Zvinyorwa zveMutemo zvaArchimedes
Wakamboona ngarava here? Kana usati waiona uri wega, ndinovimba wakamboiona paterevhizheni kana paindaneti. Ngarava ine huremu hwakakura kwazvo hainyuri, nepo dombo diki, rakareruka richigona kunyura. Sei zvakadaro? Mhinduro yacho iri nyore kana uchinzwisisa pfungwa dzekudzikama uye musimboti waArchimedes.
Muhupenyu hwezuva nezuva, tichaona kuti zvinhu zvakaiswa mumvura, zvakaita sedombo, zvine huremu hushoma pane kana chinhu chisiri mumvura. Ungave uchinetseka kusimudza dombo kubva pamusoro pevhu, asi dombo rimwe chete rinosimudzwa nyore nyore kubva pasi pedziva. Izvi zvinokonzerwa nesimba remvura. Kusimba kunoitika nekuda kwemusiyano wekumanikidzwa kwemvura pakadzika kwakasiyana. Kumanikidzwa kwemvura kunowedzera nekudzika, kudzika kwemvura, kumanikidzwa kwemvura kunowedzera. Kana chinhu chikaiswa mumvura, pachava nemusiyano wekumanikidzwa pakati pemvura iri pamusoro pechinhu nemvura iri pasi pechinhu. Mvura iri pasi pechinhu ine kumanikidzwa kukuru kupfuura mvura iri pamusoro pechinhu.
Kushingaira
Mumufananidzo, chinhu chinoonekwa chichiyangarara mumvura. Mvura iri pasi pechinhu ine kumanikidzwa kukuru kupfuura mvura iri pamusoro pechinhu. Izvi zvinodaro nekuti mvura iri pasi pechinhu ine kudzika kukuru kupfuura mvura iri pamusoro pechinhu (h2 > h1).
F 2 = simba rinoitwa nemvura iri pasi pechinhu, F 1 = simba rinoitwa nemvura iri pamusoro pechinhu, A = nzvimbo yepamusoro yechinhu
Musiyano uripo pakati peF2 neF1 isimba rose rinoitwa nemvura iri pachinhu chacho, chatinoziva sesimba rinofamba-famba. Hukuru hwesimba rinofamba-famba ndehwekuti:
F inoyerera = F 2 − F 1
F buoyant = (ρ gh 2 A ) − (ρ gh 1 A)
F inoyangarara = ρ g A ( h 2 − h 1 )
F inoyerera = ρ g A h
F inoyerera = ρ g V
Information :
ρ = kuwanda kwemvura
g = kukurumidza nekuda kwesimba rinokwevera pasi
V = huwandu hwechinhu chiri mumvura
saka equation inotaura hukuru hwesimba rinoyerera (F rinoyerera) pamusoro apa inogona kunyorwa seizvi:
F inoyangarara = ρ F g V → m = ρ V
F inoyerera = m F g
F inoyerera = w F
m F g = w F = huremu hwemvura ine huwandu hwakafanana nehukuru hwechinhu chakanyudzwa mumvura.
Nheyo yaArchimedes
Zvichibva pamuenzaniso uri pamusoro apa, tinogona kutaura kuti simba rinopfungaira rakaenzana nehuremu hwemvura yakabviswa, huwandu hwemvura yakabviswa hwakaenzana nehuwandu hwechinhu chakanyudzwa mumvura.
Kana chinhu chikanyudzwa mumvura yoyangarara, chikamu chechinhu chikanyudzwa mumvura, huwandu hwemvura inobviswa hunoenderana nehuwandu hwechikamu chechinhu chakanyudzwa mumvura. Pasinei nechimiro kana saizi yechinhu chacho, chinhu chimwe chete chichaitika kune vese. Iri ndiro basa raArchimedes (287-212 BC), iro rava kuzivikanwa seArchimedes' Principle.
Nheyo yaArchimedes inoti:
Kana chinhu chikanyudzwa chose kana kuti chikamu chacho mumvura, mvura yacho inozoshandisa simba rinokwira (simba rinokwira) pachinhu chacho, uko hukuru hwesimba rinokwira (simba rinokwira) hwakaenzana nehuremu hwemvura yakabviswa.
Nyaya yaArchimedes
Archimedes, akararama pakati pa287 na212 BC, akatumwa naMambo Hieron II kuti aongorore kana korona yakagadzirirwa mambo yakagadzirwa nendarama chaiyo. Pakutanga Archimedes akavhiringidzika kuti korona yacho yakagadzirwa nendarama chaiyo here kana kuti yaiva nedzimwe simbi. Dambudziko raiva rekuti korona yacho yakanga isina kurongeka uye yaisagona kuparadzwa kuti zvionekwe kana yaiva ndarama chaiyo.
Pfungwa iri shure kwekuona kana korona yamambo yakagadzirwa nendarama chaiyo ndeyekutanga kuona kukura kwekorona chaiyo wobva waienzanisa nekukura kwegoridhe chaiyo. Kana korona yakagadzirwa nendarama chaiyo, saka kukura kwekorona chaiyo = kukura kwegoridhe chaiyo.
Huremu hwechinhu hunoenderana nehuremu hwechinhu chiri mumhepo nehuremu hwemvura ine huwandu hwakafanana nehwechinhu chacho. Panyaya yemasvomhu, zvakanyorwa kuti:
Nzira yekuziva sei huremu hwemvura ine huwandu hwakafanana nehukuru hwechinhu?
Sekureva kwaArchimedes, huremu hwemvura ine huwandu hwakafanana nehukuru hwechinhu = hukuru hwesimba rinoyerera kana chinhu chanyura (chinhu chose chinonyudzwa mumvura). Izvi zvakafanana nehuremu hwechinhu chinorasika kana chayerwa mumvura. Saka:
Kuti uone kuti korona inokweva sei, korona inotanga yayerwa mumhepo (Huremu hweKorona muMhepo). Zvadaro, korona inoiswa mumvura yozoyerwa zvakare kuti iwane huremu hwekorona yakarasika. Saka:
Kana simba rekorona rawanikwa, rinoenzaniswa nesimba regoridhe chairo. Simba regoridhe chairo i19,3. Kana simba rekorona rakaenzana nesimba regoridhe chairo, saka korona yakagadzirwa negoridhe rakachena. Zvisinei, kana korona isina kugadzirwa negoridhe rakachena, simba rekorona harizove rakafanana nesimba regoridhe chairo.
Sei Ngarava Dzisinganyuri?
Kana huwandu hwechinhu hudiki pane huwandu hwemvura, chinhu chinoyangarara. Kusiyana neizvi, kana huwandu hwechinhu hwakakura kupfuura huwandu hwemvura, chinhu chinonyura. Ngarava zhinji dzakagadzirwa nesimbi nesimbi. Huwandu hwesimbi nesimbi = 7,8 x 103 kg /m3 ukuwo huwandu hwemvura = 1,00 x 103 kg /m3 . Zvinoita sekuti huwandu hwesimbi nesimbi hwakakura kupfuura huwandu hwemvura. Muchiitiko ichi, simba resimbi nesimbi = 7,8. Ngarava dzakagadzirwa nesimbi nesimbi dzinofanira kunyura. Sei ngarava dzisinganyure? Huwandu hwese hwengarava hudiki pane huwandu hwemvura kana mvura yegungwa.
Mienzaniso yemibvunzo pamusoro pemutemo waArchimedes
Muenzaniso wemubvunzo wechi1:
Dombo rinorema 40 kg riri pasi pedziva. Kana vhoriyamu yedombo iri = 0,2 m 3, simba shoma rinodiwa kusimudza dombo nderei?
Kukurukurirana
Zvinozivikanwa kuti:
Huremu hwedombo (m) = 40 Kg
Vhoriyamu yedombo (V) = 0,02 m 3
Kuwanda kwemvura = 1000 Kg/ m3
Kukurumidza kunokonzerwa negiravhiti (g) = 10 m/s 2
Akabvunzwa: F zvishoma
Mhinduro:
F inoyerera = w F
F inoyerera = m F g → m = pV
F inoyerera = ρ F g V
Kufamba-famba kweF = (1000 kg/m3 ) (10 m/s 2 )(0,02 m3 )
Kuyerera kweF = 200 kg m/s 2
Kudzika kwemvura (F) = 200 N
Kurema kwedombo (w) = mg
Kurema kwedombo = (40 kg)(10 m/s 2 )
Kurema kwedombo = 400 kg m/s 2
Kurema kwedombo = 400 N
Simba shoma rinodiwa kusimudza dombo:
Kurema kwedombo - Simba rekuvaka = 400 N - 200 N = 200 Newton.
Muenzaniso wemubvunzo wechi2:
Kurema kwechinhu chiri mumhepo = 5000 kg m/s 2 uye huremu hwechinhu chiri mumvura = 4000 kg m/s 2 . Kana huwandu hwechinhu = 2000 kg/m 3 , huremu nehukuru hwechinhu chacho chii? g = 10 m/s 2
Kukurukurirana
Kukurumidza kunokonzerwa negiravhiti (g) = 10 m/s 2
Kuwanda kwechinhu = 2000 kg/ m3
Kuwanda kwemvura = 1000 kg/ m3
Kurema kwechinhu chiri mumhepo = 5000 kg m/s 2
Kurema kwechinhu chiri mumvura = 4000 kg m/s 2
Simba rinopenya (F rinopenya) = Huremu hwechinhu chiri mumhepo - Huremu hwechinhu chiri mumvura
Kuyerera kweF = 5000 kg m/s 2 – 4000 kg m/s 2
Kuyerera kweF = 1000 kg m/s 2
F inoyerera = Huremu hwemvura yakabviswa
F inoyerera = (huremu hwemvura)(g)
F inoyerera = (huwandu hwemvura yakabviswa)(huwandu hwemvura)(g)
Huwandu hwemvura yakabviswa = Huwandu hwechinhu chakanyudzwa mumvura 😉
Saka vhoriyamu yechinhu = 0,1 m 3
Huremu hwechinhu = ?
ρ = m / V
m = ρ V
m = ( 2000 kg / m 3 )( 0,1 m 3 )
m = 200 kg
Huremu hwechinhu = 200 kg
Muenzaniso wemubvunzo wechi3:
Ihuwandu hupi hwehelium hunodiwa kana bharumu richifanira kusimudza mutoro we500 kg?
Kukurukurirana
Kuwanda kweHelium = 0,1786 kg/ m3
Kuwanda kwemhepo = 1,293 kg/ m3
Simba rinorema = Huremu hwemhepo yakabviswa = Huremu hwemutoro + Huremu hwehelium
Simba rinorema = Huremu hwemutoro + huremu hwehelium
Simba rekusimudzira = (huremu hwemutoro)(g) + (huremu hwehelium)(g)
Simba rekufamba = (huremu hwemutoro + huremu hwehelium)g —- equation 1
Simba remhepo inobhururuka = Huremu hwemhepo inobviswa
Simba remhepo inobhururuka = (huremu hwemhepo yakabviswa)(g) —- equation 2
Tinosanganisa equation 1 ne equation 2:
(huremu hwemutoro + huremu hwehelium)(g) = (huremu hwemhepo yakabviswa)(g)
huwandu hwemutoro + huwandu hwehelium = huwandu hwemhepo yakabviswa
500 kg + (ρ helium)(V helium) = (ρ mhepo)(V mhepo)
500 kg = (ρ mhepo)(V mhepo) – (ρ helium)(V helium)
Huwandu hwemhepo yakabviswa (V air) = Huwandu hwehelium inozadza bharumu (V helium)
500 kg = (ρ mweya – ρ helium)(V)
Iri ndiro huwandu hushoma hwehelium hunodiwa kuti munhu akwire huremu pamusoro penyika. Kuti bharumu rikwanise kuyerera rakakwirira, huwandu hwehelium hunofanira kuwedzerwa. Izvi zvinodaro nekuti huwandu hwemhepo hunoderera nekukwirira.
