Chitsanzo cha Mafunso Okambirana za Ubale
Kugwirizana ndi chimodzi mwa mfundo zofunika kwambiri mu sayansi ya masiku ano, zomwe zinayambitsidwa ndi Albert Einstein kumayambiriro kwa zaka za m'ma 20. Nkhaniyi ikambirana za chiphunzitso cha kugwirizana ndi momwe chimagwirira ntchito pa moyo watsiku ndi tsiku kudzera mu zitsanzo za mavuto ndi mafotokozedwe.
Chiyambi cha Kugwirizana
Chiphunzitso cha ubale chimaphatikizapo magawo awiri akuluakulu: Chiphunzitso Chapadera cha Ubale ndi Chiphunzitso Chachikulu cha Ubale. Chiphunzitso Chapadera cha Ubale, chomwe chinafalitsidwa mu 1905, chinasintha kwambiri kumvetsetsa kwathu malo ndi nthawi. Mu chiphunzitsochi, Einstein anati liwiro la kuwala ndilo malire othamanga kwambiri omwe sangadutse ndipo malamulo a fizikisi ndi ofanana kwa owonera onse omwe akuyenda pa liwiro losasintha.
Pakadali pano, Chiphunzitso Chachikulu cha Kugwirizana, chomwe chinayambitsidwa mu 1915, chimakhudza mphamvu yokoka. Malinga ndi chiphunzitsochi, mphamvu yokoka si mphamvu yachikhalidwe, koma ndi kupindika kwa nthawi ndi malo komwe kumachitika chifukwa cha kulemera.
Kumvetsetsa mfundo yofunikira iyi n'kofunika kwambiri tisanapite ku mafunso achitsanzo ndi kukambirana kwawo.
Mafunso ndi Kukambirana Zitsanzo
Funso 1: Kuchuluka kwa Nthawi
Funso:
Woyenda mumlengalenga amayenda kupita ku nyenyezi yakutali pa liwiro la 0,8c (komwe c ndi liwiro la kuwala). Ngati ulendowu umatenga zaka 10 za Dziko Lapansi, kodi woyenda mumlengalenga amakumana ndi nthawi yochuluka bwanji malinga ndi wotchi yake (nthawi yoyenera)?
Kukambirana:
Kuchuluka kwa nthawi ndi chinthu chomwe chimachitika chifukwa cha kusiyana kwa liwiro pakati pa owonera awiri. Nthawi imapita pang'onopang'ono kwambiri kwa chinthu chomwe chikuyenda poyerekeza ndi wowonera wosasuntha.
Njira yowonjezera nthawi ndi iyi:
\[ \Delta t' = \frac{\Delta t}{\sqrt{1 – \frac{v^2}{c^2}}}\]
Kumene:
– \(\Delta t'\) ndi nthawi yowonedwa ya chinthu choyenda.
– \(\Delta t\) ndi nthawi yowonedwa ya chinthu chosasuntha.
– \(v\) ndi liwiro la chinthu choyenda.
– \(c\) ndi liwiro la kuwala.
Ikani mfundo zodziwika bwino mu fomula iyi:
\[v = 0,8c \]
\[ \Delta t = 10 \, \malemba{year} \]
\[ \Delta t' = \frac{10}{\sqrt{1 – \frac{(0,8c)^2}{c^2}}}\]
\[ \Delta t' = \frac{10}{\sqrt{1 – 0,64}}\]
\[ \Delta t' = \frac{10}{\sqrt{0,36}}\]
\[ \Delta t' = \frac{10}{0,6}\]
\[ \Delta t' \pafupifupi 16.67 \, \text{year}\]
Kotero, nthawi yomwe woyendetsa ndegeyo amakumana nayo malinga ndi wotchi yake ndi pafupifupi zaka 16,67.
Funso 2: Kutalika kwa Kufupika
Funso:
Chinthu chili ndi kutalika kwa mamita 100 ndipo chimayesedwa chili pamalo opumula. Ngati chinthucho chikuyenda pa liwiro la 0,6c, kodi kutalika kwa chinthucho ndi kotani malinga ndi wowonera wosasuntha?
Kukambirana:
Kufupika kwa kutalika ndi chinthu chomwe kutalika kwa chinthu chomwe chikuyenda poyerekeza ndi wowonera kumakhala kochepa kuposa pamene chinthucho chili pamalo opumulira.
Fomula yochepetsera kutalika ndi iyi:
\[ L = L_0 \sqrt{1 – \frac{v^2}{c^2}} \]
Kumene:
– \(L\) ndi kutalika kwa chinthu choyenda.
– \(L_0\) ndi kutalika koyenera (kutalika kwa chinthucho chikakhala pamalo ake).
– \(v\) ndi liwiro la chinthucho.
– \(c\) ndi liwiro la kuwala.
Ikani mfundo zodziwika bwino mu fomula iyi:
\[ L_0 = 100 \, \text{meter} \]
\[v = 0,6c \]
\[ L = 100 \sqrt{1 – \frac{(0,6c)^2}{c^2}}\]
\[ L = 100 \sqrt{1 - 0,36}\]
\[ L = 100 \sqrt{0,64}\]
\[L = 100 \nthawi 0,8\]
\[ L = 80 \, \text{meter}\]
Kotero, kutalika kwa chinthu choyenda malinga ndi wowonera wosasuntha ndi mamita 80.
Funso 3: Misa Yogwirizana ndi Zinthu Zina
Funso:
Tinthu tating'onoting'ono timakhala ndi kulemera kopumula kwa 2 kg. Ngati tinthu tating'onoting'ono timeneti tikuyenda pa liwiro la 0,9c, kodi kulemera kwa tinthu tating'onoting'ono ndi kotani?
Kukambirana:
Kulemera kwa chinthu chogwirizana ndi chinthu chomwe chimawonjezeka pamene chinthucho chikuyandikira liwiro la kuwala.
Fomula ya relativistic mass ndi iyi:
\[ m = \frac{m_0}{\sqrt{1 – \frac{v^2}{c^2}}} \]
Kumene:
– \(m\) ndi kuchuluka kwa zinthu zomwe zimagwirizana ndi zomwe zikuchitika.
– \(m_0\) ndi kulemera kotsala (kulemera koyenera).
– \(v\) ndi liwiro la chinthucho.
– \(c\) ndi liwiro la kuwala.
Ikani mfundo zodziwika bwino mu fomula iyi:
\[ m_0 = 2 \, \malemba{kg} \]
\[v = 0,9c \]
\[ m = \frac{2}{\sqrt{1 – \frac{(0,9c)^2}{c^2}}}\]
\[ m = \frac{2}{\sqrt{1 – 0,81}}\]
\[ m = \frac{2}{\sqrt{0,19}}\]
\[ m \pafupifupi \frac{2}{0,436}\]
\[ m \pafupifupi 4,59 \, \malemba{kg}\]
Kotero, kulemera kwa tinthu tomwe timayenderana ndi zinthu zina tikamayenda pa liwiro la 0,9c ndi pafupifupi 4,59 kg.
Funso 4: E=mc^2
Funso:
Kodi mphamvu yochuluka imapangidwa bwanji ngati gramu imodzi ya chinthu yawonongeka kwathunthu motsatira njira ya Einstein \(E=mc^2\)?
Kukambirana:
Fomula yotchuka ya Einstein \(E=mc^2\) imapereka ubale wolunjika pakati pa kulemera (m) ndi mphamvu (E), ndipo \(c\) ndi liwiro la kuwala.
Mu dongosolo la SI (International System of Units):
– Kulemera (m) kumayesedwa mu makilogalamu (kg).
– Liwiro la kuwala (c) ndi \(3 \times 10^8 \, \text{m/s}\).
Tiyeni tiwerengere mphamvu yopangidwa kuchokera ku gramu imodzi ya chinthu:
– 1 gramu = 0,001 kg
\[ E = mc^2 \]
\[ E = (0,001) (3 \nthawi 10^8)^2 \]
\[ E = (0,001) (9 \nthawi 10^{16}) \]
\[ E = 9 \nthawi 10^{13} \, \malemba{majoules} \]
Kotero, mphamvu yomwe imapangidwa ngati gramu imodzi ya chinthu yawonongedwa kwathunthu ndi \(9 \times 10^{13}\) joules.
Mapeto
Kugwirizana ndi lingaliro lofunikira komanso lofunika kwambiri mu fizikisi, lomwe lili ndi tanthauzo lalikulu pazochitika zosiyanasiyana zakuthupi. Kudzera mu zitsanzo zomwe takambirana pamwambapa, taona momwe chiphunzitso chapadera cha kugwirizana chingagwiritsidwire ntchito kumvetsetsa kufalikira kwa nthawi, kupindika kwa kutalika, kuchuluka kwa kugwirizana, komanso ubale pakati pa kulemera ndi mphamvu.
Mwa kumvetsetsa ndi kuchita zinthu mogwirizana ndi mavuto amenewa, tingathe kuyamikira bwino kukongola kwa chiphunzitso cha ubale ndi tanthauzo lake pomvetsetsa chilengedwe chonse.
