Mienzaniso yeMibvunzo Inokurukura Kushandiswa kweZvibvumirano muFizikisi
Kushandiswa kwezvinobatanidza mufizikisi ipfungwa yakakosha uye yakafara. Kushandiswa kwezvinobatanidza kunobvumira nyanzvi dzefizikisi nemainjiniya kuverenga zviitiko zvakasiyana-siyana zvakaoma zvechisikigo, zvingave zvine chekuita nekufamba, simba, simba, kana zvimwe zvinhu. Chinyorwa chino chichaongorora mienzaniso yakati wandei yezvinetso uye chichakurukura kushandiswa kwezvinobatanidza mufizikisi.
1. Kuverenga Basa Nesimba Rinochinja-chinja
Mubvunzo
Simba rinosiyana zvichienderana nenzvimbo \(x\) rinopihwa ne \( F(x) = 3x^2 \). Verenga basa rinoitwa nesimba iri kana chinhu chichifamba kubva pa \(x = 0\) kuenda pa \(x = 2 \) mamita.
Kukurukurirana
Basa rinoitwa nesimba rinochinja ndiro chinhu chikuru chesimba maererano nedaro. Kana simba \( F(x) \) sebasa renzvimbo \(x\) rikapihwa, tinogona kuratidza basa seizvi:
\[ W = \int_{a}^{b} F(x) \, dx \]
Muchiitiko ichi:
\[ F(x) = 3x^2 \]
\[ a = 0 \, \text{meter} \]
\[ b = 2 \, \text{meter} \]
Zvadaro basa \(W\) nderekuti:
\[ W = \int_{0}^{2} 3x^2 \, dx \]
Tinoverenga chikamu ichi:
\[
W = 3 \int_{0}^{2} x^2 \, dx
= 3 \kuruboshwe[ \frac{x^3}{3} \kurudyi]_{0}^{2}
= 3 \kuruboshwe( \frac{2^3}{3} – \frac{0^3}{3} \kurudyi)
= 3 \kuruboshwe( \frac{8}{3} – 0 \kurudyi)
= 8 \, \chinyorwa{Joule}
\]
Saka, basa rinoitwa nemauto i8 Joules.
2. Kuverenga Pakati Pesimba reTsvimbo Yakafanana
Mubvunzo
Tsvimbo yakafanana ine urefu \(L\) iri pa x-axis kubva \( x = 0 \) kusvika \( x = L \). Verenga nzvimbo yepakati pehukuru hwetsvimbo.
Kukurukurirana
Kana iri tsvimbo yakafanana, huremu hunogoverwa zvakaenzana pakureba kwayo. Tinogona kufunga kuti tsvimbo ine huremu hwakafanana \(\lambda\) (huremu pahurefu hweyuniti).
Pakati pehukuru (\(x_{cm}\)) panopiwa na:
\[ x_{cm} = \frac{\int x \, dm}{\int dm} \]
Sezvo huremu hwakagoverwa zvakaenzana, tinogona kuratidza \(dm = \lambda \, dx\), uye muganho wepakati kubva \(x = 0\) kusvika \(x = L\):
\[
x_{cm} = \frac{\int_{0}^{L} x \lambda \, dx}{\int_{0}^L \lambda \, dx}
\]
Kubatanidzwa pamusoro pe \(\lambda\) kunogara kuripo uye kunogona kugadziriswa:
\[
x_{cm} = \frac{\int_{0}^{L} x \, dx}{\int_{0}^{L} dx}
= \frac{\left[ \frac{x^2}{2} \right]_{0}^{L}}{ \left[ x \right]_{0}^{L} }
= \frac{\frac{L^2}{2} – 0}{L – 0}
= \frac{L^2 /2}{L}
= \frac{L}{2}
\]
Saka, nzvimbo yepakati pehukuru hwetsvimbo iri pa \( \frac{L}{2} \), kana kuti pakati petsvimbo.
3. Kuverenga Simba reElectrostatic Zvichibva paMutemo waCoulomb
Mubvunzo
Machaji maviri \(q_1\) uye \(q_2\) ari padivi pe x-axis pa \(x = 0\) uye \(x = L\) zvichiteerana. Verenga simba remagetsi pakati pemachaji maviri.
Kukurukurirana
Mutemo waCoulomb unoti simba riri pakati pemapoinzi maviri rinoenderana zvakananga nechibereko chemari uye rinoenderana nechikamu chedaro riri pakati pawo:
\[ F = k_e \frac{|q_1 q_2|}{r^2} \]
Dimana:
– \(k_e\) ishoko reCoulomb risingaperi \((8.99 \times 10^9 \, \text{N} \cdot \text{m}^2 / \text{C}^2)\)
– \(r\) ndiyo daro riri pakati pemari dzinobhadhariswa
Muchiitiko ichi, \(q_1\) uye \(q_2\) dziri pa \(x = 0\) uye \(x = L\), wobva waona daro \(r = L\).
Simba remagetsi (electrostatic force) ndiro:
\[ F = k_e \frac{|q_1 q_2|}{L^2} \]
Iyi inzira inowanzo shandiswa pakuverenga simba remagetsi pakati pemapoinzi maviri akaiswa padaro rakati.
4. Kuverenga Magnetic Flux
Mubvunzo
Chidimbu chewaya chedenderedzwa cheradius \(r\) chinoiswa mumunda wemagineti wakaenzana \(B\), uyo wakatarisana nendege yelupu. Verenga mafambiro emagineti kuburikidza nelupu.
Kukurukurirana
Kuyerera kwemagineti (\(\Phi_B\)) kuburikidza nenzvimbo \(A\) mumunda wemagineti \(B\) kunopiwa na:
\[ \Phi_B = \int B \cdot dA \]
Sezvo simba remagineti \(B\) rakafanana uye rakamira panzvimbo ye loop, chinhu chiri nyore chinobatanidzwa chinova:
\[ \Phi_B = B \cdot A \]
Apo nzvimbo \(A\) yedenderedzwa rine radius \(r\) iri:
\[ A = \pi r^2 \]
Zvadaro magnetic flux inopinda nepa loop ndeiyi:
\[ \Phi_B = B \cdot \pi r^2 \]
Saka, magnetic flux inopinda nepa loop ndeye \( B \pi r^2 \).
Mhedziso
Kushandiswa kwezvinobatanidza mufizikisi hakudzivisiki kana tichifanira kuverenga ruzivo rwakabatana nezvinhu zvakaoma zvechisikigo. Kubva pakuverenga basa rinoitwa nesimba rinoshanduka, kuona pakati pehuremu hwechinhu, kuverenga masimba emagetsi zvichibva pamutemo waCoulomb, kusvika pakuverenga magnetic flux kuburikidza netambo yewaya mumunda wemagineti, zvese zvinotsamira pazvinobatanidza kugadzirisa matambudziko. Kunzwisisa kwakakwana mashandiro anoita zvinobatanidza mumamiriro akasiyana efizikisi hakungorerutsi kugadzirisa matambudziko chete asiwo kunopa ruzivo rwakadzama pamusoro pemagadzirirwo emuchadenga padanho remamorekuru neregalactic.
