Kuwedzera kweVectors

Chinyorwa pamusoro peKuwedzerwa kweVectors

1. Huwandu hwevector nescalar

Kuwedzera kune huwandu hwakakosha uye hwakatorwa, huwandu hwemuviri hunogona kukamurwa kuita mamwe marudzi maviri, kureva huwandu hwe scalar nehuwandu hwe vector. Huwandu hwakadai sehukuru, daro, nguva uye vhoriyamu, huwandu hwe scalar, huwandu hune hukuru chete asi husina gwara. Nepo hukuru hwakadai sekutama, kumhanya, kukurumidza, uye simba huri huwandu hwe vector, huwandu hune hukuru uye hune gwara.

a. Musiyano uripo pakati pehuwandu hwe s calar nehuwandu hwe vector

Kana ukati huremu hwebhora magiramu mazana mana, chirevo ichi chakakwana kuti uzive huremu hwebhora. Haudi gwara kuti uzive huremu hwebhora. Saizvozvowo nenguva, tembiricha, vhoriyamu, density, nezvimwewo. Kune huwandu hwakawanda hwemuviri husingagone kuratidzwa muhukuru chete. Kana ukati mwana anofamba kusvika pamamita zana, chirevo ichi hachina kukwana. Ungabvunza kuti, akatamira kupi? Kuchamhembe, kumaodzanyemba, kumabvazuva, kana kumadokero here? Saizvozvowo, kana ukati unosunda tafura nesimba re200 N.

Unotyaira kupi? Zvakanaka, huwandu hwakadaro hunonzi huwandu hwevector, hunoda tsananguro yehukuru negwara. Mienzaniso yehuwandu hwevector ndeye displacement, acceleration, impulse, momentum , nezvimwewo. Unogona kuinzwisisa zvakajeka paunenge uchidzidza zvidzidzo zvine chekuita nehuwandu ihwohwo.

b. Dhirowa vhekitari

Vector inoratidzwa nemuseve. Museve unodhonzwa nguva dzose kuitira kuti unongedzere kwakananga vector. Kureba kwemuseve kunotsanangurwa sehukuru hwevector. Semuenzaniso, mumufananidzo wevector yesimba (F) ine hukuru hwe2 N iyo divi rayo riri kuchamhembe kwakadziva kumabvazuva kana 45 ^o pamusoro pe x-axis.

c. Mitemo yekunyora huwandu hwevector

Pakunyora vhekitari, kana ukashandisa rugwaro rwemaoko, chiratidzo chevhekitari chinowanzo nyorwa nemabhii akatsveyama uchishandisa mabhii makuru, uye pamusoro pacho panofanira kuwedzerwa nemuseve. Kumabhuku akadhindwa, zviratidzo zvevhekitari zvinonyorwa nemabhii makuru nemabhii matema, semuenzaniso, F. Pahukuru hwevhekitari, kana tikashandisa rugwaro rwemaoko, ipapo hukuru hwevhekitari hunonyorwa, semuenzaniso, |F|. Kumabhuku akadhindwa, hukuru hwevhekitari hunonyorwa nemabhii akatsveyama, semuenzaniso , F.

2. Kuwedzera mavectors—nzira dzemifananidzo

Kune nzira dzakasiyana siyana dzekuwedzera mavectors nemifananidzo, kusanganisira nzira yeTail-to-tip uye nzira yeparallelogram.

a. Nzira yekuwedzera mavector kubva pamuswe kusvika kumucheto

Mavector A naB anozivikanwa. Vector A = 3 cm inoenderana ne x-axis (kumabvazuva). Vector B = 2 cm inoumba kona ye30 ^o ku x-axis (kumabvazuva kwakadziva kumabvazuva). Wedzera A naB uchishandisa girafu uchishandisa nzira yeTail-to-tip. a) R = A + B b) R = A – B

Hukuru hwevector inobuda (R) hunoyerwa uchishandisa ruler. Kutungamira kwevector inobuda kunoyerwa uchishandisa protractor.

Mavector anozivikanwa A, B, naC. Vector A = 3 cm inoenderana ne x-axis (kumabvazuva). Vector B = 2 cm inoumba kona ye30 ^o ku x-axis (kumabvazuva kwakadziva kumabvazuva). Vector C = 1 cm inoumba kona ye60 ^o ku x-axis (kumabvazuva kwakadziva kumabvazuva). Wedzera A, B, naC uchishandisa mifananidzo uchishandisa nzira yeTail-to-tip.

a) R = A + B + C

b) R = A – B – C

Vekitari inobuda (R) inoyerwa uchishandisa rula. Kutungamira kwevekitari inobuda kunoyerwa uchishandisa protractor.

b. Nzira yeParalelogram

Mavector anozivikanwa A, B, naC. Vector A = 3 cm inoenderana ne x-axis (kumabvazuva). Vector B = 2 cm inoumba kona ye30 ^o ku x-axis (kumabvazuva kwakadziva kumabvazuva). Vector C = 1 cm inoumba kona ye60 ^o ku x-axis (kumabvazuva kwakadziva kumabvazuva). Wedzera A, B, naC uchishandisa girafu uchishandisa parallelogram.

a) R = A + B

b) R = A – B

c) R = A + B + C

d) R = A – B – C

Vekitari inobuda (R) inoyerwa uchishandisa rula. Kutungamira kwevekitari inobuda kunoyerwa uchishandisa protractor.

3. Kuwedzera mavectors - akuongorora nzira

Kuziva hukuru negwara remuchina unobuda uchishandisa nzira yemifananidzo ndeimwe nzira. Kururama kwemhedzisiro kunoenderana nekururama kwako nekunyatsorongeka pakudhirowa nekuverenga chikero. Hukuru negwara remuchina unobuda zvinowanikwa nemazvo kuburikidza nekuverenga kwemasvomhu.

a. Kuverenga huwandu hwemavector maviri uchishandisa mutemo wecosine

Fomura yekuona hukuru hwevector inobuda:

Fomura yekuona divi remugumisiro wevector:

C = vhekitori inoguma

A = vhekitori 1

B = vhekitari 2

cos ∠(A, B) = kona inoumbwa nemavectors A naB

Dambudziko remuenzaniso 1:

F ₁ = 2 N inoumba kona ye30 inenge x-axis, F ₂ = 3 N inoumba kona ye60 ^o inenge x-axis, θ = 30 ^o.

Dambudziko remuenzaniso 2:

F ₁ = 2 N inoenderana ne x-axis, F ₂ = 3 N inoumba kona ye 90 ^o pamusoro pe x-axis, θ = 90 ^o.

b. Kuwedzera mavector nezvikamu

Ongorora vector F inoumba kona yakati sandara pamusoro pe x-axis, sezvakaratidzwa mumufananidzo uri pazasi. F _x na F _y ndiwo mavector echikamu chevector F.

Hukuru hwevector yechikamu hunotsanangurwa uchishandisa fomura:

F _x = F cos θ

F _y = F sin θ

Ongorora mavector maviri F₁ uye F₂ iyo inoumba kona yakati kuti pamusoro pe x-axis, sezvakaratidzwa mumufananidzo uri pazasi._1x uye F_1y zvikamu zvevector F₁, saka F_2x uye F_2y zvikamu zvevector F₂.

Vector yechikamu inosarudzwa uchishandisa fomura:

F_1x =F₁ cos θ

F _1y = F ₁ sin θ

F _2x = F ₂ cos θ

F _1y = F ₁ sin θ

Kuwedzera mavector echikamu:

F _x = F _1x + F _2x

F _y = F _1y + F _2y

Vector inobuda inosarudzwa uchishandisa fomura:

Kutungamira kwevector inobuda kunosarudzwa uchishandisa fomura:

Dambudziko remuenzaniso 1:

Sarudza zvikamu zvevector F ine hukuru hwe20 N uye gadzira kona ye30 ^o pamusoro pe x-axis.

F _x = (20 N)(cos 30 ^o ) = 17 N

F _y = (20 N)(chivi 30 ^o ) = 10 N

Dambudziko remuenzaniso 2:

F ₁ = 20 N inoumba kona ye30 ^o pamusoro pe x-axis uye F ₂ = 15 N inoumba kona ye180 o pamusoro pe x-axis. Sarudza hukuru uye gwara re vector inobuda.

F _1x = (20 N)(cos 30 ^o ) = 17 N

F _2x = F ₁ = – 15 N

F _1y = (20 N)(chivi 30 ^o ) = 10 N

F _2y = 0

Kuwedzera mavector echikamu:

F _x = F _1x – F _2x = 17 N – 15 N = 2 N

F _y = 10 N

Vekitori inoguma:

F ₂ = F _x ² + F _y ² = 2 ² + 10 ² = 4 + 100 = 104

F = 10.2N

Kutungamirirwa kwevector inobuda:

θ = tan −15 = 78.7 ^o pamusoro pe x-axis

Dambudziko remuenzaniso 3:

F₁, F_2, uye F₃ dziri 20 N, 30 N uye 40 N. F₁ inoumba kona ye60^o nezve x-axis, F₂ inoumba kona ye150^o nezve x-axis, uye F₃ inoumba kona ye315^o nezve x-axis. Sarudza hukuru uye gwara revector inobuda.

F _1x = (20 N)(cos 60 ^o ) = 10 N

F _1y = (20 N)(chivi 60 ^o ) = 17 N

F _2x = (30 N)(cos 30 ^o ) = -26 N

F _2y = (30 N)(chivi 30 ^o ) = 15 N

F _3x = (40 N)(cos 45 ^o ) = 28 N

F _3y = (40 N)(chivi 45 ^o ) = -28 N

Kuwedzera vhekitari yechikamu:

F _x = F _1x – F _2x + F _3x = 10 N – 26 N + 28 N = 12 N

F _y = F _1y + F _2y – F _3y = 17 N + 15 N – 28 N = 4 N

Vekitari inobuda:

F ² = F _x ² + F _y ² = 12 ² + 4 ² = 144 + 16 = 160

F = 13N

Kutungamirirwa kwevector inobuda:

θ = tan ⁻¹ 0.3 = 17 ^o pamusoro pe x-axis