos 30^o) = (30)(0.5√3) = 15√3. Zoo vim tias cov vector no taw tes raws txoj kab x zoo (sab xis).

V_1y = (V)₁)(kev txhaum 30^o) = (30)(0.5) = 15. Zoo vim tias cov khoom vector no taw tes raws txoj kab y zoo (sab saud).

V_2x = (V)₂)(cos 30^o) = (30)(0.5√3) = -15√3. Tsis zoo vim tias cov khoom vector no taw tes raws txoj kab x tsis zoo (sab laug).

V_2y = (V)₂)(kev txhaum 30^o) = (30)(0.5) = 15. Zoo vim tias cov khoom vector no taw tes raws txoj kab y zoo (sab saud).

V_3x = (V)₃)(cos 0^o) = (40)(1) = 40. Zoo vim tias cov khoom vector no taw tes raws txoj kab x zoo (sab xis).

V_3y = (V)₃)(kev txhaum 0^o) = (40)(0) = 0

Cov khoom ntawm cov vectors resultant:

V_x =V_1x - V_2x +V_3x = 15√3 – 15√3 + 40 = 40

V_y =V_1y +V_2y +V_3y Luas = 15 + 15 = 30

Tus vector uas tau tshwm sim :

2. Ob lub zog uas sib ncaj nraim rau ib leeg, F₁ = 12 N thiab F₂ = 5 N. Qhov tshwm sim ntawm ob lub zog yog dab tsi.

Paub:

Force 1 (F)₁) = 12 Newtons

Force 2 (F)₂) = 5 Newtons

Xav tau: Cov vectors tshwm sim (ΣF)

Tshuaj:

ΣF² =F₁² +F₂² = 12² + 5² Luas = 144 + 25 = 169

ΣF = √169 = 13 Newtons

3. Peb lub vectors,

V₁ = 30

V₂ = 30

V₃ = 40

Txheeb xyuas cov vectors uas tau los.

Paub:

v₁ = 30, ua 30^o txog qhov tsis zoo x axis

v₂ = 30, ua 30^o txog qhov x axis zoo

v₃ = 40, ua 0^o txog qhov x axis zoo

Xav tau: Cov vectors tshwm sim

Tshuaj:

Cov khoom ntawm vectors:

v_1x = v₁ coj 30^o = (30)(0.5√3) = -15√3 (Tsis zoo vim tias cov khoom vector no taw tes raws txoj kab x tsis zoo (sab laug))

v_1y = v₁ kev txhaum 30^o = (30)(0.5) = 15 (Zoo vim tias cov khoom vector no taw tes raws txoj kab y zoo (sab saud))

v_2x = v₂ coj 30^o = (30)(0.5√3) = 15√3 (Zoo vim tias cov khoom vector no taw tes raws txoj kab x zoo (sab xis)))

v_2y = v₂ kev txhaum 30^o = (30)(0.5) = 15 (Zoo vim tias cov khoom vector no taw tes raws txoj kab y zoo (sab saud).)

v_3x = v₃ coj 0^o = (40)(1) = 40 (Zoo vim tias cov khoom vector no taw tes raws txoj kab x zoo (sab xis).)

v_3y = v₃ kev txhaum 0^o = (40)(0) = 0

Cov khoom ntawm cov vectors resultant:

v_x = – v_1x +v_2x +v_3x = -15√3 + 15√3 + = 40 40

v_y = v_1y +v_2y +v_3y Luas = 15 + 15 = 30

Tus vector tshwm sim:

4. Qhov tshwm sim ntawm peb lub vectors raws li qhia hauv daim duab hauv qab no yog dab tsi:

Paub:

F₁ = 3 Newtons, ua 60^o txog qhov x axis zoo

F₂ = 3 Newtons, ua 0^o txog qhov tsis zoo x axis

F₃ = 6 Newtonsn, ua 60^o txog qhov tsis zoo ntawm y axis

Xav tau: Tus vector uas tau tshwm sim

Tshuaj:

Cov khoom ntawm vectors:

F_1x =F₁ coj 60^o = (3)(0.5) = 1.5 N (Zoo vim tias cov khoom vector no taw tes raws txoj kab x zoo (sab xis)))

F_1y =F₁ kev txhaum 60^o = (3)(0.5√3) = 1.5√3 N (Zoo vim tias cov khoom vector no taw tes raws txoj kab y zoo (sab saud))

F_2x =F₂ coj 0^o = (3)(1) = -3 N (Tsis zoo vim tias cov khoom vector no taw tes raws txoj kab x tsis zoo (sab laug))

F_2y =F₂ kev txhaum 0^o = (3)(0) = 0

F_3x =F₃ coj 60^o = (6)(0.5) = 3 N (Zoo vim tias cov khoom vector no taw tes raws txoj kab x zoo (sab xis)))

F_3y =F₃ kev txhaum 60^o = (6)(0.5√3) = -3√3 N (Tsis zoo vim tias cov khoom vector no taw tes rau ntawm qhov tsis zoo y axes (ciachav kawm))

Cov khoom ntawm cov vectors resultant:

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

Tus vector tshwm sim:

5. Ob lub zog, F₁ = 15 N thiab F₂ = 9 N. Lub kaum sab xis ntawm ob lub vectors yog 60°. Qhov tshwm sim ntawm cov vectors yog dab tsi.

Xav tau:

Yuam Kev 1 (F₁) = 15 Newtons

Force 2 (F)₂) = 9 Newtons

lub (θ) = 60^o

SE pob: Tus vector uas tau tshwm sim

Tshuaj:

6. Qhov tshwm sim ntawm peb lub vectors raws li qhia hauv daim duab hauv qab no yog dab tsi?

Paub:

F₁ = 20 Newton, lub kaum sab xis ntawm F₁ thiab x axis = 0

F₂ = 20 Newton, lub kaum sab xis ntawm F₂ thiab x axis = 60

F₃ = 24 Newton, lub kaum sab xis ntawm F₃ thiab x axis = 60

Xav tau: Tus vector uas tau tshwm sim

Tshuaj:

Cov khoom ntawm vectors:

F_1x = (F₁)(cos 0) = (20)(1) = 20. Zoo vim tias cov khoom vector no taw tes raws txoj kab x zoo (sab xis))

F_1y = (F₁)(kev txhaum 0) = (20)(0) = 0

F_2x = (F₂)(cos 60) = (20)(0.5) = -10. Tsis zoo vim tias cov khoom vector no taw tes raws txoj kab x tsis zoo (sab laug)

F_2y = (F₂)(kev txhaum 60) = (20)(0.5√3) = 10√3. Zoo vim tias cov khoom vector no taw tes raws txoj kab y zoo (sab saud)

F_3x = (F₃)(cos 60) = (24)(0.5) = -12. Tsis zoo vim tias cov khoom vector no taw tes raws txoj kab x tsis zoo (sab laug)

F_3y = (F₃)(sin 60) = (24)(0.5√3) = -12√3. Ntsis zoo vim tias cov khoom vector no taw tes rau ntawm qhov tsis zoo y axes (ciachav kawm)

Cov khoom ntawm cov vectors resultant:

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

Tus vector tshwm sim: