Tsab xov xwm hais txog Archimedes lub hauv paus ntsiab lus
Ib lub nkoj uas muaj qhov hnyav loj heev yeej tsis tog, thaum lub pob zeb uas muaj qhov me me kuj tog tau. Vim li cas? Cov lus teb yog yooj yim yog tias koj nkag siab txog lub tswv yim ntawm kev ntab thiab Archimedes txoj cai.
Hauv lub neej txhua hnub, peb yuav pom tias cov khoom uas raug ntxig rau hauv cov kua dej, zoo li pob zeb, muaj qhov hnyav me dua li thaum cov khoom tsis nyob hauv cov kua dej. Tej zaum koj yuav pom tias nws nyuaj rau tsa lub pob zeb los ntawm hauv av, tab sis tib lub pob zeb raug tsa los ntawm hauv qab dej hiav txwv yam tsis muaj zog. Qhov no yog vim lub zog ntab. Kev ntab tshwm sim vim qhov sib txawv ntawm cov kua dej siab ntawm qhov tob sib txawv. Lub kua dej siab nce nrog qhov tob, cov kua dej tuab dua, qhov siab ntawm cov kua dej ntau dua. Thaum ib yam khoom raug ntxig rau hauv cov kua dej, yuav muaj qhov sib txawv ntawm lub siab ntawm cov kua dej nyob rau sab saum toj ntawm cov khoom thiab cov kua dej nyob rau hauv qab ntawm cov khoom. Cov kua dej nyob rau hauv qab ntawm cov khoom muaj lub siab siab dua li cov kua dej nyob rau sab saum toj ntawm cov khoom.
Hauv daim duab, koj tuaj yeem pom ib yam khoom ntab hauv dej. Cov kua dej nyob hauv qab ntawm yam khoom muaj lub siab siab dua li cov kua dej nyob rau sab saum toj ntawm yam khoom. Qhov no yog vim tias cov kua dej hauv qab yam khoom muaj qhov tob dua li cov kua dej saum yam khoom (p2 > h1).
Qhov ntau ntawm cov kua dej siab ntawm qhov tob h2 yog:
Qhov ntau ntawm cov kua dej siab ntawm qhov tob h1 yog:
F2 = lub zog uas cov kua dej siv rau hauv qab ntawm yam khoom, F1 = lub zog uas cov kua dej siv rau saum cov khoom, A = thaj chaw ntawm cov khoom
Qhov sib txawv ntawm F2 thiab F1 yog tag nrho lub zog uas cov kua dej muab rau ntawm qhov khoom, uas peb paub tias yog lub zog ntab. Qhov ntau ntawm qhov ntab yog:
F ntab yaj =F2 − F1
F ntab yaj = (ρ gh2 A) − (ρ gh1 A)
F ntab yaj = ρ g A (h)2 - h1)
F ntab yaj = ρ Fg A h
F ntab yaj = ρ F g V
ρF = qhov ceev ntawm cov kua dej, g = qhov nrawm ntawm lub ntiajteb txawj nqus, V = qhov ntim ntawm cov khoom hauv cov kua dej
Yog li, peb tuaj yeem sau cov qauv uas hais txog qhov ntau ntawm buoyancy (F buoyancy) saum toj no:
F ntab yaj = ρF g V → m = ρ V
F ntab yaj = kuvF g
F ntab yaj = wbF
mF g = wF = qhov hnyav ntawm cov kua dej uas muaj tib lub ntim li qhov ntim ntawm cov khoom uas tau dipped.
Raws li qhov sib npaug saum toj no, peb tuaj yeem hais tias lub zog ntab yog sib npaug rau qhov hnyav ntawm cov kua dej uas raug tshem tawm, qhov ntim ntawm cov kua dej uas raug tshem tawm zoo ib yam li qhov ntim ntawm cov khoom uas raug muab tso rau hauv cov kua dej.
Yog tias cov khoom raug ntxig rau hauv cov kua dej, ntab, qhov twg qhov ntawm cov khoom uas raug ntxig tsuas yog ib feem xwb,
ces qhov ntim ntawm cov kua dej uas raug tshem tawm = qhov ntim ntawm qhov khoom uas tau muab tso rau hauv cov kua dej. Txawm tias cov khoom ntawd yog dab tsi thiab nws cov duab zoo li cas los xij, txhua tus neeg yuav ntsib tib yam. Qhov no yog qhov tshwm sim ntawm Archimedes (287-212 BC), uas hu ua Archimedes' Principle.
Txoj cai Archimedes hais tias:
Thaum ib yam khoom raug muab tag nrho lossis ib feem tso rau hauv cov kua, cov kua yuav muab lub zog nce mus rau sab saud (lub zog ntab) rau yam khoom, qhov twg qhov ntau ntawm lub zog nce mus rau sab saud (lub zog ntab) sib npaug qhov hnyav ntawm cov kua uas raug tshem tawm.
Zaj dab neeg ntawm Archimedes
Archimedes, uas nyob nruab nrab ntawm 287-212 BC, tau raug Vaj Ntxwv Hieron II txib kom tshawb xyuas seb lub kaus mom uas ua rau Vaj Ntxwv puas yog ua los ntawm kub ntshiab lossis tsis yog. Txhawm rau nrhiav seb lub kaus mom puas yog ua los ntawm kub ntshiab lossis lub kaus mom muaj lwm yam hlau, Archimedes thaum xub thawj tsis meej pem. Qhov teeb meem yog, cov duab ntawm lub kaus mom tsis sib xws thiab tsis tuaj yeem rhuav tshem ua ntej kom nws thiaj li txiav txim siab seb lub kaus mom puas yog ua los ntawm kub ntshiab lossis tsis yog.
Lub tswv yim ntawm kev txiav txim siab seb lub kaus mom puas yog ua los ntawm kub ntshiab lossis tsis yog yog thawj zaug txiav txim siab qhov hnyav ntawm lub kaus mom thiab tom qab ntawd piv rau qhov hnyav tshwj xeeb ntawm kub. Yog tias lub kaus mom yog ua los ntawm kub ntshiab, ces qhov hnyav tshwj xeeb ntawm lub kaus mom = qhov hnyav tshwj xeeb ntawm kub.
Qhov hnyav tshwj xeeb ntawm ib yam khoom yog qhov sib piv ntawm qhov hnyav ntawm yam khoom hauv huab cua thiab qhov hnyav ntawm dej uas muaj tib lub ntim li qhov ntim ntawm yam khoom. Sau ua lej:
Yuav ua li cas thiaj txiav txim tau qhov hnyav ntawm dej uas muaj tib lub ntim li qhov ntim ntawm cov khoom?
Raws li Archimedes, qhov hnyav ntawm dej uas muaj tib lub ntim li qhov ntim ntawm ib yam khoom = qhov ntau ntawm lub zog ntab thaum yam khoom poob (tag nrho ib feem ntawm yam khoom raug tsau rau hauv dej). Qhov no yog tib yam li qhov hnyav ntawm yam khoom poob thaum hnyav hauv dej. Yog li ntawd:
Yuav kom paub qhov hnyav ntawm lub kaus mom hlau, ua ntej yuav tsum muab lub kaus mom hlau hnyav rau hauv huab cua (qhov hnyav ntawm lub kaus mom hlau hauv huab cua). Tom qab ntawd muab lub kaus mom hlau tso rau hauv dej thiab tom qab ntawd hnyav dua kom tau qhov hnyav uas poob ntawm lub kaus mom hlau. Yog li:
Tom qab tau txais qhov hnyav tshwj xeeb ntawm lub kaus mom, ces muab piv rau qhov hnyav tshwj xeeb ntawm kub. Qhov hnyav tshwj xeeb ntawm kub = 19.3. Yog tias qhov hnyav tshwj xeeb ntawm lub kaus mom = qhov hnyav tshwj xeeb ntawm kub, lub kaus mom yog ua los ntawm kub ntshiab. Tab sis yog tias lub kaus mom tsis yog ua los ntawm kub ntshiab, ces qhov hnyav tshwj xeeb ntawm lub kaus mom tsis zoo ib yam li qhov hnyav tshwj xeeb ntawm kub.
Vim li cas lub nkoj thiaj tsis tog?
Yog tias qhov ceev ntawm ib yam khoom me dua qhov ceev ntawm dej, ces yam khoom ntawd yuav ntab. Ntawm qhov tod tes, yog tias qhov ceev ntawm ib yam khoom loj dua qhov ceev ntawm dej, ces yam khoom ntawd yuav tog. Feem ntau cov nkoj yog ua los ntawm hlau thiab hlau. Qhov ceev ntawm hlau thiab hlau = 7.8 x 103 kg / m3 thaum lub zog ntawm dej = 1.00 x 103 kg / m3. Zoo li qhov ceev ntawm hlau thiab hlau loj dua qhov ceev ntawm dej. Hauv qhov no, qhov hnyav tshwj xeeb ntawm hlau thiab hlau = 7.8. Lub nkoj yuav tsum yog lub dab dej. Vim li cas lub nkoj thiaj tsis tog? Qhov ceev tag nrho ntawm lub nkoj me dua qhov ceev ntawm dej lossis dej hiav txwv.
Piv txwv teeb meem 1:
Ib lub pob zeb uas hnyav 40 kg nyob hauv qab pas dej. Yog tias qhov ntim ntawm pob zeb = 0.2 m3, lub zog tsawg kawg nkaus uas xav tau los tsa lub pob zeb yog dab tsi?
Paub:
Qhov hnyav ntawm pob zeb (m) = 40 kg
Ntim ntawm pob zeb (V) = 0.02 m3
Qhov ceev ntawm dej = 1000 kg/m33
Kev nrawm ntawm lub ntiajteb txawj nqus (g) = 10 m/s2
SE pob: F yam tsawg kawg nkaus
tshuaj:
F ntab yaj = wbF
F ntab yaj = kuvF g → m = pV
F ntab yaj = ρF g V
F ntab yaj = (1000 kg/m33)(10 m/s2)(0.02 m3)
F ntab yaj = 200 kg m/s2
F ntab yaj = 200 N
Qhov hnyav ntawm pob zeb (w) = mg
qhov hnyav ntawm pob zeb = (40 kg)(10 m/s)2)
Qhov hnyav ntawm pob zeb = 400 kg m/s2
Qhov hnyav ntawm pob zeb = 400 N
Lub zog tsawg kawg nkaus uas xav tau los tsa lub pob zeb:
Qhov hnyav ntawm pob zeb - lub zog ntab = 400 N - 200 N = 200 N
Piv txwv teeb meem 2:
Qhov hnyav ntawm cov khoom hauv huab cua = 5000 kg m/s2 thiab qhov hnyav ntawm yam khoom hauv dej = 4000 kg m/s2Yog tias qhov ceev ntawm yam khoom = 2000 kg/m33 , qhov hnyav thiab qhov ntim ntawm yam khoom yog dab tsi? g = 10 m/s2
tshuaj
Kev nrawm ntawm lub ntiajteb txawj nqus (g) = 10 m/s2
Qhov ceev ntawm yam khoom = 2000 kg/m33
Qhov ceev ntawm dej = 1000 kg/m33
Qhov hnyav ntawm cov khoom hauv huab cua = 5000 kg m/s2
Qhov hnyav ntawm yam khoom hauv dej = 4000 kg m/s2
Lub zog ntab (F buoyancy) = qhov hnyav ntawm yam khoom hauv huab cua - qhov hnyav ntawm yam khoom hauv dej
F buoyancy = 5000 kg m/s2 – 4000 kg m/s2
F buoyancy = 1000 kg m/s2
F buoyancy = qhov hnyav ntawm dej uas raug tshem tawm
F buoyancy = (qhov hnyav ntawm dej)(g)
F buoyancy = (ntim dej uas raug tshem tawm) (qhov ceev ntawm dej) (g)
Qhov ntim ntawm cov dej uas raug tshem tawm = qhov ntim ntawm cov khoom hauv dej
Qhov ntim ntawm yam khoom = 0.1 m3
Qhov hnyav ntawm yam khoom = ?
ρ = m / V
m = ρ V
m = (2000 kg / m23)(0.1 m3)
m = 200 kg
Qhov hnyav ntawm yam khoom = 200 kg
Piv txwv teeb meem 3:
Yog tias lub npas yuav tsum nqa 500 kg ntawm qhov hnyav, yuav tsum muaj helium ntau npaum li cas?
tshuaj:
Qhov ceev ntawm helium = 0.1786 kg/m33
Qhov ceev ntawm huab cua = 1.293 kg/m33
Lub zog ntab = qhov hnyav ntawm huab cua uas raug tshem tawm = qhov hnyav ntawm yam khoom + qhov hnyav ntawm helium
Lub zog ntab = qhov hnyav ntawm yam khoom + qhov hnyav ntawm helium
Lub zog ntab = (qhov hnyav ntawm lub nra) (g) + (qhov hnyav ntawm helium) (g)
Lub zog ntab = (qhov hnyav ntawm lub nra hnyav + qhov hnyav ntawm helium)g —- kab zauv 1
Lub zog ntab = qhov hnyav ntawm huab cua uas raug tshem tawm
Lub zog ntab = (qhov hnyav ntawm huab cua uas raug tshem tawm) (g) —- kab zauv 2
Peb muab cov qauv 1 thiab cov qauv 2 ua ke:
(qhov hnyav ntawm lub nra hnyav + qhov hnyav ntawm helium) (g) = (qhov hnyav ntawm huab cua uas raug tshem tawm) (g)
qhov hnyav ntawm lub nra hnyav + qhov hnyav ntawm helium = qhov hnyav ntawm huab cua uas raug tshem tawm
500 kg + (ρ helium)(V helium) = (ρ dej)(V dej)
500 kg = (ρ dej)(V dej) - (ρ helium)(V helium)
Qhov ntim ntawm huab cua uas tau tshem tawm (V huab cua) = Qhov ntim ntawm helium hauv lub npas (V helium)
500 kg = (ρ dej - ρ helium) (V)
Qhov no yog qhov tsawg kawg nkaus ntawm helium uas xav tau los tsa cov hnyav ntawm lub ntiaj teb. Rau lub npas kom ntab siab dua, qhov ntim ntawm helium yuav tsum tau ntxiv. Qhov ntim ntawm helium yuav tsum tau nce vim tias qhov ceev ntawm huab cua txo qis nrog qhov siab.
