Isihloko mayelana nomthetho kaNewton wamandla adonsela phansi omhlaba wonke
Esihlokweni somthetho kaNewton, kwafundwa ukuthi yonke into eqala ukuphumula iba yizinyathelo, noma noma iyiphi into eqala ukunyakaza iba yizinyathelo uma kukhona “into” ehambayo noma evimba into. Into ethile ibizwa ngokuthi “amandla”. Kungani isithelo siwa noma sihamba siye ebusweni bomhlaba ngemva kokuba sikhishwe esiqwini? Umthetho kaNewton uthi uma isithelo sihamba, kumele kube namandla asebenza esithelweni. Amandla abangela isithelo noma iyiphi into ukuba iwele ebusweni bomhlaba abizwa ngokuthi amandla adonsela phansi.
Inkinga yezinto eziwayo ezihilela amandla adonsela phansi, oyifundayo njengamanje, icatshangelwe futhi yafundwa ngu-Isaac Newton, usosayensi waseBrithani. Le nkinga uNewton ayecabanga ukuthi ikhona kusukela eGrisi Lasendulo. Kunezinkinga ezimbili eziyisisekelo eziye zahlolwa amaGreki, esikhathini eside ngaphambi kokuba uNewton azalwe. Umbuzo ohlala ubuzwa ukuthi kungani izinto zihlala ziwela ebusweni bomhlaba nokuthi amaplanethi ahamba kanjani, okuhlanganisa ilanga nenyanga. AmaGreki ngaleso sikhathi ayebona ukukhathazeka ngezinto eziwayo kanye nokunyakaza kwamaplanethi njengezinto ezimbili ezihlukene. Ngakho-ke, kwaqhubeka kwaze kwaba yisikhathi sikaNewton. Ngakho-ke, lokho uNewton akukhiqizayo kwakhelwe emsebenzini wabantu ababengaphambi kwakhe. Okuhlukanisa uNewton nabantu ababengaphambi kwakhe, ukuthi uNewton wabona ubunzima bezinto eziwayo kanye nokunyakaza kwamaplanethi okubangelwa yinto eyodwa kuphela futhi kumele alalele umthetho ofanayo. Ngamanye amazwi, uNewton waphikisana ngokuthi amandla abangela izinto ukuba ziwele ebusweni bomhlaba ngamandla afanayo, abangela inyanga ukuba ihambe emhlabeni.
Ubudlelwano phakathi kwamandla adonsela phansi nebanga kanye nobunzima
Lapho esungula umthetho wamandla adonsela phansi, uNewton waqhathanisa ukusheshisa kwezithelo eziwela eduze komhlaba nokusheshisa kwenyanga okuphakathi lapho ijikeleza umhlaba. Ngokusho kukaNewton, ukusheshisa okubonwa yizithelo eziwela phansi kanye nokusheshisa kwenyanga okuphakathi lapho inyanga ijikeleza umhlaba kubangelwa amandla afanayo, amandla adonsela phansi omhlaba. UNewton uphikisa ngokuthi ukusheshisa kwenyanga lapho ijikeleza umhlaba kuhambelana no-1/r2 lapho u-r = ibanga eliphakathi kwesikhungo somhlaba kanye nesikhungo senyanga = 3.84 x 10 8 m. Ukusheshisa kwezithelo eziwela phansi kuhambelana no-1/R 2 , lapho u-R = ibanga eliphakathi kwesikhungo somhlaba kanye nesikhungo sezithelo. Izithelo ziseduze nobuso bomhlaba ukuze u-R = R F , lapho u-R E = irediyasi yomhlaba = 6.37 x 10 6 m. Ngakho-ke, ukuqhathanisa phakathi kokusheshisa kwenyanga (a M ) kanye nokusheshisa kwezithelo (g):
Ngakho-ke, ukusheshisa kwenyanga okuphakathi nendawo:
a M = (2.75 x 10 -4 )(g) = (2.75 x 10 -4 )(9.8 m/s 2 ) = 2.7 x 10 -3 m/s 2
UNewton uphinde wabala ukusheshisa kwenyanga okuphakathi nendawo ngendlela ehlukile. Kuyaziwa ukuthi isikhathi sokuzungeza kwenyanga noma inyanga yesikhathi sokwenza uguquko olulodwa = izinsuku ezingama-27.3 = 2.36 x 10 imizuzwana eyi-6 . Ubude bendlela ehanjwa yinyanga = umjikelezo womjikelezo wenyanga = 2 (3.14) (r) lapho u-r = ibanga eliphakathi kwenyanga kanye nendawo yomhlaba. Ukusheshisa kweNyanga okuphakathi nendawo:
Ukusheshisa kwenyanga okuphakathi okutholwe kulesi sibalo kucishe kufane nemiphumela yokubala kwangaphambilini. Umthetho Wesibili kaNewton uthi amandla alingana nokusheshisa (F = ma). Izibalo ezingenhla zibonisa ukuthi ukusheshisa kuyafana no-1/r 2 noma ukusheshisa kuyafana ngokuphambene nesikwele sebanga (r 2 ). Ngakho-ke, kungaphethwa ngokuthi amandla adonsela phansi alingana no-1/r 2 noma amandla adonsela phansi alingana ngokuphambene nesikwele sebanga. Ngokwezibalo:
Ngaphezu kokuphenya ubudlelwano phakathi kwamandla adonsela phansi kanye nebanga phakathi kwezinto, uNewton uphinde wahlola ubudlelwano phakathi kwamandla adonsela phansi kanye nobuningi bezinto. Umthetho Wesithathu kaNewton uthi uma kukhona amandla esenzo, kukhona amandla okusabela. Amandla esenzo kanye namandla okusabela anobukhulu obufanayo kanye nesiqondiso esiphambene (isenzo se-F = -F, uphawu olubi lubonisa ukuthi isiqondiso samandla siphambene). Uma amandla adonsela phansi omhlaba edonsa isithelo, amandla adonsela phansi esithelo nawo adonsela umhlaba. Amandla adonsela phansi omhlaba asebenza esithelweni, kanti amandla adonsela phansi esithelo asebenza emhlabeni. Ngokufanayo, amandla adonsela phansi phakathi komhlaba nenyanga. Amandla adonsela phansi omhlaba kanye namandla adonsela phansi esithelo noma amandla adonsela phansi ngamandla adonsela phansi enyanga angamandla okusabela. Ngenxa yokuthi amandla alingana nobunzima (F = ma) futhi ngenxa yokuthi amandla esenzo kanye namandla okusabela anobukhulu obufanayo, amandla adonsela phansi phakathi kwezinto ezimbili kumele alingane nobunzima bezinto ezimbili. Ngokwezibalo:
Umthetho kaNewton wamandla adonsela phansi omhlaba wonke
Umthetho kaNewton wokudonsa umhlaba wonke uthi yonke into endaweni yonke iyadonselana, lapho ukukhangana phakathi kwezinto kuhambisana nobunzima bazo futhi kuhambisana ngokuphambene nesikwele sebanga lazo. Uma izinto ezimbili ezinesisindo esingu-m 1 no-m 2 zihlukaniswe ngebanga elingu-r khona-ke ubukhulu bamandla adonsela phansi phakathi kwezinto ezimbili yilokhu:
I-G = i-consistent yamandla adonsela phansi (6.673 x 10 -11 Nm 2 / kg 2 ). I-G ilinganiswa ngokuhlolwa.
F12 amandla adonsela phansi asetshenziswa ku-m1 ku-m2 kuyilapho u-F21 amandla adonsela phansi asetshenziswa ku-m2 ku-m1. F12 usebenza e-m2 futhi udonsa m2 kuya ku-m1, kuyilapho u-F21 usebenza e-m1 futhi udonsa m1 kuya ku-m2. F21 noF12 zinobukhulu obufanayo kanye nesiqondiso esiphambene. Ngakho-ke u-F21 noF12 ziyizibhangqwana zesenzo-ukusabela. r yibanga eliphakathi kwezikhungo zika-m1 kanye nesikhungo se-m2Isikhungo se-m1 itholakala maphakathi nento, njengoba kunjalo maphakathi no-m2Uma u-r eshiwo ku-km, khona-ke kuqala uguqulwa abe amamitha (iyunithi yesistimu yamazwe ngamazwe).
Inkinga yesampula 1 (amandla adonsela phansi phakathi kwezinhlayiya ezimbili)
Bala amandla adonsela phansi phakathi kwabafundi ababili, ngamunye enesisindo esingu-30 kg no-40 kg, kanye nebanga elingamamitha angu-1.
Isixazululo
Ubukhulu bamandla adonsela phansi buncane kakhulu kangangokuthi lezi zinto ezimbili azikhangi.
Inkinga yesampula 2 (amandla adonsela phansi phakathi kwezinhlayiya ezimbili)
Bala amandla adonsela phansi aphelele atholwe ngu-m2 ngenxa yamandla adonsela phansi asetshenziswa ku-m1 ku-m2 kanye namandla adonsela phansi asetshenziswa ku-m3 ku-m2Ibanga eliphakathi kwezikhungo m1 kanye no-m2 ingamamitha ama-2 kanti ibanga eliphakathi kwezikhungo m2 kanye no-m3 yi-1 m.
Isixazululo:
Amandla adonsela phansi ka-m 1 ku-m 2 :
Amandla adonsela phansi ka-m 3 ku-m 2 :
Amandla adonsela phansi aphelele atholwe yi- m2 :
Ingqikithi ye-Fg = (6.673 – 1.668) x 10 -11 N = 5.005 x 10 -11 N. Esifanekisweni esingezansi, umcibisholo we-F 32 mude kunomcibisholo we-F 12. Ngakho-ke isiqondiso samandla adonsela phansi aphelele siya ku-m 3.
Inkinga yesampula 3 (amandla adonsela phansi aphelele = u-zero):
Amabhola amabili u-A no-B, ngalinye linesisindo esingu-m kanye no-5 m. Womabili amabhola anobubanzi obufanayo. Uma amandla adonsela phansi endaweni ephakathi kwebhola u-A nebhola u-B elingana no-zero, khona-ke ibanga lalelo phuzu ukusuka ebusweni bebhola u-A lingu-...
Isixazululo:
Ububanzi bamabhola u-A no-B buyimitha eli-1, ngakho-ke irediyasi yamabhola u-A no-B ingamamitha angu-0.5. Ibanga eliphakathi kwezikhungo zamabhola u-A no-B lingamamitha ayi-6.
Sibeka inhlayiya yokuhlola enobunzima m endaweni ephakathi kwebhola A nebhola B.
F A = amandla adonsela phansi asetshenziswa ibhola A ku-particle yokuhlola (isiqondiso samandla adonsela phansi ebholeni A).
F B = amandla adonsela phansi asetshenziswa ibhola B ku-particle yokuhlola (isiqondiso samandla adonsela phansi ebholeni B).
Ngakho-ke amandla adonsela phansi atholwa yinhlayiya yokuhlola ayi-zero, khona-ke i-F A = F B (i-F A kanye ne-F B zinezindlela eziphambene).
Sebenzisa ifomula ye-quadratic ukuthola inani lika-x
Ngakho-ke x = amamitha angu-4.88
4.88 m – 0.5 m = 4.38 m. Amandla adonsela phansi ayi-zero, amamitha angu-4.38 ukusuka ebusweni bebhola A. Lingakanani ibanga ukusuka ebusweni bebhola B?
Ukulinganiswa kwe-universal gravity constant (G)
Ukuze uthole isisindo somzimba wakho, udinga nje ukuma esikalini bese ufunda isikali sesisindo somzimba wakho. Kulula ukukala isisindo somzimba wakho. Nokho, ungalinganisa kanjani isisindo somhlaba? Azikho izikali ezinkulu ezisetshenziselwa ukukala isisindo somhlaba. Uma kungekho sikali, asikwazi ukukala isisindo somhlaba sisebenzisa lezi zikali ngoba umhlaba uhlala uhamba ngaso sonke isikhathi. Ubunzima bomhlaba buyaziwa ngokubala ngemva kokuba i-universal gravitational constant (G) ilinganiswe ngokuhlolwa.
Isisindo
Isisindo sento singamandla adonsela phansi aphelele asebenza entweni ngenxa yamandla adonsela phansi asetshenziswa yizo zonke izinto endaweni yonke kuleyo nto. Uma into itholakala ngaphezu komhlaba noma ebusweni bomhlaba, khona-ke asiwanaki amandla adonsela phansi athwalwa ezinye izinto endaweni yonke. Cabanga ngesisindo sento njengamandla adonsela phansi omhlaba asebenza entweni.
w = isisindo sento, m E = isisindo somhlaba, m = isisindo sento, R E = irediyasi yomhlaba.
Uma into ingu-h ngaphezu komhlaba (izinto zingaphezu kokuphakama okuthile njengendiza, isibonelo) noma izinto ezibekwe izikhala phakathi kuka-r ngaphezu komhlaba lapho u-r = R E + h,
khona-ke amandla adonsela phansi asebenza entweni noma isisindo sento yile:
Lesi sibalo sibonisa ukuthi isisindo sento sincipha sibe yisikwele sebanga elisuka enkabeni yomhlaba. Ngakho-ke lapho siqhelelana nobuso bomhlaba, isisindo sezinto sincipha.
Ukusheshisa kwamandla adonsela phansi
Ngokusekelwe emthethweni wesibili kaNewton, siyazi ukuthi isisindo sento ngamandla abangela ukuba into ibhekane nokusheshisa kokuwa okukhululekile (ukusheshisa okudonsela phansi):
w = mg
Hlanganisa zombili izibalo w = F g kanye w = mg:
Lesi sibalo sichaza ukusheshisa kwamandla adonsela phansi okutholwa yinto ephakeme kakhulu ngaphezu komhlaba. Ngalesi sibalo, kwaziwa ukuthi ukusheshisa kwamandla adonsela phansi kwehla ngokuphakama okwandayo futhi akuxhomekile ebuningini bezinto eziwa ngokukhululeka.
Ukusheshisa amandla adonsela phansi kwezinto ezitholakala ngaphezu komhlaba noma ngaphezu komhlabathi:
Ubunzima bomhlaba bungabalwa ngokushintsha i-equation engenhla ibe yi:
Bala isisindo somhlaba usebenzisa lesi sibalo!
Izinkinga Nezixazululo
1. Izinto ezimbili m 1 kanye m 2 ngayinye enesisindo esingu-6 kg kanye no-9 kg ezihlukaniswe ngebanga elingu-5 cm. Into m 3 = 1 kg ibekwa phakathi kwalezi ezimbili. Uma amandla adonsela phansi etholakala ku-m 3 = 0 khona-ke ibanga m 3 ukusuka ku-m1 lingu …
Amandla adonsela phansi = 0 uma F 13 = F 23.
a = -1, b = -20, c = 50
Sebenzisa ifomula ye-quadratic:
Imiphumela ayikwazi ukuba negative. Ngakho-ke u-x = r 13 = ibanga m 3 kanye no-m 1 = 2.25 cm.
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2. Izinto ezimbili u-A no-B ziqhelelene ngamasentimitha angu-60. Isisindo u-A singama-24 kg kanti isisindo u-B singama-10 kg. Ikuphi indawo yephuzu elinensimu enamandla yamandla adonsela phansi elingana no-zero?
Inkambu yamandla adonsela phansi = 0 uma g A = g B.
a =7
b = -1440
c =43200
Sebenzisa ifomula ye-quadratic:
x = r A = 169.25 cm noma
x = r A = 36.46 cm
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