Kuwedzera mavector uchishandisa zvikamu - matambudziko nemhinduro

Kuwedzera mavector uchishandisa zvikamu - matambudziko nemhinduro

1. Maveki matatu sezvakaratidzwa mumufananidzo uri pazasi.

V₁ = 30

V ₂ = 30

V ₃ = 40

Ndezvipi zviratidzo zvinobuda?

Zvinozivikanwa:

V ₁ = 30, kona iri pakati peV ₁ ne x axis = 30 ^o

V ₂ = 30, kona iri pakati peV ₂ ne x axis = 30 ^o

V ₃ = 40, kona iri pakati peV ₃ ne x axis = 0 ^o

Zvinodiwa: Mavector anobuda

Solution:

Zvikamu zvemavector :

V _1x = (V ₁ )(cos 30 ^o ) = (30)(0.5√3) = 15√3. Yakanaka nekuti chikamu ichi chevector chinonongedza padivi pe x axis yakanaka (kurudyi).

V _1y = (V ₁ )(sin 30 ^o ) = (30)(0.5) = 15. Yakanaka nekuti chikamu ichi chevector chinonongedza padivi pe positive y axis (kumusoro).

V _2x = (V ₂ )(cos 30 ^o ) = (30)(0.5√3) = -15√3. Negative nekuti chikamu ichi chevector chinonongedza padivi pe x axis ine negative (kuruboshwe).

V _2y = (V ₂ )(sin 30 ^o ) = (30)(0.5) = 15. Yakanaka nekuti chikamu ichi chevector chinonongedza padivi pe positive y axis (kumusoro).

V _3x = (V ₃ )(cos 0 ^o ) = (40)(1) = 40. Yakanaka nekuti chikamu ichi chevector chinonongedza padivi pe x axis yakanaka (kurudyi).

V _3y = (V ₃ )(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

Vekitori inobuda :

2. Masimba maviri akatarisana, F ₁ = 12 N uye F ₂ = 5 N. Chii chinoguma nemasimba ese ari maviri?

Zvinozivikanwa:

Simba 1 (F ₁ ) = 12 Newton

Simba 2 (F ₂ ) = 5 Newton

Zvinodiwa: Mavector anobuda ( ΣF)

Solution:

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

ΣF = √ 169 = 13 Newton

3. Maveji matatu,

V₁ = 30

V ₂ = 30

V ₃ = 40

Sarudza mavector anouya.

Zvinozivikanwa:

v ₁ = 30, inoita 30 ^o pamusoro pe x axis ine negative

v ₂ = 30, inoita 30 ^o pamusoro pe x axis yakanaka

v ₃ = 40, inoita 0 ^o pamusoro pe x axis yakanaka

Zvinodiwa: Maveji anobuda

Solution:

Zvikamu zvemavector:

v _1x = v ₁ cos 30 ^o = (30)(0.5 √ 3) = -15 √ 3 ( Negative nekuti chikamu ichi chevector chinonongedza padivi pe x axis ine negative (kuruboshwe) )

v _1y = v ₁ sin 30 ^o = (30)(0.5) = 15 ( Yakanaka nekuti chikamu ichi chevector chinonongedzera padivi pe positive y axis (kumusoro) )

v _2x = v ₂ cos 30 ^o = (30)(0.5 √ 3) = 15 √ 3 ( Yakanaka nekuti chikamu ichi chevector chinonongedza padivi pe x axis yakanaka (kurudyi ) )

v _2y = v ₂ sin 30 ^o = (30)(0.5) = 15 ( Yakanaka nekuti chikamu ichi chevector chinonongedza padivi pe positive y axis (kumusoro). )

v _3x = v ₃ cos 0 ^o = (40)(1) = 40 ( Yakanaka nekuti chikamu ichi chevector chinonongedza padivi pe x axis yakanaka (kurudyi). )

v _3y = v ₃ 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

Vekitori inoguma:

4. Chii chinokonzerwa nemavector matatu sezvakaratidzwa mumufananidzo uri pazasi :

Zvinozivikanwa:

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

F ₂ = 3 maNewton, anoita 0 ^o pamusoro pe x axis ine negative

F ₃ = 6 maNewton , anoita 60 ^o pamusoro pe negative y axis

Zvinodiwa: Mugumisiro wemhedzisiro

Solution:

Zvikamu zvemavector:

F _1x = F ₁ cos 60 ^o = (3)(0.5) = 1.5 N ( Yakanaka nekuti chikamu ichi chevector chinonongedza padivi pe x axis yakanaka (kurudyi ) )

F _1y = F ₁ sin 60 ^o = (3)(0.5√3) = 1.5√3 N ( Yakanaka nekuti chikamu ichi chevector chinonongedza padivi pe positive y axis (kumusoro) )

F _2x = F ₂ cos 0 ^o = (3)(1) = -3 N ( Negative nekuti chikamu ichi chevector chinonongedzera padivi pe x axis (kuruboshwe) )

F _2y = F ₂ chivi 0 ^o = (3)(0) = 0

F _3x = F ₃ cos 60 ^o = (6)(0.5) = 3 N ( Yakanaka nekuti chikamu ichi chevector chinonongedza padivi pe x axis yakanaka (kurudyi ) )

F _3y = F ₃ sin 60 ^o = (6)(0.5√3) = -3√3 N ( Negative nekuti chikamu ichi chevector chinonongedzera padivi pe negative y axis ( down ward) )

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, F ₁ = 15 N uye F 2 ₌ 9 N. Kona iri pakati pemavector ese ari maviri i60°. Chii chinobuda mumavector.

Zvaidiwa:

Simba 1 (F ₁ ) = 15 Newton

Simba 2 (F ₂ ) = 9 Newton

Angle ( θ) = 60 ^o

Zvinodiwa: Mugumisiro wemhedzisiro

Solution:

6. Chii chinokonzerwa nemavector matatu sezvakaratidzwa mumufananidzo uri pazasi?

Zvinozivikanwa:

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

F ₂ = 20 Newtons, kona iri pakati peF ₂ ne x axis = 60

F ₃ = 24 Newtons, kona iri pakati peF ₃ ne x axis = 60

Zvinodiwa: Mugumisiro wemhedzisiro

Solution:

Zvikamu zvemavector:

F _1x = (F ₁ )(cos 0) = (20)(1) = 20. Yakanaka nekuti chikamu ichi chevector chinonongedza padivi pe x axis yakanaka (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. Yakanaka 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. N negative nekuti chikamu ichi chevector chinonongedzera padivi pe negative y axis ( pasi ward)

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: