Kuwedzera mavector uchishandisa zvikamu - matambudziko nemhinduro

Kuwedzera mavector uchishandisa zvikamu - matambudziko nemhinduro

1. Maveki matatu sezvakaratidzwa mumufananidzo uri pazasi.

V₁ = 30

V₂ = 30

V₃ = 40

Chii chinobuda? vector.

Zvinozivikanwa:

V₁ = 30, kona iri pakati paV₁ uye x axis = 30^o

V₂ = 30, kona iri pakati paV₂ uye x axis = 30^o

V₃ = 40, kona iri pakati paV₃ uye x axis = 0^o

Zvaidiwa: Mavectors anokonzerwa

Solution:

Zvikamu zvemavector :

V_1x = (V₁)(cos 30^o) = (30)(0.5√3) = 15√3. Yakanaka nekuti chikamu ichi chevector chinonongedza padivi pe x positive axis (kurudyi).

V_1y = (V₁(chivi 30)^o) = (30)(0.5) = 15. Yakanaka nekuti chikamu ichi chevector chinonongedzera padivi pe positive y axis (kumusoro).

V_2x = (V₂)(cos 30^o) = (30)(0.5√3) = -15√3. Negative nekuti chikamu ichi chevector chinonongedza padivi pe x axis ine negative (kuruboshwe).

V_2y = (V₂(chivi 30)^o) = (30)(0.5) = 15. Yakanaka nekuti chikamu ichi chevector chinonongedzera padivi pe positive y axis (kumusoro).

V_3x = (V₃)(cos 0^o) = (40)(1) = 40. Yakanaka nekuti chikamu ichi chevector chinonongedza padivi pe x positive axis (kurudyi).

V_3y = (V₃(chivi 0)^o) = (40)(0) = 0

Zvikamu zvemavector anobuda:

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

Vector inoguma :

2. Masimba maviri akatarisana, F₁ = 12 N uye F₂ = 5 N. Chii chinoguma nemasimba ese ari maviri?

Zvinozivikanwa:

simba 1 (F)₁) = 12 Newton

simba 2 (F)₂) = 5 Newton

Zvaidiwa: Mavectors anokonzerwa (ΣF)

Solution:

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

ΣF = √169 = 13 Newton

3. Maveji matatu,

V₁ = 30

V₂ = 30

V₃ = 40

Sarudza mavector anouya.

Zvinozivikanwa:

v₁ = 30, kunoita 30^o nezve negative x axis

v₂ = 30, kunoita 30^o nezve positive x axis

v₃ = 40, kunoita 0^o nezve positive x axis

Zvaidiwa: Mavectors anokonzerwa

Solution:

Zvikamu zvemavector:

v_1x =v₁ kusvika 30^o = (30)(0.5√3) = -15√3 (Negative nekuti chikamu ichi chevector chinonongedza padivi pe negative x axis (kuruboshwe))

v_1y =v₁ pasina 30^o = (30)(0.5) = 15 (Zvakanaka nekuti chikamu ichi chevector chinonongedza padivi pe positive y axis (kumusoro))

v_2x =v₂ kusvika 30^o = (30)(0.5√3) = 15√3 (Zvakanaka nekuti chikamu ichi chevector chinonongedza padivi pe positive x axis (kurudyi)))

v_2y =v₂ pasina 30^o = (30)(0.5) = 15 (Yakanaka nekuti chikamu ichi chevector chinonongedza padivi pe positive y axis (kumusoro).)

v_3x =v₃ kusvika 0^o = (40)(1) = 40 (Yakanaka nekuti chikamu ichi chevector chinonongedza padivi pe positive x axis (kurudyi).)

v_3y =v₃ pasina 0^o = (40)(0) = 0

Zvikamu zvemavector anobuda:

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

Vekitori inoguma:

4. Chii chinokonzerwa nemavector matatu sezvakaratidzwa mumufananidzo uri pazasi:

Zvinozivikanwa:

F₁ = 3 maNewton, kunoita 60^o nezve positive x axis

F₂ = 3 maNewton, kunoita 0^o nezve negative x axis

F₃ = 6 Newtonsn, inoita 60^o nezve negative y axis

Zvaidiwa: Vector inoguma

Solution:

Zvikamu zvemavector:

F_1x =F₁ kusvika 60^o = (3)(0.5) = 1.5 N (Zvakanaka nekuti chikamu ichi chevector chinonongedza padivi pe positive x axis (kurudyi)))

F_1y =F₁ pasina 60^o = (3)(0.5√3) = 1.5√3 N (Zvakanaka nekuti chikamu ichi chevector chinonongedza padivi pe positive y axis (kumusoro))

F_2x =F₂ kusvika 0^o = (3)(1) = -3 N (Negative nekuti chikamu ichi chevector chinonongedza padivi pe negative x axis (kuruboshwe))

F_2y =F₂ pasina 0^o = (3)(0) = 0

F_3x =F₃ kusvika 60^o = (6)(0.5) = 3 N (Zvakanaka nekuti chikamu ichi chevector chinonongedza padivi pe positive x axis (kurudyi)))

F_3y =F₃ pasina 60^o = (6)(0.5√3) = -3√3 N (Negative nekuti chikamu ichi chevector chinonongedzera kune negative y akisi (pasiwadhi))

Zvikamu zvemavector anobuda:

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

Vekitori inoguma:

5. Masimba maviri, F₁ = 15 N uye F₂ = 9 N. Kona iri pakati pemavector ese ari maviri i60°. Chii chinobuda mumavectors?

Zvaidiwa:

Simba 1 (F₁) = 15 Newton

simba 2 (F)₂) = 9 Newton

Angle (θ) = 60^o

Kuda: Vector inoguma

Solution:

6. Chii chinokonzerwa nemavector matatu sezvakaratidzwa mumufananidzo uri pazasi?

Zvinozivikanwa:

F₁ = 20 Newton, kona iri pakati peF₁ uye x axis = 0

F₂ = 20 Newton, kona iri pakati peF₂ uye x axis = 60

F₃ = 24 Newton, kona iri pakati peF₃ uye x axis = 60

Zvaidiwa: Vector inoguma

Solution:

Zvikamu zvemavector:

F_1x = (F)₁)(cos 0) = (20)(1) = 20. Zvakanaka nekuti chikamu ichi chevector chinonongedza padivi pe positive x axis (kurudyi))

F_1y = (F)₁)(chivi 0) = (20)(0) = 0

F_2x = (F)₂)(cos 60) = (20)(0.5) = -10. Negative nekuti chikamu ichi chevector chinonongedza padivi pe negative x axis (kuruboshwe)

F_2y = (F)₂)(chivi 60) = (20)(0.5√3) = 10√3. Zvakanaka nekuti chikamu ichi chevector chinonongedza padivi pe positive y axis (kumusoro)

F_3x = (F)₃)(cos 60) = (24)(0.5) = -12. Negative nekuti chikamu ichi chevector chinonongedza padivi pe negative x axis (kuruboshwe)

F_3y = (F)₃)(chivi 60) = (24)(0.5√3) = -12√3. Nnegative nekuti chikamu ichi chevector chinonongedzera kune negative y akisi (pasiwadhi)

Zvikamu zvemavector anobuda:

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

Vekitori inoguma: