Litaba tsa Molao tsa Archimedes
Na o kile wa bona sekepe? Haeba o so ka o se bona ka seqo, re tshepa hore o se bone thelevisheneng kapa inthaneteng. Sekepe se nang le boima bo boholo ha se teba, athe lefika le lenyenyane, le bobebe le ka teba. Hobaneng ho le jwalo? Karabo e bonolo haholo haeba o utlwisisa mehopolo ya ho phaphamala le molaomotheo wa Archimedes.
Bophelong ba letsatsi le letsatsi, re tla fumana hore lintho tse behiloeng ka har'a mokelikeli, joalo ka lefika, li na le boima bo fokolang ho feta ha ntho e se ka har'a mokelikeli. U ka 'na ua thatafalloa ke ho phahamisa lefika holim'a lefatše, empa lefika le tšoanang le phahamisoa habonolo ho tloha tlase ho letamo. Sena se bakoa ke matla a ho phaphamala. Ho phaphamala ho etsahala ka lebaka la phapang ea khatello ea mokelikeli botebong bo fapaneng. Khatello ea mokelikeli e eketseha ka botebo, ha mokelikeli o teba, khatello ea mokelikeli e ba kholoanyane. Ha ntho e kenngoa ka har'a mokelikeli, ho tla ba le phapang ea khatello pakeng tsa mokelikeli o ka holimo ho ntho le mokelikeli o ka tlase ho ntho. Mokelikeli o ka tlase ho ntho o na le khatello e kholo ho feta mokelikeli o ka holimo ho ntho.
Boikhohomoso
Setšoantšong, ntho e bonoa e phaphametse ka metsing. Mokelikeli o ka tlase ho ntho o na le khatello e kholo ho feta mokelikeli o ka holimo ho ntho. Lebaka ke hobane mokelikeli o ka tlase ho ntho o na le botebo bo boholo ho feta mokelikeli o ka holimo ho ntho (h2 > h1).
F 2 = matla a sebelisoang ke mokelikeli o ka tlase ho ntho, F 1 = matla a sebelisoang ke mokelikeli o ka holimo ho ntho, A = sebaka sa bokaholimo ba ntho
Phapang pakeng tsa F 2 le F 1 ke matla ohle a sebelisoang ke mokelikeli nthong eo, eo re e tsebang e le matla a ho phaphamala. Boholo ba matla a ho phaphamala ke:
F ho phaphamala = F 2 − F 1
F buoyant = (ρ gh 2 A ) − (ρ gh 1 A)
F float = ρ g A ( h 2 − h 1 )
F ho phaphamala = ρ g A h
F ho phaphamala = ρ g V
Lintlha :
ρ = bongata ba mokelikeli
g = ho potlaka ka lebaka la matla a khoheli
V = bophahamo ba ntho e ka hara mokelikeli
e le hore equation e bolelang boholo ba matla a ho phaphamala (F ho phaphamala) ka holimo e ka ngolwa tjena:
F phaphamala = ρ F g V → m = ρ V
F ho phaphamala = m F g
F ho phaphamala = w F
m F g = w F = boima ba mokelikeli o nang le bophahamo bo lekanang le ba ntho e qoelitsoeng.
Mohlala oa matla a ho phaphamala
Molao-motheo oa Archimedes
Ho latela equation e ka hodimo, re ka re matla a ho phaphamala a lekana le boima ba mokelikeli o falliseditsweng, bophahamo ba mokelikeli o falliseditsweng bo lekana le bophahamo ba ntho e qoelitsoeng mokelikeling.
Haeba ntho e qoelisoa ka har'a mokelikeli 'me e phaphamala, karolo e le 'ngoe feela ea ntho e qoelisoa, joale bophahamo ba mokelikeli o fallisitsoeng bo lekana le bophahamo ba karolo ea ntho e qoelitsoeng ka har'a mokelikeli. Ho sa tsotelehe sebōpeho kapa boholo ba ntho, ntho e tšoanang e tla etsahala ho bohle. Ena ke mosebetsi oa Archimedes (287-212 BC), eo hona joale e tsejoang e le Molao-motheo oa Archimedes.
Molao-motheo oa Archimedes o re:
Ha ntho e qoelisoa ka botlalo kapa ka karolo e itseng ka har'a mokelikeli, mokelikeli o tla sebelisa matla a holimo (matla a ho phaphamala) holim'a ntho eo, moo boholo ba matla a holimo (matla a ho phaphamala) bo lekanang le boima ba mokelikeli o tlositsoeng.
Pale ea Archimedes
Archimedes, ea phetseng pakeng tsa 287 le 212 BC, o ile a laeloa ke Morena Hieron II ho batlisisa hore na moqhaka o etselitsoeng morena o entsoe ka khauta e hloekileng. Qalong Archimedes o ne a ferekane mabapi le hore na moqhaka o entsoe ka khauta e hloekileng kapa hore na o na le litšepe tse ling. Bothata e ne e le hore moqhaka o ne o sa tsitsa 'me o ne o ke ke oa senngoa ho fumana hore na ke khauta e hloekileng.
Khopolo e ka morao ho ho fumana hore na moqhaka oa morena o entsoe ka khauta e hloekileng ke ho qala ka ho fumana hore na boima ba moqhaka bo itseng ke bofe ebe o bo bapisa le boima ba khauta bo itseng. Haeba moqhaka o entsoe ka khauta e hloekileng, joale boima ba moqhaka bo itseng ke boima ba khauta bo itseng.
Boima ba ntho bo itseng ke karolelano ya boima ba ntho e moyeng le boima ba metsi ka bophahamo bo tshwanang le ba ntho eo. Ho ya ka dipalo, ho ngotswe:
Mokhoa oa ho fumana boima ba metsi a nang le bophahamo bo lekanang le bophahamo ba ntho?
Ho ya ka Archimedes, boima ba metsi a nang le bophahamo bo lekanang le bophahamo ba ntho = boholo ba matla a ho phaphamala ha ntho e teba (ntho yohle e qoelisoa ka metsing). Sena se tshwana le boima ba ntho e lahlehileng ha e lekanngwa ka metsing. Ka hona:
Ho fumana boima bo itseng ba moqhaka, moqhaka o bewa pele moeeng (Boima ba Moqhaka Moyeng). Ka mor'a moo, moqhaka o kenngoa ka metsing ebe o bewa hape ho fumana boima ba moqhaka o lahlehileng. Kahoo:
Hang ha matla a khoheli a moqhaka a fumanoe, joale a bapisoa le matla a khoheli a itseng a khauta. Matla a khoheli a itseng a khauta ke 19,3. Haeba matla a khoheli a itseng a moqhaka a lekana le matla a khoheli a itseng a khauta, joale moqhaka o entsoe ka khauta e hloekileng. Leha ho le joalo, haeba moqhaka o sa etsoa ka khauta e hloekileng, joale matla a khoheli a itseng a moqhaka a ke ke a tšoana le matla a khoheli a itseng a khauta.
Ke Hobane'ng ha Likepe li sa Tebe?
Haeba boima ba ntho bo le bonyenyane ho feta boima ba metsi, ntho eo e tla phaphamala. Ka lehlakoreng le leng, haeba boima ba ntho bo le boholo ho feta boima ba metsi, ntho eo e tla teba. Likepe tse ngata li entsoe ka tšepe le tšepe. Boima ba tšepe le tšepe = 7,8 x 103 kg /m3 ha boima ba metsi = 1,00 x 103 kg /m3 . Ho bonahala eka boima ba tšepe le tšepe bo boholo ho feta boima ba metsi. Tabeng ena, matla a khoheli a itseng a tšepe le tšepe = 7,8. Likepe tse entsoeng ka tšepe le tšepe li lokela ho teba. Hobaneng likepe li sa tebe? Boima bohle ba sekepe bo bonyenyane ho feta boima ba metsi kapa metsi a leoatle.
Mehlala ea lipotso mabapi le molao oa Archimedes
Mohlala oa potso ea 1:
Lefika la boima ba 40 kg le ka tlase ho letamo. Haeba bophahamo ba lefika = 0,2 m 3, matla a bonyane a hlokahalang ho phahamisa lefika ke afe?
Puisano
Hoa tsebahala hore:
Boima ba lejoe (m) = 40 Kg
Bophahamo ba lejoe (V) = 0,02 m 3
Boima ba metsi = 1000 Kg/ m3
Ho potlaka ka lebaka la matla a khoheli (g) = 10 m/s 2
E botsitsoe: bonyane F
Karabo:
F ho phaphamala = w F
F ho phaphamala = m F g → m = pV
F ho phaphamala = ρ F g V
F ho phaphamala ha metsi = (1000 kg/m3 ) (10 m/s 2 )(0,02 m3 )
Ho phaphamala ha F = 200 kg m/s 2
Ho phaphamala ha F = 200 N
Boima ba lejoe (w) = mg
Boima ba lejwe = (40 kg)(10 m/s 2 )
Boima ba lejoe = 400 kg m/s 2
Boima ba lejoe = 400 N
Matla a fokolang a hlokahalang ho phahamisa lefika:
Boima ba lejwe – Matla a ho tjhesa = 400 N – 200 N = 200 Newton.
Mohlala oa potso ea 2:
Boima ba ntho e moeeng = 5000 kg m/s 2 le boima ba ntho e metsing = 4000 kg m/s 2 . Haeba boima ba ntho e le = 2000 kg/m 3 , boima le bophahamo ba ntho ke bokae? g = 10 m/s 2
Puisano
Ho potlaka ka lebaka la matla a khoheli (g) = 10 m/s 2
Boima ba ntho = 2000 kg/ m3
Boima ba metsi = 1000 kg/ m3
Boima ba ntho e moeeng = 5000 kg m/s 2
Boima ba ntho ka metsing = 4000 kg m/s 2
Matla a ho phaphamala (F a ho phaphamala) = Boima ba ntho e moeeng – Boima ba ntho e ka metsing
F ho phaphamala = 5000 kg m/s 2 – 4000 kg m/s 2
Ho phaphamala ha F = 1000 kg m/s 2
F ho phaphamala = Boima ba metsi a tlositsoeng
F ho phaphamala = (boima ba metsi)(g)
F ho phaphamala = (bophahamo ba metsi bo tlositsweng)(bongata ba metsi)(g)
Bongata ba metsi a tlositsoeng = Bongata ba ntho e qoelitsoeng ka metsing 😉
Kahoo bophahamo ba ntho = 0,1 m 3
Boima ba ntho = ?
ρ = m / V
m = ρ V
m = ( 2000 kg / m 3 )( 0,1 m 3 )
m = 200 Kg
Boima ba ntho = 200 kg
Mohlala oa potso ea 3:
Ke bophahamo bofe ba helium bo hlokahalang haeba balune e tlameha ho phahamisa mojaro oa 500 kg?
Puisano
Boima ba Heliamo = 0,1786 kg/ m3
Boima ba moea = 1,293 kg/ m3
Matla a matla = Boima ba moea o fallang = Boima ba mojaro + Boima ba helium
Matla a matla = Boima ba mojaro + boima ba helium
Matla a ho phaphamala = (boima ba mojaro)(g) + (boima ba helium)(g)
Matla a ho phaphamala = (boima ba mojaro + boima ba helium) g —- equation 1
Matla a ho phaphamala = Boima ba moea o fallang
Matla a ho phaphamala = (boima ba moya o fallang)(g) —- equation 2
Re kopanya equation 1 le equation 2:
(boima ba mojaro + boima ba helium)(g) = (boima ba moya o fallang)(g)
boima ba mojaro + boima ba helium = boima ba moea o fallang
500 kg + (ρ helium)(V helium) = (ρ moea)(V moea)
500 kg = (ρ moea)(V moea) – (ρ helium)(V helium)
Bophahamo ba moea o fallang (moea oa V) = Bophahamo ba helium bo tlatsang balune (V helium)
500 kg = (ρ moya – ρ helium)(V)
Ena ke bophahamo ba bonyane ba helium bo hlokahalang ho phahamisa boima holim'a Lefatše. Ho lumella balune ho phaphamala hodimo, bophahamo ba helium bo hloka ho eketsoa. Lebaka ke hobane bongata ba moya bo fokotseha ha bophahamo bo ntse bo eketseha.
