Izinto Zomthetho zika-Archimedes
Wake wawubona umkhumbi? Uma ungakaze uwubone mathupha, ngethemba ukuthi uwubonile kuthelevishini noma ku-inthanethi. Umkhumbi onobunzima obukhulu kakhulu awucwili, kuyilapho itshe elincane, elilula lingakwazi. Kungani kunjalo? Impendulo ilula kakhulu uma uqonda imiqondo yokuntanta kanye nesimiso sika-Archimedes.
Empilweni yansuku zonke, sizothola ukuthi izinto ezibekwe oketshezini, njengedwala, zinesisindo esincane kunalapho into ingekho oketshezini. Ungase ube nobunzima bokuphakamisa idwala ebusweni bomhlaba, kodwa idwala elifanayo liphakanyiswa kalula phansi kwechibi. Lokhu kungenxa yamandla okuntanta. Ukuqina kwenzeka ngenxa yomehluko wokucindezela koketshezi ekujuleni okuhlukene. Ukucindezela koketshezi kuyanda ngokujula, lapho uketshezi lujula, kulapho ukucindezela koketshezi kuba kukhulu. Uma into ifakwa oketshezini, kuzoba nomehluko wokucindezela phakathi koketshezi olungaphezu kwento noketshezi olungaphansi kwento. Uketshezi olutholakala phansi kwento lunokucindezela okukhulu kunoketshezi olutholakala phezulu kwento.
Ukuqina
Esithombeni, into ibonakala intanta emanzini. Uketshezi olungaphansi kwento lunomfutho omkhulu kunoketshezi olungaphezu kwento. Lokhu kungenxa yokuthi uketshezi olungaphansi kwento lunobunzulu obukhulu kunoketshezi olungaphezu kwento (h2 > h1).
F 2 = amandla asetshenziswa uketshezi olungaphansi kwento, F 1 = amandla asetshenziswa uketshezi oluphezulu kwento, A = indawo engaphezulu kwento
Umehluko phakathi kuka-F2 no -F1 amandla aphelele asetshenziswa uketshezi entweni, esiyazi ngokuthi amandla okubutha. Ubukhulu bamandla okubutha yilokhu:
F ukuthamba = F 2 − F 1
F buoyant = (ρ gh 2 A ) − (ρ gh 1 A)
F iflothi = ρ g A ( h 2 − h 1 )
ukubutha kuka-F = ρ g A h
ukubutha kwe-F = ρ g V
Imininingwane:
ρ = ukuminyana koketshezi
g = ukusheshisa ngenxa yamandla adonsela phansi
V = ivolumu yento eketshezini
ukuze isibalo esisho ubukhulu bamandla okugobhoza (u-F ogobhoza) ngenhla singabhalwa kanje:
F float = ρ F g V → m = ρ V
ukubutha kwe-F = m F g
ukubutha kwe-F = w F
m F g = w F = isisindo soketshezi olunomthamo ofanayo nomthamo wento ecwiliswe emanzini.
Isibonelo samandla okuphaphazela
Isimiso sika-Archimedes
Ngokusekelwe kulesi sibalo esingenhla, singasho ukuthi amandla okubutha alingana nesisindo soketshezi olususiwe, umthamo woketshezi olususiwe ulingana nomthamo wento ecwiliswe oketshezini.
Uma into icwiliswa oketshezini bese intanta, ingxenye kuphela yento icwiliswe emanzini, khona-ke umthamo woketshezi olususiwe ulingana nomthamo wengxenye yento ecwiliswe oketshezini. Kungakhathaliseki ukuma noma usayizi wento, into efanayo izokwenzeka kubo bonke. Lona umsebenzi ka-Archimedes (287-212 BC), manje owaziwa ngokuthi yi-Archimedes' Principle.
Isimiso sika-Archimedes sithi:
Uma into icwiliswe ngokuphelele noma ngokwengxenye oketshezini, uketshezi luzosebenzisa amandla aphezulu (amandla avuselelayo) entweni, lapho ubukhulu bamandla aphezulu (amandla avuselelayo) bulingana nesisindo soketshezi olususiwe.
Indaba ka-Archimedes
U-Archimedes, owaphila phakathi kuka-287 no-212 BC, wathunywa yiNkosi uHieron II ukuthi ahlole ukuthi umqhele owenzelwe inkosi wawenziwe ngegolide elicwengekileyo. Ekuqaleni u-Archimedes wayedidekile ngokuthi umqhele wawenziwe ngegolide elicwengekileyo noma ukuthi wawunezinye izinsimbi. Inkinga kwakuwukuthi umqhele wawungajwayelekile ngesimo futhi wawungenakubhujiswa ukuze kutholakale ukuthi wawuyigolide elicwengekileyo.
Umqondo ongemuva kokunquma ukuthi umqhele wenkosi wenziwe ngegolide elicwengekileyo yini ukuqala ngokunquma amandla adonsela phansi athile omqhele bese uwuqhathanisa namandla adonsela phansi athile egolide. Uma umqhele wenziwe ngegolide elicwengekileyo, khona-ke amandla adonsela phansi athile omqhele = amandla adonsela phansi athile egolide.
Ubukhulu besisindo sento ethile buyisilinganiso sesisindo sento esemoyeni nesisindo samanzi anomthamo ofanayo nento. Ngokwezibalo, kulotshiwe:
Ungasinquma kanjani isisindo samanzi esinomthamo ofanayo nomthamo wento?
Ngokusho kuka-Archimedes, isisindo samanzi esinomthamo ofanayo nomthamo wento = ubukhulu bamandla agelezayo lapho into ishona (yonke into icwiliswa emanzini). Lokhu kufana nesisindo sento elahlekile lapho ilinganiswa emanzini. Ngakho-ke:
Ukuze kutholakale amandla adonsela phansi athile omqhele, umqhele uqala ulinganiswa emoyeni (Isisindo somqhele emoyeni). Okulandelayo, umqhele ufakwa emanzini bese ulinganiswa futhi ukuze kutholakale isisindo somqhele olahlekile. Ngakho-ke:
Uma sekutholakale amandla adonsela phansi athile omqhele, aqhathaniswa namandla adonsela phansi athile egolide. Amandla adonsela phansi athile egolide angu-19,3. Uma amandla adonsela phansi athile omqhele elingana namandla adonsela phansi athile egolide, khona-ke umqhele wenziwe ngegolide elihlanzekile. Kodwa-ke, uma umqhele ungenziwanga ngegolide elihlanzekile, amandla adonsela phansi athile omqhele ngeke afane namandla adonsela phansi athile egolide.
Kungani Imikhumbi Ingacwili?
Uma ubukhulu bento buncane kunobukhulu bamanzi, khona-ke into izontanta. Ngokuphambene nalokho, uma ubukhulu bento bukhulu kunobukhulu bamanzi, khona-ke into izocwila. Imikhumbi eminingi yenziwe ngensimbi nensimbi. Ubukhulu bensimbi nensimbi = 7,8 x 103 kg /m3 kuyilapho ubukhulu bamanzi = 1,00 x 103 kg /m3 . Kubonakala sengathi ubukhulu bensimbi nensimbi bukhulu kunobukhulu bamanzi. Kulokhu, amandla adonsela phansi ensimbi nensimbi = 7,8. Imikhumbi eyenziwe ngensimbi nensimbi kufanele icwile. Kungani imikhumbi ingacwili? Ubuningi bemikhumbi buncane kunobukhulu bamanzi noma bamanzi olwandle.
Imibuzo eyisibonelo ngomthetho ka-Archimedes
Isibonelo sombuzo 1:
Idwala elingamakhilogremu angu-40 liphansi kwechibi. Uma umthamo wedwala = 0,2 m 3, yimaphi amandla amancane adingekayo ukuze kuphakanyiswe idwala?
Ingxoxo
Kuyaziwa ukuthi:
Isisindo setshe (m) = 40 kg
Umthamo wetshe (V) = 0,02 m 3
Ubuningi bamanzi = 1000 Kg/ m3
Ukusheshisa ngenxa yamandla adonsela phansi (g) = 10 m/s 2
Kubuziwe: Okungenani okungu-F
Impendulo:
ukubuthana kuka-F = w F
ukubutha kwe-F = m F g → m = pV
ukubutha kwe-F = ρ F g V
Ukuthamba kwe-F = (1000 kg/m 3 )(10 m/s 2 )(0,02 m 3 )
Ukuthamba kwe-F = 200 kg m/s 2
Ukuntanta kwe-F = 200 N
Isisindo setshe (w) = mg
Isisindo setshe = (40 kg)(10 m/s 2 )
Isisindo setshe = 400 kg m/s 2
Isisindo setshe = 400 N
Amandla amancane adingekayo ukuze kuphakanyiswe idwala:
Isisindo setshe – Amandla okuqina = 400 N – 200 N = 200 Newton.
Isibonelo sombuzo 2:
Isisindo sento esemoyeni = 5000 kg m/s 2 kanye nesisindo sento esemanzini = 4000 kg m/s 2 . Uma ubukhulu bento = 2000 kg/m 3 , buyini ubunzima kanye nomthamo wento? g = 10 m/s 2
Ingxoxo
Ukusheshisa ngenxa yamandla adonsela phansi (g) = 10 m/s 2
Ubuningi bento = 2000 kg/ m3
Ubuningi bamanzi = 1000 kg/ m3
Isisindo sento esemoyeni = 5000 kg m/s 2
Isisindo sento emanzini = 4000 kg m/s 2
Amandla okuqina (F aqina) = Isisindo sento esemoyeni – Isisindo sento esemanzini
Ukuthamba kwe-F = 5000 kg m/s 2 – 4000 kg m/s 2
Ukuthamba kwe-F = 1000 kg m/s 2
F ukubutha = Isisindo samanzi asusiwe
F ukuthamba = (isisindo samanzi)(g)
F ukuthamba = (umthamo wamanzi osusiwe)(ubuningi bamanzi)(g)
Umthamo wamanzi osusiwe = Umthamo wento ecwiliswe emanzini 😉
Ngakho-ke ivolumu yento = 0,1 m 3
Isisindo sento = ?
ρ = m / V
m = ρ V
m = ( 2000 kg / m 3 )( 0,1 m 3 )
m = 200 kg
Isisindo sento = 200 kg
Isibonelo sombuzo 3:
Yimuphi umthamo we-helium odingekayo uma ibhaluni kufanele liphakamise umthwalo ongama-500 kg?
Ingxoxo
Ubuningi be-Helium = 0,1786 kg/ m3
Ubuningi bomoya = 1,293 kg/ m3
Amandla amakhulu = Isisindo somoya osusiwe = Isisindo somthwalo + Isisindo se-helium
Amandla amakhulu = Isisindo somthwalo + isisindo se-helium
Amandla okuqina = (isisindo somthwalo)(g) + (isisindo se-helium)(g)
Amandla okuqina = (isisindo somthwalo + isisindo se-helium)g —- isibalo 1
Amandla okuqina = Isisindo somoya osusiwe
Amandla okuqina = (isisindo somoya osusiwe)(g) —- isibalo 2
Sihlanganisa i-equation 1 kanye ne-equation 2:
(isisindo somthwalo + isisindo se-helium)(g) = (isisindo somoya osusiwe)(g)
isisindo somthwalo + isisindo se-helium = isisindo somoya osusiwe
500 kg + (ρ helium)(V helium) = (ρ umoya)(V umoya)
500 kg = (umoya we-ρ)(umoya we-V) – (ρ i-helium)(i-V i-helium)
Umthamo womoya osusiwe (umoya we-V) = Umthamo we-helium ogcwalisa ibhaluni (i-helium ye-V)
500 kg = (ρ air – ρ helium)(V)
Lona umthamo omncane we-helium odingekayo ukuze kuphakanyiswe isisindo ebusweni boMhlaba. Ukuze ibhaluni likwazi ukuntanta phezulu, umthamo we-helium udinga ukwanda. Lokhu kungenxa yokuthi ubuningi bomoya buyancipha lapho kuphakama.
