Muenzaniso weMibvunzo yeKukurukurirana kweUkama
Kuwirirana ndeimwe yepfungwa dzakakosha mufizikisi yemazuva ano, yakatangwa naAlbert Einstein pakutanga kwezana remakore rechi20. Chinyorwa chino chichakurukura dzidziso yekuwirirana uye kuti inoshanda sei muhupenyu hwezuva nezuva kuburikidza nematambudziko emuenzaniso netsananguro.
Nhanganyaya kuRelativity
Dzidziso ye relativity ine zvikamu zviviri zvikuru: Special Theory of Relativity uye General Theory of Relativity. The Special Theory of Relativity, yakaburitswa muna 1905, yakachinja kunzwisisa kwedu nzvimbo nenguva. Mudzidziso iyi, Einstein akataura kuti kumhanya kwechiedza ndiwo muganho wekukurumidza usingagone kudarika uye kuti mitemo yefizikisi yakafanana kune vese vanocherechedza vachifamba nekumhanya kwakafanana.
Zvichakadaro, Dzidziso yeGeneral of Relativity, yakatangwa muna 1915, inobata negravity. Pasi pedzidziso iyi, gravity haisi simba rekare, asi kutenderera kwenzvimbo nenguva kunokonzerwa nehuremu.
Kunzwisisa pfungwa iyi kwakakosha zvikuru tisati tapinda mumibvunzo yemuenzaniso nehurukuro yayo.
Mibvunzo yemuenzaniso nekukurukurirana
Mubvunzo 1: Kuwedzerwa Kwenguva
Mubvunzo:
Mutyairi wendege anofamba achienda kunyeredzi iri kure nekumhanya kwe0,8c (apo c iri kumhanya kwechiedza). Kana rwendo rwacho ruchitora makore gumi ePasi, mutyairi wendege anowana nguva yakareba sei zvichienderana newachi yake (nguva yakakodzera)?
Kukurukurirana:
Kuwedzerwa kwenguva chiitiko chinoitika nekuda kwekusiyana kwekumhanya pakati pevacherechedzi vaviri. Nguva inopfuura zvishoma nezvishoma kune chinhu chinofamba kana tichienzanisa nemucherechedzi akamira.
Nzira yekuwedzera nguva ndeiyi:
\[ \Delta t' = \frac{\Delta t}{\sqrt{1 – \frac{v^2}{c^2}}}\]
Di mana:
– \(\Delta t'\) inguva inoonekwa yechinhu chinofamba.
– \(\Delta t\) inguva inoonekwa yechinhu chisina kumira.
– \(v\) ndiko kumhanya kwechinhu chiri kufamba.
– \(c\) ndiko kumhanya kwechiedza.
Batanidza kukosha kunozivikanwa mufomura:
\[v = 0,8c \]
\[ \Delta t = 10 \, \chinyorwa{gore} \]
\[ \Delta t' = \frac{10}{\sqrt{1 – \frac{(0,8c)^2}{c^2}}}\]
\[ \Delta t' = \frac{10}{\sqrt{1 – 0,64}}\]
\[ \Delta t' = \frac{10}{\sqrt{0,36}}\]
\[ \Delta t' = \frac{10}{0,6}\]
\[ \Delta t' \approx 16.67 \, \text{year}\]
Saka, nguva inowanikwa nemuchadenga zvichienderana newachi yake ndeye makore angangoita 16,67.
Mubvunzo 2: Kureba kwehurefu
Mubvunzo:
Chinhu chakareba mamita zana uye chinoyerwa chiri pakamira. Kana chinhu chiri kufamba nekumhanya kwe0,6c, kureba kwechinhu chacho kwakadii zvichienderana nemunhu akatarisa akamira?
Kukurukurirana:
Kudzikira kwehurefu chiitiko umo hurefu hwechinhu chinofamba kana tichienzanisa nemuoni hupfupi pane kana chinhu chacho chakazorora.
Nzira yekudzikisa hurefu hwehuremu ndeiyi:
\[ L = L_0 \sqrt{1 – \frac{v^2}{c^2}} \]
Di mana:
– \(L\) kureba kwechinhu chiri kufamba.
– \(L_0\) ndiyo urefu hwakakodzera (hurefu hwechinhu kana chakamira).
– \(v\) ndiko kumhanya kwechinhu.
– \(c\) ndiko kumhanya kwechiedza.
Batanidza kukosha kunozivikanwa mufomura:
\[ L_0 = 100 \, \text{meter} \]
\[v = 0,6c \]
\[ L = 100 \sqrt{1 – \frac{(0,6c)^2}{c^2}}\]
\[ L = 100 \sqrt{1 - 0,36}\]
\[ L = 100 \sqrt{0,64}\]
\[L = 100 \kawa 0,8\]
\[ L = 80 \, \text{meter}\]
Saka, kureba kwechinhu chiri kufamba maererano nemucherechedzi asingamiri mamita makumi masere.
Mubvunzo 3: Kuwanda kweZvinhu Zvinoenderana Nezvinodiwa Nevamwe
Mubvunzo:
Kanhu kane huremu hwe2 kg. Kana kanhu aka kari kufamba nekumhanya kwe0,9c, huremu hwekanhu kacho hunonzi relativistic hupi?
Kukurukurirana:
Huremu hwechinhu hunochinja-chinja kana chinhu chichifamba pedyo nekumhanya kwechiedza.
Fomura yehuwandu hwezvinhu zvinoenderana nehukuru hwemunhu ndeiyi:
\[ m = \frac{m_0}{\sqrt{1 – \frac{v^2}{c^2}}} \]
Di mana:
– \(m\) inhamba yehuwandu hunoreva kuti zvinhu zvinoenderana nezvinodiwa nemunhu.
– \(m_0\) ndiyo huremu hwasara (huremu hwakakodzera).
– \(v\) ndiko kumhanya kwechinhu.
– \(c\) ndiko kumhanya kwechiedza.
Batanidza kukosha kunozivikanwa mufomura:
\[ m_0 = 2 \, \mashoko{kg} \]
\[v = 0,9c \]
\[ m = \frac{2}{\sqrt{1 – \frac{(0,9c)^2}{c^2}}}\]
\[ m = \frac{2}{\sqrt{1 – 0,81}}\]
\[ m = \frac{2}{\sqrt{0,19}}\]
\[ m \approx \frac{2}{0,436}\]
\[ m \inenge 4,59 \, \text{kg}\]
Saka, huwandu hwechinhu chinoenderana nezvinodiwa nemunhu kana chichifamba nekumhanya kwe0,9c hunosvika 4,59 kg.
Mubvunzo 4: E=mc^2
Mubvunzo:
Simba rakawanda sei rinogadzirwa kana giramu rimwe chete rechinhu rikaparadzwa zvachose zvichienderana nefomura yaEinstein \(E=mc^2\)?
Kukurukurirana:
Fomura raEinstein rakakurumbira \(E=mc^2\) rinopa hukama hwakananga pakati pehukuru (m) nesimba (E), \(c\) richiva kumhanya kwechiedza.
Muhurongwa hweSI (International System of Units):
– Huremu (m) hunoyerwa mumakirogiramu (kg).
– Kumhanya kwechiedza (c) ndiko \(3 \kawa 10^8 \, \text{m/s}\).
Ngativerenge simba rinogadzirwa kubva pa 1 gramu yechinhu:
– 1 gramu = 0,001 kg
\[ E = mc^2 \]
\[ E = (0,001) (3 \kawa 10^8)^2 \]
\[ E = (0,001) (9 \kawa 10^{16}) \]
\[ E = 9 \kawa 10^{13} \, \text{joules} \]
Saka, simba rinogadzirwa kana 1 gramu yezvinhu zvikaparadzwa zvachose i \(9 \ times 10^{13}\) joules.
Mhedziso
Kuwirirana ipfungwa inokosha uye inokosha mufizikisi, ine zvazvinoreva zvikuru pazviitiko zvakasiyana-siyana zvepanyama. Kuburikidza nemienzaniso yakurukurwa pamusoro apa, taona kuti dzidziso yakakosha yehukama inogona kushandiswa sei kunzwisisa kuwedzera kwenguva, kupfupika kwenguva, huwandu hunoenderana, uye hukama huripo pakati pehukuru nesimba.
Nekunzwisisa nekushandisa matambudziko aya, tinogona kunzwisisa kunaka kwedzidziso ye relativity uye zvazvinoreva pakunzwisisa zvakasikwa.
