Isihloko mayelana nesimiso sika-Archimedes
Umkhumbi onobunzima obukhulu awucwili, kanti itshe elincane lingacwili. Kungani kunjalo? Impendulo iqondile uma uqonda umqondo wokuntanta kanye nesimiso sika-Archimedes.
Empilweni yansuku zonke, sizothola ukuthi izinto ezifakwa oketshezini, njengedwala, zinesisindo esincane kunalapho izinto zingekho oketshezini. Ungase ukuthole kunzima ukuphakamisa itshe phansi, kodwa itshe elifanayo liphakanyiswa kalula lisuka phansi emanzini olwandle. Lokhu kungenxa yamandla okugeleza. Ukuqina kwenzeka ngenxa yokwehluka kokucindezela koketshezi ekujuleni okuhlukene. Ukucindezela koketshezi kuyanda ngokujula, lapho uketshezi lujiya, kulapho ukucindezela koketshezi kuba kukhulu. Lapho into ifakwa oketshezini, kuzoba nokwehluka kokucindezela phakathi koketshezi oluphezulu lwento noketshezi oluphansi lwento. Uketshezi olutholakala phansi kwento lunokucindezela okuphezulu kunoketshezi oluphezulu lwento.
Kulesi sithombe, ungabona into intanta emanzini. Uketshezi olungaphansi kwento lunomfutho ophezulu kunoketshezi olutholakala phezulu kwento. Lokhu kungenxa yokuthi uketshezi olungaphansi kwento lunokujula okuphawulekayo kunoketshezi olungaphezu kwento (p2 > h1).
Inani lokucindezela koketshezi ekujuleni kwe-h2 yilokhu :
Inani lokucindezela koketshezi ekujuleni kwe-h1 yilokhu :
F 2 = amandla asetshenziswa uketshezi oluphansi kwento, F 1 = amandla asetshenziswa uketshezi oluphezulu kwento, A = indawo engaphezulu kwento
Umehluko phakathi kuka-F2 no -F1 amandla aphelele anikezwa uketshezi olusentweni, esiwazi ngokuthi amandla okubutha. Inani lokubutha yileli:
F ukuthamba = F 2 − F 1
F buoyancy = (ρ gh 2 A) − (ρ gh 1 A)
I-F buoyancy = ρ g A (h 2 − h 1 )
F ukubutha = ρ F g A h
ukubutha kwe- F = ρ F g V
ρ F = ubuningi boketshezi, g = ukusheshisa kwamandla adonsela phansi, V = ivolumu yezinto ezikuketshezi
Ngakho-ke, singabhala isibalo esichaza inani lokuhambahamba (i-F buoyancy) ngenhla:
F buoyancy = 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 ecwilisiwe.
Ngokusekelwe kulesi sibalo esingenhla, singasho ukuthi amandla okubutha alingana nesisindo soketshezi olususwayo, umthamo woketshezi olususwayo ufana nomthamo wento ecwiliswe oketshezini.
Uma into ifakwa oketshezini, intanta, lapho ingxenye yento efakiwe iyingxenye nje,
bese kuba umthamo woketshezi olususwayo = umthamo wengxenye yento ecwiliswe oketshezini. Kungakhathaliseki ukuthi into iyini nokuthi injani, wonke umuntu uzobhekana nento efanayo. Lona umphumela womsebenzi ka-Archimedes (287-212 BC), owaziwa ngokuthi yi-Archimedes' Principle.
Isimiso sika-Archimedes sithi:
Uma into icwiliswe ngokuphelele noma kancane oketshezini, uketshezi luzonikeza into amandla aphezulu (amandla avuselelayo), lapho inani lamandla aphezulu (amandla avuselelayo) lilingana nesisindo soketshezi olususwayo.
Indaba ka-Archimedes
U-Archimedes, owaphila phakathi kuka-287-212 BC, wathunywa yiNkosi uHieron II ukuthi ahlole ukuthi umqhele owenzelwe iNkosi wawenziwe ngegolide elicwengekileyo noma cha. Ukuze athole ukuthi umqhele wenziwe ngegolide elicwengekileyo noma umqhele uqukethe ezinye izinsimbi, u-Archimedes waqale wadideka. Inkinga iwukuthi, ukuma komqhele akujwayelekile futhi akunakubhujiswa kuqala ukuze kutholakale ukuthi umqhele wenziwe ngegolide elicwengekileyo noma cha.
Umqondo wokunquma ukuthi umqhele wenziwe ngegolide elicwengekileyo noma cha ukuqala ngokunquma isisindo somqhele bese usiqhathanisa nobukhulu begolide obuthile. Uma umqhele wenziwe ngegolide elicwengekileyo, khona-ke ubukhulu begolide obuthile = ubukhulu begolide obuthile.
Ubukhulu besisindo sento ethile buyisilinganiso esiphakathi kwesisindo sento esemoyeni kanye nesisindo samanzi esinomthamo ofanayo nomthamo wezinto. Kubhalwe ngokwezibalo:
Ungasinquma kanjani isisindo samanzi esinomthamo ofanayo nomthamo wezinto?
Ngokusho kuka-Archimedes, isisindo samanzi esinomthamo ofanayo nomthamo wento = inani lamandla okuntanta lapho into ishona (ingxenye yonke yento ifakwa emanzini). Lokhu kufana nesisindo sezinto ezilahlekile lapho zilinganiswa emanzini. Ngakho-ke:
Ukuze kutholakale ukuthi umqhele unamandla kangakanani, umqhele uqala ulinganiswa emoyeni (isisindo somqhele emoyeni). Bese umqhele ufakwa emanzini bese ulinganiswa futhi ukuze kutholakale isisindo esilahlekile somqhele. Ngakho-ke:
Ngemva kokuthola amandla adonsela phansi athile omqhele, khona-ke kuqhathaniswa namandla adonsela phansi athile egolide. Amandla adonsela phansi athile egolide = 19.3. Uma amandla adonsela phansi athile omqhele = amandla adonsela phansi athile egolide, umqhele wenziwe ngegolide elihlanzekile. Kodwa uma umqhele ungenziwanga ngegolide elihlanzekile, khona-ke amandla adonsela phansi athile omqhele awafani namandla adonsela phansi athile egolide.
Kungani umkhumbi ungacwili?
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. Ubuningi bensimbi nensimbi = 7.8 x 10 3 kg/m 3 kuyilapho ubukhulu bamanzi = 1.00 x 10 3 kg/m 3 . Kubonakala sengathi ubukhulu bensimbi nensimbi bukhulu kunobukhulu bamanzi. Kulokhu, amandla adonsela phansi athile ensimbi nensimbi = 7.8. Umkhumbi kufanele ube yisinki. Kungani umkhumbi ungacwili? Ubuningi bemikhumbi buncane kunobuningi bamanzi noma bamanzi olwandle.
Inkinga yesibonelo 1:
Itshe elinobunzima obungama-40 kg liphansi echibini. Uma ubukhulu betshe = 0.2 m3, yimaphi amandla amancane adingekayo ukuze kuphakanyiswe itshe?
Kwaziwa:
Isisindo setshe (m) = 40 kg
Umthamo wetshe (V) = 0.02 m 3
Ubuningi bamanzi = 1000 kg/ m3
Ukusheshisa kwamandla adonsela phansi (g) = 10 m/s 2
Kufunwa: Okungenani okungu-F
Isixazululo:
ukubutha kwe- 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 ukuphakamisa itshe :
isisindo setshe – amandla okuntanta = 400 N – 200 N = 200 N
Inkinga yesibonelo 2:
Isisindo sento emanzini = 5000 kg m/s 2 kanye nesisindo sento emanzini = 4000 kg m/s 2 . Uma ubukhulu bento = 2000 kg/m 3 , buyini ubunzima kanye nomthamo wento? g = 10 m/s 2
Isixazululo
Ukusheshisa kwamandla 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 ukugoba) = isisindo sento emoyeni – isisindo sento emanzini
Ukuthamba kwe-F = 5000 kg m/s 2 – 4000 kg m/s 2
Ukuthamba kwe-F = 1000 kg m/s 2
F ukubuthana = isisindo samanzi asusiwe
F ukuthamba = (isisindo samanzi)(g)
F ukuthamba = (umthamo wamanzi osusiwe)(ubuningi bamanzi)(g)
Umthamo wamanzi osusiwe = umthamo wento emanzini
Umthamo wento = 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
Inkinga yesibonelo 3:
Yimuphi umthamo we-helium odingekayo uma ibhaluni kufanele liphakamise umthwalo ongama-500 kg?
Isixazululo:
Ubuningi be-helium = 0.1786 kg/ m3
Ubuningi bomoya = 1.293 kg/ m3
Amandla okuqina = isisindo somoya osusiwe = isisindo sento + isisindo se-helium
Amandla okuqina = isisindo sento + 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 esisusiwe
Amandla okuqina = (isisindo somoya esisusiwe)(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 amanzi)(V amanzi)
500 kg = (ρ amanzi) (V amanzi) – (ρ helium) (V helium)
Umthamo womoya ohambile (umoya we-V) = Umthamo we-helium ebhaluni (i-helium ye-V)
500 kg = (ρ amanzi – ρ helium)(V)
Lona umthamo omncane we-helium odingekayo ukuphakamisa izinsimbi ebusweni bomhlaba. Ukuze ibhaluni lintante phezulu, umthamo we-helium udinga ukwengezwa. Umthamo we-helium kufanele wande ngoba ubuningi bomoya buyancipha ngokuphakama.
