Chinyorwa pamusoro pemutemo weArchimedes
Ngarava ine huremu hwakakura hainyuri, asi dombo rine hudiki rinogona kunyura. Sei zvakadaro? Mhinduro yacho iri nyore kana uchinzwisisa pfungwa yekudzikama uye musimboti waArchimedes.
Muhupenyu hwezuva nezuva, tichaona kuti zvinhu zvinopinzwa mumvura, sedombo, zvine huremu hudiki pane zvinhu zvisiri mumvura. Ungawana zvakaoma kusimudza dombo kubva pasi, asi dombo rimwe chete rinosimudzwa nyore nyore kubva pasi pemvura yegungwa. Izvi zvinokonzerwa nesimba rinoyerera. Kusimba kunoitika nekuda kwekusiyana kwekumanikidzwa kwemvura pakadzika kwakasiyana. Kumanikidzwa kwemvura kunowedzera nekudzika, ukobvu hwemvura, kumanikidzwa kwemvura kunowedzera. Kana chinhu chikapinzwa mumvura, pachava nemusiyano mukumanikidzwa pakati pemvura iri pamusoro pechinhu nemvura iri pasi pechinhu. Mvura iri pasi pechinhu ine kumanikidzwa kwakakwira kupfuura mvura iri pamusoro pechinhu.
Mumufananidzo, unogona kuona chinhu chiri kuyerera mumvura. Mvura iri pasi pechinhu ine kumanikidzwa kwakanyanya kupfuura mvura iri pamusoro pechinhu. Izvi zvinodaro nekuti mvura iri pasi pechinhu ine kudzika kwakakura kupfuura mvura iri pamusoro pechinhu (p).2 > h1).
Huwandu hwekumanikidzwa kwemvura pakadzika kwe h 2 ndehwekuti:
Huwandu hwekumanikidzwa kwemvura pakadzika kwe h 1 ndehwekuti:
F 2 = simba rinoshandiswa nemvura iri pasi pechinhu, F 1 = simba rinoshandiswa nemvura iri pamusoro pechinhu, A = nzvimbo yepamusoro yechinhu
Musiyano uripo pakati peF2 neF1 isimba rose rinopihwa nemvura iri pachinhu, iyo yatinoziva sesimba rekufamba. Huwandu hwekufamba hunotevera :
F inoyerera = F 2 − F 1
F buoyancy = (ρ gh 2 A) − (ρ gh 1 A)
F buoyancy = ρ g A (h 2 − h 1 )
F inoyerera = ρ F g A h
F inoyerera = ρ F g V
ρ F = kuwanda kwemvura, g = kukurumidza kwegiravhiti, V = huwandu hwezvinhu zviri mumvura
Saka, tinogona kunyora equation inotaura huwandu hwe buoyancy (F buoyancy) pamusoro apa:
F buoyancy = 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 chakanyikwa.
Zvichibva pamuenzaniso uri pamusoro apa, tinogona kutaura kuti simba rinopfungaira rakaenzana nehuremu hwemvura iri kuburitswa, huwandu hwemvura inoburitswa hwakafanana nehuwandu hwechinhu chakanyikwa mumvura.
Kana chinhu chacho chikaiswa mumvura, chiri kuyangarara, uko chikamu chechinhu chacho chiri chikamu chimwe chete,
ipapo huwandu hwemvura inoyerera = huwandu hwechikamu chechinhu chakanyikwa mumvura. Hazvina mhosva kuti chinhu chacho chii uye kuti chimiro chacho chakadii, munhu wese achasangana nechinhu chimwe chete. Uyu ndiwo mhedzisiro yebasa raArchimedes (287-212 BC), inozivikanwa seArchimedes' Principle.
Nheyo yaArchimedes inoti:
Kana chinhu chikanyikwa chose kana kuti chikamu chacho mumvura, mvura yacho inopa simba rekusimudzira (simba rinosimudzira) kuchinhu chacho, uko huwandu hwesimba rekusimudzira (simba rinosimudzira) hwakaenzana nehuremu hwemvura iri kubviswa.
Nyaya yaArchimedes
Archimedes, akararama pakati pa287-212 BC, akatumwa naMambo Hieron II kuti aongorore kana korona yakagadzirirwa Mambo yakagadzirwa nendarama chaiyo kana kuti kwete. Kuti aone kana korona yakagadzirwa nendarama chaiyo kana kuti korona yacho ine zvimwe simbi, Archimedes pakutanga akavhiringidzika. Dambudziko nderekuti, chimiro chekorona hachina kurongeka uye hachigone kuparadzwa kutanga kuitira kuti zvionekwe kana korona yakagadzirwa nendarama chaiyo kana kwete.
Pfungwa yekuona kana korona yakagadzirwa negoridhe rakachena kana kuti kwete ndeyekutanga waona huremu hwekorona wobva waenzanisa nehuremu hwegoridhe chaihwo. Kana korona yakagadzirwa negoridhe rakachena, saka huremu hwekorona chaihwo = huremu hwegoridhe chaihwo.
Huremu hwechinhu hunoenderana nehuremu hwechinhu chiri mumhepo nehuremu hwemvura hune huwandu hwakafanana nehukuru hwezvinhu. Yakanyorwa nemasvomhu:
Nzira yekuziva sei huremu hwemvura ine huwandu hwakafanana nehukuru hwezvinhu?
Sekureva kwaArchimedes, huremu hwemvura ine huwandu hwakafanana nehukuru hwechinhu = huwandu hwesimba rinoyerera kana chinhu chanyura (chikamu chose chechinhu chinonyikwa mumvura). Izvi zvakafanana nehuremu hwezvinhu zvinorasika kana zvayerwa mumvura. Saka:
Kuti uone kuti korona inokweva sei, korona inotanga yayerwa mudenga (huremu hwekorona mudenga). Ipapo korona inopinzwa mumvura yozoyerwa zvakare kuti iwane huremu hwakaraswa hwekorona. Saka:
Mushure mekunge korona yawanikwa, inoenzaniswa nehukuru hwegoridhe. Huremu hwegoridhe = 19.3. Kana huremu hwegoridhe = hukuru hwegoridhe, korona yakagadzirwa negoridhe rakachena. Asi kana korona isina kugadzirwa negoridhe rakachena, saka huremu hwegoridhe hahuna kufanana nehuremu hwegoridhe rakachena.
Sei ngarava isinganyuri?
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. Kuwanda kwesimbi nesimbi = 7.8 x 10 3 kg/m 3 ukuwo huwandu hwemvura = 1.00 x 10 3 kg/m 3 . Zvinoita sekuti huwandu hwesimbi nesimbi hwakakura kupfuura huwandu hwemvura. Muchiitiko ichi, simba resimbi nesimbi = 7.8. Ngarava inofanira kunge iri sinki. Sei ngarava isinganyuri? Kuwanda kwese kwengarava kudiki pane huwandu hwemvura kana mvura yegungwa.
Muenzaniso wedambudziko 1:
Dombo rine huremu hwe40 kg riri pasi pedziva. Kana dombo riri 0.2 m3, simba ripi shoma rinodiwa kuti dombo risimudzwe?
Anozivikanwa:
Huremu hwedombo (m) = 40 kg
Vhoriyamu yedombo (V) = 0.02 m 3
Kuwanda kwemvura = 1000 kg/ m3
Kukurumidza kwegiravhiti (g) = 10 m/s 2
Zvinodiwa: F zvishoma
Solution:
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
huremu hwedombo (w) = mg
huremu hwedombo = (40 kg)(10 m/s 2 )
huremu hwedombo = 400 kg m/s 2
huremu hwedombo = 400 N
Simba shoma rinodiwa kusimudza dombo :
huremu hwedombo – simba rekudzikamisa = 400 N – 200 N = 200 N
Muenzaniso wedambudziko 2:
Kurema kwechinhu chiri mumvura = 5000 kg m/s 2 uye huremu hwechinhu chiri mumvura = 4000 kg m/s 2 . Kana huwandu hwechinhu = 2000 kg/m 3 , huremu uye vhoriyamu yechinhu chacho chii? g = 10 m/s 2
mhinduro
Kukurumidza kwegiravhiti (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 rekufamba (F rinofamba) = 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 inobviswa = huwandu hwechinhu chiri mumvura
Huwandu hwechinhu = 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 wedambudziko 3:
Ihuwandu hupi hwehelium hunodiwa kana bharumu richida kusimudza mutoro unorema 500 kg?
Solution:
Kuwanda kwehelium = 0.1786 kg/ m3
Kuwanda kwemhepo = 1.293 kg/ m3
Simba remhepo inobhururuka = huremu hwemhepo yakabviswa = huremu hwechinhu + huremu hwehelium
Simba rekusimudzira = huremu hwechinhu + huremu hwehelium
Simba rekusimudzira = (huremu hwemutoro)(g) + (huremu hwehelium)(g)
Simba rekufamba = (huremu hwemutoro + huremu hwehelium)g —- equation 1
Simba remhepo rinorema = huremu hwemhepo inobviswa
Simba remhepo rinoputika = (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 mvura)(V mvura)
500 kg = (ρ mvura) (V mvura) – (ρ helium) (V helium)
Huwandu hwemhepo yakabviswa (V air) = Huwandu hwehelium mubharumu (V helium)
500 kg = (ρ mvura – ρ helium)(V)
Iyi ndiyo vhoriyamu shoma inodiwa kusimudza zvinorema pamusoro penyika. Kuti bharumu riyambuke zvakanyanya, vhoriyamu yehelium inofanira kuwedzerwa. Vhoriyamu yehelium inofanira kuwedzerwa nekuti density yemhepo inoderera nekukwirira.
