Sengoloa se buang ka molao-motheo oa Archimedes
Sekepe se nang le boima bo boholo ha se tebe, athe lejoe le lenyenyane le ka tebeha. Hobaneng ho le jwalo? Karabo e otlolohile haeba o utlwisisa mohopolo wa ho phaphamala le molao-motheo wa Archimedes.
Bophelong ba letsatsi le letsatsi, re tla fumana hore lintho tse kenngoang ka har'a mokelikeli, joalo ka lefika, li na le boima bo bonyenyane ho feta ha lintho li se ka har'a mokelikeli. U ka 'na ua thatafalloa ho phahamisa lejoe fatše, empa lejoe le tšoanang le phahamisoa habonolo ho tloha tlase metsing a leoatle. Sena se bakoa ke matla a ho phaphamala. Ho phaphamala ho etsahala ka lebaka la phapang khatellong ea mokelikeli botebong bo fapaneng. Khatello ea mokelikeli e eketseha ka botebo, ha mokelikeli o le motenya, khatello ea mokelikeli e ba kholo. Ha ntho e kenngoa ka har'a mokelikeli, ho tla ba le phapang khatellong 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 phahameng ho feta mokelikeli o ka holimo ho ntho.
Setšoantšong, o ka bona ntho e phaphametseng ka metsing. Mokelikeli o ka tlase ho ntho o na le khatello e phahameng ho feta mokelikeli o ka holimo ho ntho. Lebaka ke hobane mokelikeli o ka tlas'a ntho o na le botebo bo boholo ho feta mokelikeli o ka holimo ho ntho (p2 > h1).
Bongata ba kgatello ya mokelikeli botebong ba h 2 ke:
Bongata ba kgatello ya mokelikeli botebong ba h 1 ke:
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 fanoang ke mokelikeli nthong, eo re e tsebang e le matla a ho phaphamala. Palo ea ho phaphamala ke:
F ho phaphamala = F 2 − F 1
F buoyancy = (ρ gh 2 A) − (ρ gh 1 A)
F buoyancy = ρ g A (h 2 − h 1 )
F ho phaphamala = ρ F g A h
F ho phaphamala = ρ F g V
ρ F = bongata ba mokelikeli, g = ho potlaka ha matla a khoheli, V = bophahamo ba lintho tse ka har'a mokelikeli
Kahoo, re ka ngola equation e bolelang bongata ba ho phaphamala (F ho phaphamala) ka holimo:
F buoyancy = 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 bophahamo ba ntho e qoelitsoeng.
Ho latela equation e ka hodimo, re ka re matla a ho phaphamala a lekana le boima ba mokelikeli o ntseng o falla, bophahamo ba mokelikeli o fallang bo tshwana le bophahamo ba ntho e qoelitsoeng mokelikeling.
Haeba ntho e kentswe ka hara mokelikeli, e phaphametse, moo karolo ya ntho e kentsweng e leng karolo feela,
ebe bophahamo ba mokelikeli o suthiswang = bophahamo ba karolo ya ntho e qoelitsoeng mokelikeling. Ho sa tsotelehe hore na ntho eo ke efe le hore na e na le sebopeho sefe, bohle ba tla ba le phihlelo e tshwanang. Ena ke sephetho sa mosebetsi sa Archimedes (287-212 BC), ya tsejwang e le Molaotheo wa Archimedes.
Molao-motheo oa Archimedes o re:
Ha ntho e qoelisoa ka botlalo kapa ka karolo e itseng ka hara mokelikeli, mokelikeli o tla fa ntho eo matla a nyolohang (matla a phallang), moo matla a nyolohang (matla a phallang) a lekanang le boima ba mokelikeli o ntseng o tloswa.
Pale ea Archimedes
Archimedes, ea phetseng pakeng tsa 287-212 BC, o ile a laeloa ke Morena Hieron II ho batlisisa hore na moqhaka o etselitsoeng Morena o entsoe ka khauta e hloekileng kapa che. Ho fumana hore na moqhaka o entsoe ka khauta e hloekileng kapa moqhaka o na le litšepe tse ling, Archimedes o ile a ferekane qalong. Bothata ke hore, sebopeho sa moqhaka ha sea tloaeleha 'me se ke ke sa senngoa pele e le hore ho ka fumanoa hore na moqhaka o entsoe ka khauta e hloekileng kapa che.
Khopolo ea ho fumana hore na moqhaka o entsoe ka khauta e hloekileng kapa che ke ho qala ka ho fumana boima ba moqhaka ebe o o bapisa le matla a khoheli a itseng a khauta. Haeba moqhaka o entsoe ka khauta e hloekileng, joale matla a khoheli a itseng a moqhaka = matla a khoheli a itseng a khauta.
Matla a khoheli a itseng a ntho ke karolelano pakeng tsa boima ba ntho e moeeng le boima ba metsi bo nang le bophahamo bo lekanang le bophahamo ba lintho. E ngotsoe ka lipalo:
Mokhoa oa ho fumana boima ba metsi a nang le bophahamo bo lekanang le bophahamo ba lintho joang?
Ho ya ka Archimedes, boima ba metsi bo nang le bophahamo bo lekanang le bophahamo ba ntho = bongata ba matla a ho phaphamala ha ntho e teba (karolo yohle ya ntho e qoelisoa ka metsing). Sena se tshwana le boima ba dintho tse lahlehang ha di lekanngwa ka metsing. Ka hona:
Ho fumana boima bo itseng ba moqhaka, moqhaka o bewa pele moeeng (boima ba moqhaka moeeng). Ebe moqhaka o kenngwa ka metsing ebe o bewa hape ho fumana Boima bo Lahlehileng ba Moqhaka. Kahoo:
Kamora hore matla a khoheli a itseng a moqhaka a fumanoe, joale a bapisoa le matla a khoheli a itseng a khauta. Matla a khoheli a itseng a khauta = 19.3. Haeba matla a khoheli a itseng a moqhaka = matla a khoheli a itseng a khauta, moqhaka o entsoe ka khauta e hloekileng. Empa haeba moqhaka o sa etsoa ka khauta e hloekileng, joale matla a khoheli a itseng a moqhaka ha a tšoane le matla a khoheli a itseng a khauta.
Ke hobane'ng ha sekepe se sa teba?
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 10 3 kg/m 3 ha boima ba metsi = 1.00 x 10 3 kg/m 3 . Ho bonahala boima ba tšepe le tšepe bo le boholo ho feta boima ba metsi. Tabeng ena, matla a khoheli a itseng a tšepe le tšepe = 7.8. Sekepe e lokela ho ba sinki. Hobaneng ha sekepe se sa tebe? Boima bohle ba sekepe bo bonyenyane ho feta boima ba metsi kapa metsi a leoatle.
Mohlala oa bothata ba 1:
Lejoe le boima ba 40 kg le ka tlase ho letamo. Haeba bophahamo ba lejoe = 0.2 m3, matla a fokolang a hlokahalang ho phahamisa lejoe ke afe?
Tse tsejoang:
Boima ba lejoe (m) = 40 kg
Bophahamo ba lejoe (V) = 0.02 m 3
Boima ba metsi = 1000 kg/ m3
Ho potlaka ha matla a khoheli (g) = 10 m/s 2
Ho batloa: bonyane F
tharollo:
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 lejoe = (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 lejoe :
boima ba lejoe – matla a ho phaphamala = 400 N – 200 N = 200 N
Mohlala oa bothata ba 2:
Boima ba ntho ka metsing = 5000 kg m/s 2 le boima ba ntho ka metsing = 4000 kg m/s 2. Haeba boima ba ntho = 2000 kg/m 3 , boima le bophahamo ba ntho ke bokae? g = 10 m/s 2
tharollo
Ho potlaka ha 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 ho phaphamala) = boima ba ntho e moeeng – boima ba ntho e 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)
Bophahamo ba metsi a tlositsoeng = bophahamo ba ntho ka metsing
Bophahamo ba ntho = 0.1 m 3
Boima ba ntho = ?
ρ = m / V
m = ρ V
m = (2000 lik'hilograma / m 3 ) (0.1 m 3 )
m = 200 kg
Boima ba ntho = 200 kg
Mohlala oa bothata ba 3:
Ke bophahamo bofe ba helium bo hlokahalang haeba balune e tlameha ho phahamisa moroalo oa 500 kg?
tharollo:
Botenya ba helium = 0.1786 kg/ m3
Boima ba moea = 1.293 kg/ m3
Matla a ho phaphamala = boima ba moya o fallang = boima ba ntho + boima ba helium
Matla a ho thothomela = boima ba ntho + 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 suthisitsoeng
Matla a ho phaphamala = (boima ba moya o ileng wa falliswa)(g) —- equation 2
Re kopanya equation 1 le equation 2:
(boima ba mojaro + boima ba helium)(g) = (boima ba moya o ileng wa falla)(g)
boima ba mojaro + boima ba helium = boima ba moea o fallang
500 kg + (ρ helium)(V helium) = (ρ metsi)(V metsi)
500 kg = (metsi a ρ)(metsi a V) – (ρ helium)(V helium)
Bophahamo ba moea o ileng oa falla (moea oa V) = Bophahamo ba helium ka balune (V helium)
500 kg = (ρ metsi – ρ helium)(V)
Ena ke bophahamo ba bonyane ba helium bo hlokahalang ho phahamisa boima bo hodima lefatshe. Hore balune e phaphamale ho feta, bophahamo ba helium bo hloka ho eketsoa. Bophahamo ba helium bo lokela ho eketsoa hobane boima ba moya bo a fokotseha ha bophahamo bo ntse bo eketseha.
