Muenzaniso weMubvunzo Uchikurukura Kuwedzerwa kweVectors mbiri Uchishandisa Nzira yeParallelogram
Kuwedzerwa kwevector ipfungwa yakakosha mufizikisi nemasvomhu, inowanzoshandiswa kutsanangura zviitiko zvechisikigo nematambudziko ehupenyu hwezuva nezuva. Kune nzira dzakasiyana siyana dzekuwedzera mavector maviri, imwe yacho iri nzira yeparallelogram. Nzira iyi haisi kungonzwisisika chete asi inopawo mufananidzo wakasimba wekuti mavector maviri anobatana sei kuti aumbe vector inobuda. Muchinyorwa chino, tichatarisa mienzaniso yakati wandei yekuwedzera vector uchishandisa nzira yeparallelogram, pamwe chete nemhinduro dzayo.
Chii chinonzi Vector?
Tisati tapinda mumatambudziko emuenzaniso, tinofanira kunzwisisa tsananguro huru yevector. Vector huwandu hune hukuru (hurefu) uye gwara. Mienzaniso yekare yevectors inosanganisira velocity, acceleration, force, uye displacement. Vector inogona kumiririrwa sezvikamu zvayo (i, j, k) muCartesian coordinates kana sehurefu hwayo negwara (angle).
Nzira yeParalelogram
Nzira yeparallelogram inzira imwe yekuwedzera mavector maviri. Munzira iyi, tinomiririra mavector maviri semativi maviri eparallelogram. Vector inobuda ndiyo diagonal yeparallelogram inotangira kubva panotangira mavector maviri. Pamasvomhu, kana tine mavector maviri \(\vec{A}\) uye \(\vec{B}\), mhedzisiro yacho \( \vec{R} = \vec{A} + \vec{B} \).
Nzira yekushandisa nzira ye parallelogram nhanho nhanho ndeiyi inotevera:
1. Dhirowa vhekitari \(\vec{A}\) kubva panotangira.
2. Kubva kumagumo evector \(\vec{A}\), dhirowa vector \(\vec{B}\).
3. Dhirowa mutsetse wakaenzana nevector \(\vec{B}\) kubva panotangira \(\vec{A}\).
4. Dhirowa mutsetse wakafanana nevector \(\vec{A}\) kubva kumagumo evector \(\vec{B}\).
5. Dhirowa dhayagiramu kubva panotangira kuenda pakona yakatarisana kuti uwane vhekitari inobuda \(\vec{R}\).
Mibvunzo yemuenzaniso nekukurukurirana
Mubvunzo 1
Ngatitii tine mavector maviri \(\vec{A}\) uye \(\vec{B}\):
– \(\vec{A}\) ine urefu (hukuru) hwemayuniti mashanu uye gwara re0° (kana kuti iri padivi pe x-axis yakanaka),
– \(\vec{B}\) ine hurefu hwemayuniti matatu uye gwara re90° (kana kuti pamwe chete ne positive y-axis).
Chii chinokonzerwa nekuwedzera mavector maviri aya uchishandisa nzira yeparallelogram?
Kukurukurirana:
1. Dhirowa vhekita \(\vec{A}\) pamwe chete ne x-axis ine urefu hwemayuniti mashanu.
2. Kubva kumagumo evector \(\vec{A}\), dhirowa vector \(\vec{B}\) pamwe chete ne positive y-axis ine hurefu hwemayuniti matatu.
3. Kubva pakutanga \(\vec{A}\), dhirowa mutsetse wakafanana ne \(\vec{B}\).
4. Kubva kumagumo e \(\vec{B}\), dhirowa mutsetse wakafanana ne \(\vec{A}\).
5. Mhedzisiro yacho iparallelogram ine diagonal iyo iri vhekitori inobuda \(\vec{R}\).
Sezvo \(\vec{A}\) uye \(\vec{B}\) dzakamira dzakatarisana, tinogona kushandisa dzidziso yePythagorean kuverenga hurefu hwevector inobuda:
\[ R = \sqrt{A^2 + B^2} = \sqrt{5^2 + 3^2} = \sqrt{25 + 9} = \sqrt{34} \inenge 5.83 \]
Kutungamira kwevector inobuda kunogona kuverengerwa uchishandisa trigonometry. Kana \(\theta\) iri kona iri pakati peinobuda uye \(\vec{A}\):
\[ \tan(\theta) = \frac{B}{A} = \frac{3}{5} \]
saka:
\[ \theta = \tan^{-1}\left(\frac{3}{5}\right) \approx 30.96^\circ \]
Saka, vhekitari inobuda \(\vec{R}\) ine hukuru hwemayuniti angangoita 5.83 uye divi riri pa30.96° kubva \(\vec{A}\).
Mubvunzo 2
Mavector maviri \(\vec{C}\) uye \(\vec{D}\) anopiwa seizvi:
– \(\vec{C}\) ine urefu hwemayuniti mana uye divi re45°.
– \(\vec{D}\) ine urefu hwemayuniti matanhatu uye divi re120°.
Sarudza vhekitari inobuda \(\vec{R}\) kubva pakuwedzera mavekitari maviri.
Kukurukurirana:
Kuti uwedzere mavector maviri asina kuenzana kana kuti akasiyana muchimiro, unogona kushandisa zvikamu zveCartesian.
1. Kamura \(\vec{C}\) uye \(\vec{D}\) kuita zvikamu zve x na y.
Kune \(\vec{C}\):
\[ C_x = C \cos(45^\circ) = 4 \cos(45^\circ) = 4 \cdot \frac{\sqrt{2}}{2} = 2\sqrt{2} \approx 2.83 \]
\[ C_y = C \sin(45^\circ) = 4 \sin(45^\circ) = 4 \cdot \frac{\sqrt{2}}{2} = 2\sqrt{2} \approx 2.83 \]
Kune \(\vec{D}\):
\[ D_x = D \cos(120^\circ) = 6 \cos(120^\circ) = 6 \cdot (-\frac{1}{2}) = -3 \]
\[ D_y = D \sin(120^\circ) = 6 \sin(120^\circ) = 6 \cdot \frac{\sqrt{3}}{2} = 3\sqrt{3} \approx 5.20 \]
2. Wedzera zvikamu zve x na y zvemaveki ese ari maviri:
\[ R_x = C_x + D_x = 2.83 + (-3) = -0.17 \]
\[ R_y = C_y + D_y = 2.83 + 5.20 = 8.03 \]
3. Verenga hukuru negwara revector inobuda \(\vec{R}\):
\[ R = \sqrt{R_x^2 + R_y^2} = \sqrt{(-0.17)^2 + 8.03^2} = \sqrt{0.03 + 64.48} = \sqrt{64.51} \inenge 8.03 \]
\[ \theta = \tan^{-1}\left(\frac{R_y}{R_x}\right) = \tan^{-1}\left(\frac{8.03}{-0.17}\right) \approx \tan^{-1}(-47.24) \]
Sezvo mhedzisiro yacho iri negative, tinowedzera 180° kuti tiwane kona mu quadrant system chaiyo:
\[ \theta \approx \tan^{-1}(47.24) + 180^\circ \approx 271.93^\circ \]
Saka, vhekitari inobuda \(\vec{R}\) ine hukuru hwemayuniti angangoita 8.03 uye divi rinenge 271.93°, kana kuti tinogona kutaura nezve 91.93° kubva pa x-axis isina kunaka muchikamu chechina.
Penutup
Nzira yeparallelogram inzira inoshanda uye inooneka yekuwedzera mavector maviri. Kunyange zvazvo nzira iyi ingaita seiri nyore kune mavector ari nyore, zvakakosha kunzwisisa kuti kune mavector akaomarara, tinowanzo fanira kushandisa zvikamu zveCartesian uye matekiniki e algebraic epamusoro kuti tiwane mhedzisiro chaiyo. Tinovimba kuti mienzaniso iri pamusoro apa inopa mufananidzo wakajeka wekuti nzira iyi ingashandiswa sei mumamiriro akasiyana-siyana.
