Ukushayisana okunwebeka ngokuphelele
Ukungqubuzana kwezinto ezimbili kubizwa ngokuthi ukungqubuzana okunwebeka ngokuphelele uma amandla omfutho noma amandla omfutho ento ngayinye ngaphambi kokungqubuzana elingana namandla omfutho kanye namandla omfutho ento ngayinye ngemva kokungqubuzana. Ngamanye amazwi, ukulondolozwa komthetho womfutho kanye nokulondolozwa komthetho wamandla omfutho kuyasebenza ekungqubuzaneni okunwebeka ngokuphelele. Ukusetshenziswa kwegama elithi elastic kubonisa ukuthi ngemva kokungqubuzana, izinto ezimbili azinamatheli ndawonye noma azinamathelene kodwa ziyagxumagxuma. Umfutho wento ngayinye uyagcinwa.
Umfutho wento ngayinye uyalondolozwa.
m 1 v 1 + m 2 v 2 = m 1 v 1 ' + m 2 v 2 ' ………………….. Isibalo 1.5
Amandla e-kinetic ento ngayinye ayalondolozwa.
1⁄2 mv 1 2 + 1⁄2 mv 2 2 = 1⁄2 mv 1 ' 2 + 1⁄2 mv 2 ' 2 ………………….. Isibalo 1.6
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Ukungqubuzana okunwebeka ngokuphelele kumele kuthule futhi akukhiqizi ukushisa ngenxa yokungqubuzana phakathi kwezinto ezimbili ezingqubuzanayo. Uma ukungqubuzana kwezinto ezimbili kudala umsindo nokushisa, amandla e-kinetic ezinto awagcinwa. Amanye amandla e-kinetic aguqulwa abe amandla omsindo namandla okushisa, kanti amanye aguqulwa abe amandla angaphakathi. Isibonelo sokungqubuzana okunwebeka ngokuphelele ukungqubuzana kwezinhlayiya ze-athomu kanye ne-subatomic.
Enkingeni yokushayisana okunwebeka ngokuphelele, uma ijubane lokuqala laziwa kuyilapho ijubane lokugcina lingaziwa, inkinga ayinakuxazululwa ngokusebenzisa izilinganiso 1.5 no-1.6 kuphela. Ngenxa yalesi sizathu, zombili lezi zilinganiso ziyashintshwa ukuze kutholakale ezinye izilinganiso, ezingasetshenziswa ukunquma ijubane lokugcina.
Susa isici 1/2 bese ulawula u-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 ) ………………….. Izibalo 1.7
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Lawula isibalo 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 ) ………………….. Isibalo 1.8
Hlukanisa i-equation 1.7 nge-equation 1.8 ukuze uthole umphumela wokugcina
(v 1 + v 1 ') = (v 2 ' + v 2 )
v 1 – v 2 = v 2 ' – v 1 '
v 1 – v 2 = – (v 1 ' – v 2 ') ………………….. Isibalo 1.9
Izibalo 1.5 no-1.9 zingasetshenziswa ukuxazulula izinkinga zokushayisana okunwebeka ngokuphelele. Hlanganisa izilinganiso 1.5 no-1.9 ukuze uthole izilinganiso ezimbili zokunquma ijubane lokugcina lezinto ezimbili uma isisindo sazo kanye nejubane lokuqala kungaziwa.
Uma uxazulula imibuzo usebenzisa izilinganiso ezingenhla, sebenzisa uphawu olufanele lwe-v 1 kanye ne-v 2. Uma into 1 ihambela ngakwesokudla, i-v 1 ilungile, futhi ngokuphambene nalokho, uma into yesibili ihambela kwesobunxele, i-v 2 ilungile. Uma zombili izinto zihamba ngezindlela ezahlukene, kodwa kungekho lwazi mayelana neziqondiso zokunyakaza, i-v 1 kanye ne-v 2 kumele zisayinwe ngendlela ehlukile, isibonelo, i-v 1 ilungile, kanti i-v 2 ilungile.
4.1.1 Izinto ezimbili ezinobunzima obufanayo
Uma u-m 1 = m 2 , u-v 1 ' = v 2 kanye no-v 2 ' = v 1.
Kuthiwani uma izinto ezimbili zihamba ngezindlela ezahlukene?
Isibonelo, uma ngaphambi kokuthi into yokushayisana 1 iye kwesokudla futhi into 2 iye kwesobunxele, into 1 izoya kwesobunxele (v 1 ' = – v 2 ) kanti into 2 izoya kwesokudla (v 2 ' = v 1 ) ngemva kokushayisana.
Kuthiwani uma noma iyiphi yalezi zinto iqale iphumule?
Isibonelo, uma into yokushayisana 2 ngaphambi kokuba iphumule (v 2 = 0), into 1 izophumula (v 1 ' = 0) kanti into 2 izohamba ngesivinini esifanayo nesivinini sokuqala sento 1 (v 2 ' = v 1 ) ngemva kokushayisana. Uma into yokushayisana 1 ngaphambi kokuba iphumule iye kwesokudla, into 2 izohamba iye kwesokudla ngemva kokushayisana. Ngakho-ke, izinto ezimbili zishintshana ngesivinini.
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Isibonelo sombuzo 4
Izinto A (2 kg) kanye no-B (2 kg) ziya eziqondisweni eziphambene ngesivinini esingu-4 m/s kanye no-2 m/s, ngokulandelana. Uma izinto A kanye no-B zishayisana ngokushayisana okunwebeka ngokuphelele, yiziphi izivinini zokugcina zezinto A kanye no-B?
Kwaziwa:
m A = 2 kg, m B = 2 kg, v A = 4 m/s, v B = – 2 m/s
Kufunwa: v A ' kanye v B '
Isixazululo:
v A ' = – 2 m/s kanye v B ' = 4 m/s
Ngemva kokushayisana, into A ihamba ngesivinini esingu-2 m/s kanti into B ihamba ngesivinini esingu-4 m/s ngezindlela eziphambene. Uma ngaphambi kokushayisana into A iya kwesokudla bese into B iya ngakwesobunxele, into A izoya ngakwesobunxele bese into B izoya kwesokudla ngemva kokushayisana.
Isibonelo sombuzo 5
Into A (2 kg) iya kwesokudla ngesivinini esingu-2 m/s bese ishayisana nento B (2 kg) ephumule. Uma izinto ezimbili zishayisana ngokushayisana okunwebeka ngokuphelele, yiziphi izivinini zokugcina zezinto A no-B?
Kwaziwa:
m A = 2 kg, m B = 2 kg, v A = 2 m/s, v B = 0 m/s
Kufunwa: v A ' kanye v B '
Isixazululo:
v A ' = 0 kanye v B ' = 2 m/s
Ngemva kokushayisana, into A isuke iphumule, bese into B iqhubekela kwesokudla ngesivinini esingu-2 m/s.
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4.1.2 Izinto ezimbili ezinobunzima obuhlukene
Uma izinto ezimbili zinejubane lokuqala elihlukile kanye nobunzima (umehluko omncane), ijubane lokugcina laziwa ngokusebenzisa izilinganiso 1.10 kanye no-1.11.
Uma into 2 ekuqaleni iphumulile (v 2 = 0), isibalo 1.10 siba yisibalo 1.12 kanti isibalo 1.11 siba yisibalo 1.13.
Uma u-v 2 = 0, u-m 1 mkhulu kakhulu, kanti u-m 2 mncane kakhulu, ngokuxazulula izilinganiso 1.12 no-1.13 v 1 ' = v 1 kanye no-v 2 ' = 2v 1 kutholakala. Uma u-v 2 = 0, u-m 1 mncane kakhulu, kanti u-m 2 mkhulu kakhulu, ngokuxazulula izilinganiso 1.12 kanye no-1.13 v 1 ' = -v 1 kanye no-v 2 ' = 0 kutholakala. Amamaki amahle nangalungile abonisa izikhombisi-ndlela zokunyakaza eziphambene.
Isibonelo sombuzo 6
Into enesisindo esingu-1 kg ihamba ngesivinini esingu-20 m/s bese ishayisana nodonga ngendlela ethambile ngokuphelele. Ziyini izivinini zokugcina zento nodonga?
Kwaziwa:
m A = 1 kg, v A = 20 m/s, m B = kuhle kakhulu, v B = 0
Kufunwa : v A ' kanye v B '
Isixazululo:
v A ' = -20 m/s kanye v B ' = 0
Ngemva kokushayisana, into A iyagxuma ngesivinini esingama-20 m/s bese into B ihlala iphumule. Uma ngaphambi kokushayisana into A iya kwesokudla, iya ngakwesobunxele ngemva kokushayisana.
