Mibvunzo yemuenzaniso nekukurukurirana kwekuwedzera maveki maviri uchishandisa nzira yeTriangle
Pendauluan
Vector huwandu hune hukuru negwara. Mufizikisi nemasvomhu, kunzwisisa maitirwo ekuwedzera mavector maviri kwakakosha pakugadzirisa matambudziko akasiyana-siyana. Kune nzira dzakasiyana-siyana dzekuwedzera mavector, imwe yacho inzira yetriangle. Muchinyorwa chino, tichakurukura mienzaniso uye tichakurukura nezvekuwedzera mavector maviri tichishandisa nzira yetriangle zvakadzama.
Nzira yeTriangle mukuwedzera kweVector
Tisati tapinda mudambudziko remuenzaniso, ngatitangei tanzwisisa kuti nzira yetriangle inoshandiswa sei kuwedzera mavector maviri. Nzira yetriangle inosanganisira matanho anotevera:
1. Kuisa Mavector maviri panzvimbo imwe chete: Vector yekutanga inoiswa kuitira kuti muswe wayo (nzvimbo yekutanga) uve panzvimbo yekutanga yakasarudzwa.
2. Kutsanangura Vekitari Yechipiri: Vekitari yechipiri inowedzerwa kumagumo (poindi yekupedzisira) yevekitari yekutanga.
3. Kuziva Vector Inobva: Vector Inobva ndiyo vector inobatanidza pokutangira pevector yekutanga nepokugumira kwevector yechipiri.
Kunyora kweVector
Nechinangwa chechinyorwa chino, tichashandisa vector notation seinotevera:
– Maveji akanyorwa nemabhii matema kana kuti nemuseve kumusoro (semuenzaniso, A kana \(\vec{A}\)).
– Zvikamu zvevector zviri mumatanho \(x\) uye \(y\) zvakanyorwa muchimiro \(A_x\) uye \(A_y\) chevector \(\vec{A}\).
Muenzaniso wezvinetso
Zvino, ngatitarisei muenzaniso wedambudziko unotibatsira kunzwisisa kuwedzerwa kwemavector maviri tichishandisa nzira yetriangle.
Mubvunzo:
Zvichipiwa mavector maviri A naB seizvi:
– Vector A ine hukuru hwemayuniti mana uye divi rayo riri pamadhigirii makumi matatu kuchamhembe kwakadziva kumabvazuva.
– Vector B ine hukuru hwemayuniti matatu uye divi rayo riri 60 degrees kuchamhembe kwakadziva kumabvazuva.
Sarudza vhekitari R inobuda kubva pakuwedzerwa kwemavekitari maviri uchishandisa nzira yetriangle.
Kukurukurirana
Danho 1: Kudhirowa Mavheji
Kutanga, tinodhirowa vhekitari A ine hukuru hwemayuniti mana uye divi remadhigirii makumi matatu kuchamhembe kwakadziva kumabvazuva. Zvadaro, kubva kumagumo evhekitari A, tinodhirowa vhekitari B ine hukuru hwemayuniti matatu uye divi remadhigirii makumi matanhatu kuchamhembe kwakadziva kumabvazuva.
Danho rechipiri: Kuverenga Zvikamu zveVector
Tevere, tinoverenga zvikamu zvevector yega yega munzira dze \(x\) uye \(y\).
Zvikamu zvevector \(\vec{A}\):
\[
A_x = A \cos \theta_1 = 4 \cos 30^\circ = 4 \times \frac{\sqrt{3}}{2} = 2\sqrt{3}
\]
\[
A_y = A \chivi \theta_1 = 4 \chivi 30^\denderedzwa = 4 \nguva \frac{1}{2} = 2
\]
Zvikamu zvevector \(\vec{B}\):
\[
B_x = B \cos \theta_2 = 3 \cos 60^\circ = 3 \times \frac{1}{2} = 1.5
\]
\[
B_y = B \chivi \theta_2 = 3 \chivi 60^\circ = 3 \nguva \frac{\sqrt{3}}{2} = 1.5\sqrt{3}
\]
Danho rechitatu: Kuwedzera Zvikamu zveVector
Tinowedzera zvikamu zvemavector maviri kuti tiwane zvikamu zvevector inobuda \(\vec{R}\).
\[
R_x = A_x + B_x = 2\sqrt{3} + 1.5
\]
\[
R_y = A_y + B_y = 2 + 1.5\sqrt{3}
\]
Danho rechina: Verenga Hukuru neKutungamira kweResultant Vector
Hukuru hwevector inobuda \(\vec{R}\) hunoverengerwa uchishandisa dzidziso yePythagorean:
\[
R = \sqrt{R_x^2 + R_y^2}
\]
\[
R_x = 2\sqrt{3} + 1.5 \inenge 3.464 + 1.5 = 4.964
\]
\[
R_y = 2 + 1.5\sqrt{3} \inenge 2 + 2.598 = 4.598
\]
\[
R = \sqrt{(4.964)^2 + (4.598)^2} \sqrt{24.640 + 21.145} \sqrt{45.785} \sqrt{6.75 \text{ units}
\]
Kutungamira kwevector inobuda \(\vec{R}\) kunoverengwa uchishandisa basa retrigonometric tangent:
\[
\tan \phi = \frac{R_y}{R_x} = \frac{4.598}{4.964} \inenge 0.926
\]
\[
\phi = \tan^{-1}(0.926) \inenge 42.6^\denderedzwa \text{ kubva kuchamhembe kwakadziva kumabvazuva}
\]
Mhedziso
Kubva pane zvabuda pamusoro apa, tinogona kugumisa kuti vhekitari inobuda \(\vec{R}\) kubva pakuwedzera mavekitari \(\vec{A}\) uye \(\vec{B}\) uchishandisa nzira yetriangle ine hukuru hwemayuniti angangoita 6.75 uye divi re42.6 degrees kubva kuchamhembe kwakadziva kumabvazuva.
Penutup
Kuwedzera mavector maviri uchishandisa nzira yetriangle inzira inobatsira zvikuru inoshandiswa kakawanda mufizikisi neinjiniya. Nekudhirowa mavector nekuwedzera zvikamu zvavo, tinogona kuwana vector inobuda zviri nyore. Tinovimba kuti chinyorwa chino chakubatsira kunzwisisa pfungwa yekuwedzera vector uchishandisa nzira yetriangle uye chinogona kushandiswa kumatambudziko akasiyana-siyana aunosangana nawo muzvidzidzo zvako.
