Kubonderana kwakanyatsonaka
Kuroverana kwezvinhu zviviri kunonzi kuroverana kwakakwana kana simba rekufamba kana kinetic rechinhu chimwe nechimwe chisati charoverana rakaenzana nesimba rekufamba uye kinetic rechinhu chimwe nechimwe mushure mekuroverana. Nemamwe mashoko, kuchengetedza mutemo wekufamba uye kuchengetedza mutemo wesimba rekufamba zvinoshanda mukuroverana kwakakwana. Kushandiswa kweshoko rekuti elastic kunoratidza kuti mushure mekuroverana, zvinhu zviviri izvi hazvibatane kana kuti hazvina kubatana asi zvinosvetuka-svetuka. Simba rekufamba kwechinhu chimwe nechimwe rinochengetedzwa.
Simba rechinhu chimwe nechimwe rinochengetedzwa.
m 1 v 1 + m 2 v 2 = m 1 v 1 ' + m 2 v 2 ' ………………….. Equation 1.5
Simba rekinetic rechinhu chimwe nechimwe rinochengetedzwa.
1⁄2 mv 1 2 + 1⁄2 mv 2 2 = 1⁄2 mv 1 ' 2 + 1⁄2 mv 2 ' 2 ………….. Equation 1.6
Kuroverana kwakanyatsosimba kunofanira kunge kwakanyarara uye hakuburitse kupisa nekuda kwekukweshana pakati pezvinhu zviviri zviri kuroverana. Kana kuroverana kwezvinhu zviviri kukaita ruzha nekupisa, simba rekufamba kwezvinhu harichengetedzwe. Rimwe simba rekufamba rinoshandurwa kuita simba remagetsi nesimba rekupisa, uye rimwe rinoshandurwa kuita simba remukati. Muenzaniso wekuroverana kwakanyatsosimba ndiko kuroverana kwezvikamu zveatomu nezvikamu zvepasi.
Mudambudziko rekusangana kwakanyatsosimba, kana kumhanya kwekutanga kuchizivikanwa nepo kumhanya kwekupedzisira kusingazivikanwe, dambudziko harigone kugadziriswa nekushandisa ma equation 1.5 na 1.6 chete. Nekuda kweizvi, ma equation ese ari maviri anogadziriswa kuti awane mamwe ma equation, ayo anogona kushandiswa kuona kumhanya kwekupedzisira.
Bvisa factor 1/2 wobva wachinja 1.6
m 1 v 1 2 + m 2 v 2 2 = m 1 v 1 ' 2 + m 2 v 2 ' 2
m 1 v 1 2 – m 1 v 1 ' 2 = m 2 v 2 ' 2 – m 2 v 2 2
m 1 (v 1 2 – v 1 ' 2 ) = m 2 (v 2 ' 2 – v 2 2 ) —> (a + b)(a – b) = a 2 – b 2
m 1 (v 1 + v 1 ') (v 1 – v 1 ') = m 2 (v 2 ' + v 2 ) (v 2 ' – v 2 ) ………………….. Equation 1.7
Shandisa equation 1.5
m 1 v 1 – m 1 v 1 ' = m 2 v 2 ' - m 2 v 2
m 1 (v 1 – v 1 ') = m 2 (v 2 ' – v 2 ) ………………….. Equation 1.8
Govanisa equation 1.7 ne equation 1.8 kuti uwane mhedzisiro yekupedzisira
(v 1 + v 1 ') = (v 2 ' + v 2 )
v 1 – v 2 = v 2 ' – v 1 '
v 1 – v 2 = – (v 1 ' – v 2 ') ………………….. Equation 1.9
Zviyero 1.5 na 1.9 zvinogona kushandiswa kugadzirisa matambudziko ekukonana kwakanyatsosimba. Sanganisai zviyero 1.5 na 1.9 kuti muwane zviyero zviviri zvekuona kumhanya kwekupedzisira kwezvinhu zviviri kana huremu hwazvo nekumhanya kwekutanga zvisingazivikanwe.
Pakupindura mibvunzo uchishandisa maequation ari pamusoro, shandisa chiratidzo chakakodzera che v 1 na v 2. Kana chinhu 1 chikafamba kurudyi, v 1 iri positive, uye zvakasiyana, kana chinhu chechipiri chikafamba kuruboshwe, v 2 iri positive. Kana zvinhu zvese zvikafamba nenzira dzakasiyana, asi pasina ruzivo nezvemafambiro emafambiro, v 1 na v 2 dzinofanira kusainwa zvakasiyana, semuenzaniso, v 1 iri positive, uye v 2 iri positive.
4.1.1 Zvinhu zviviri zvine huremu hwakafanana
Kana m 1 = m 2 , v 1 ' = v 2 uye v 2 ' = v 1.
Ko kana zvinhu zviviri zvikafamba nenzira dzakasiyana?
Semuenzaniso, kana chinhu chekutanga chisati chasangana nechinhu chechipiri chikafamba kurudyi uye chinhu chechipiri chikafamba kuruboshwe, chinhu chekutanga chikafamba kuruboshwe (v 1 ' = – v 2 ) uye chinhu chechipiri chikafamba kurudyi (v 2 ' = v 1 ) mushure mekusangana.
Ko kana chimwe chezvinhu zvacho chave kuzorora pakutanga?
Semuenzaniso, kana chinhu 2 chisati chasangana (v 2 = 0), chinhu 1 chinenge chasangana (v 1 ' = 0) uye chinhu 2 chichafamba nekumhanya kwakafanana nekumhanya kwekutanga kwechinhu 1 (v 2 ' = v 1 ) mushure mekusangana. Kana chinhu 1 chisati chasangana chichienda kurudyi, chinhu 2 chichafamba kurudyi mushure mekusangana. Nokudaro, zvinhu zviviri izvi zvinochinjana kumhanya.
Muenzaniso wemubvunzo 4
Zvinhu A (2 kg) naB (2 kg) zvinofamba zvichienda kune dzimwe nzira dzakasiyana nekumhanya kwe4 m/s uye 2 m/s, zvichiteerana. Kana zvinhu A naB zvikabonderana mukubonderana kwakanyatsosimba, chii chiri kumhanya kwekupedzisira kwezvinhu A naB?
Zvinozivikanwa:
m A = 2 kg, m B = 2 kg, v A = 4 m/s, v B = – 2 m/s
Zvaidiwa: v A ' uye v B '
Solution:
v A ' = – 2 m/s uye v B ' = 4 m/s
Mushure mekuroverana, chinhu A chinofamba nekumhanya kwe2 m/s uye chinhu B chinofamba nekumhanya kwe4 m/s munzira dzakasiyana. Kana chinhu A chisati charoverana chikaenda kurudyi uye chinhu B chikaenda kuruboshwe, chinhu A chichaenda kuruboshwe uye chinhu B chichaenda kurudyi mushure mekuroverana.
Muenzaniso wemubvunzo 5
Chinhu A (2 kg) chinoenda kurudyi nekumhanya kwe2 m/s uye chinobonderana nechinhu B (2 kg) chiri pachigaro. Kana zvinhu zviviri izvi zvikabonderana zvine tambo dzakanyatsosimba, chii chiri kumhanya kwekupedzisira kwezvinhu A neB?
Zvinozivikanwa:
m A = 2 kg, m B = 2 kg, v A = 2 m/s, v B = 0 m/s
Zvaidiwa: v A ' uye v B '
Solution:
v A ' = 0 uye v B ' = 2 m/s
Mushure mekuroverana, chinhu A chinenge chazorora, uye chinhu B chinoenda kurudyi nekumhanya kwe2 m/s.
4.1.2 Zvinhu zviviri zvehukuru hwakasiyana
Kana zvinhu zviviri zvine mavhezheni ekutanga akasiyana uye mass (musiyano mudiki), mavhezheni ekupedzisira anozivikanwa nekushandisa equation 1.10 na 1.11.
Kana chinhu chechipiri pakutanga chiri pachigaro (v 2 = 0), equation 1.10 inova equation 1.12 uye equation 1.11 inova equation 1.13.
Kana v 2 = 0, m 1 yakakura kwazvo, uye m 2 idiki kwazvo, nekugadzirisa ma equation 1.12 na 1.13 v 1 ' = v 1 na v 2 ' = 2v 1 zvinowanikwa. Kana v 2 = 0, m 1 idiki kwazvo, uye m 2 yakakura kwazvo, nekugadzirisa ma equation 1.12 na 1.13 v 1 ' = -v 1 na v 2 ' = 0 zvinowanikwa. Ma marks akanaka neasina kunaka anoratidza nzira dzakasiyana dzekufamba.
Muenzaniso wemubvunzo 6
Chinhu chine huremu hwe1 kg chinofamba nekumhanya kwe20 m/s chobonderana nemadziro zvine simba rakanyatsosimba. Ndeipi kumhanya kwekupedzisira kwechinhu nemadziro?
Zvinozivikanwa:
m A = 1 kg, v A = 20 m/s, m B = yakanaka kwazvo, v B = 0
Zvaidiwa : v A ' uye v B '
Solution:
v A ' = -20 m/s uye v B ' = 0
Mushure mekuroverana, chinhu A chinosvetuka nekumhanya kwe20 m/s uye chinhu B chinoramba chakazorora. Kana chinhu A chikafamba kurudyi, chinoenda kuruboshwe mushure mekuroverana.
