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.
m1 v1 +m2 v2 = m1 v1 ' + m2 v2 ' ………………….. Isibalo 1.5
Amandla e-kinetic ento ngayinye ayalondolozwa.
1⁄2 mv12 + 1⁄2 mv22 = 1⁄2 mv1'2 + 1⁄2 mv2'2 ………………….. Isibalo 1.6
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
m1 v12 +m2 v22 = m1 v1 ' 2 +m2 v2 ' 2
m1 v12 -m1 v1' 2 = m2 v2 ' 2 -m2 v22
m1 (v12 - v1' 2 ) = m2 (v2 ' 2 - v2 2) —> (a + b)(a – b) = a2 - b2
m1 (v1 +v1 ') (v1 - v1 ') = m2 (v2 ' + v2 ) (v2 ' – v2 ) ………………….. Isibalo 1.7
Lawula isibalo 1.5
m1 v1 -m1 v1 ' = m2 v2 '- m2 v2
m1 (v1 - v1 ') = m2 (v2 ' – v2) ………………….. Isibalo 1.8
Hlukanisa i-equation 1.7 nge-equation 1.8 ukuze uthole umphumela wokugcina
(v1 +v1 ') = (v2 ' + v2)
v1 - v2 =v2 ' – v1 '
v1 - v2 =- (v1 ' – v2 ') ………………….. 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-v1 kanye v2Uma into 1 ihambela kwesokudla, v1 kuyinto enhle, futhi ngokuphambene nalokho, uma into yesibili ihambela kwesobunxele, v2 kuyinto engemihle. Uma zombili izinto zihamba ngezindlela ezahlukene, kodwa kungekho lwazi mayelana neziqondiso zokunyakaza, v1 kanye v2 kumele kusayinwe ngendlela ehlukile, isibonelo, v1 kuyinto enhle, futhi v2 kuyinto engemihle.
4.1.1 Izinto ezimbili ezinobunzima obufanayo
Uma m1 = m2e1 ' = v2 kanye v2' = v1 .
Kuthiwani uma izinto ezimbili zihamba ngezindlela ezahlukene?
Isibonelo, uma ngaphambi kokushayisana into 1 ithuthela kwesokudla futhi into 2 ithuthela kwesobunxele, into 1 izothuthela kwesobunxele (v1' = – v2) futhi into 2 izoya kwesokudla (v2' = v1) ngemva kokushayisana.
Kuthiwani uma noma iyiphi yalezi zinto iqale iphumule?
Isibonelo, uma into 2 ngaphambi kokushayisana iphumulile (v2 = 0), into 1 izoba sephumulweni (v1' = 0) futhi into 2 izohamba ngesivinini esifanayo nesivinini sokuqala sento 1 (v2' = v1) ngemva kokushayisana. Uma ngaphambi kokushayisana into 1 iya kwesokudla, into 2 izoya kwesokudla ngemva kokushayisana. Ngakho-ke, izinto ezimbili ziyashintshana ngesivinini.
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:
mA = 2 kg, mB = 2 kg, vA = 4 m/s, vB = – 2 m/s
Okufunayo: vA' kanye no-vB '
Isixazululo:
vA' = – 2 m/s kanye no-vB' = 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:
mA = 2 kg, mB = 2 kg, vA = 2 m/s, vB = 0m/s
Okufunayo: vA ' kanye no-vB '
Isixazululo:
vA' = 0 kanye no-vB' = 2 m/s
Ngemva kokushayisana, into A isuke iphumule, bese into B iqhubekela kwesokudla ngesivinini esingu-2 m/s.
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 iphumula ekuqaleni (v2 = 0), isibalo 1.10 siba yisibalo 1.12 kanti isibalo 1.11 siba yisibalo 1.13.
Uma v2 = 0, m1 kuhle kakhulu, futhi m2 kuncane kakhulu, ngokuxazulula izibalo 1.12 kanye no-1.13 v1' = v1 kanye v2' = 2v1 kutholakala. Uma v2 = 0, m1 incane kakhulu, futhi m2 kuhle kakhulu, ngokuxazulula izibalo 1.12 kanye no-1.13 v1 ' = -v1 kanye v2 ' = 0 kutholakala. Amamaki amahle nangalungile abonisa izinkomba 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:
mA = 1 kg, vA = 20 m/s, mB = kuhle kakhulu, vB = 0
wayefuna :vA' kanye no-vB'
Isixazululo:
vA' = -20 m/s kanye no-vB' = 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.
