Cov kua dej statics - teeb meem thiab kev daws teeb meem

Cov dej khov static - teeb meem thiab kev daws teeb meem

Kev kub siab ntawm cov kua dej

1. Qhov txawv ntawm lub zog hydrostatic ntawm cov ntshav ntawm lub hlwb thiab ntawm cov taw ntawm ib tus neeg uas siab 165 cm yog dab tsi (xav tias qhov ceev ntawm cov ntshav = 1.0 × 10 ³ kg/m ³ , kev nrawm vim lub ntiajteb txawj nqus = 10 m/s ² )

Paub:

Qhov siab (h) = 165 cm = 165/100 m = 1.65 meters

Qhov Ceev ntawm cov ntshav (ρ) = 1.0 × 10 ³ kg/ ^m3

Kev nrawm vim lub ntiajteb txawj nqus (g) = 10 m/s ²

SE pob: siab ntawm cov kua

Tshuaj:

P = ρgh

P = (1.0 × 103 ⁾ (10)(1.65)

P = (1.0 × 104 ⁾ (1.65)

P = 1.65 x 10 ⁴ N/ ^m2

U-Yeeb nkab

2. Cov yeeb nkab AU thaum xub thawj yog puv nrog dej es tsis yog ib lub yeeb nkab puv nrog roj, raws li pom hauv daim duab hauv qab no. Qhov ceev ntawm dej yog 1000 kg/m3 ^. Yog tias qhov siab ntawm roj yog 8 cm thiab qhov siab ntawm dej yog 5 cm, qhov ceev ntawm roj yog dab tsi?

Paub: Cov kua dej zoo li qub - teeb meem thiab kev daws teeb meem 1

Qhov ceev ntawm dej = 1000 kg.m ^-3

Qhov siab ntawm dej (h ₂ ) = 5 cm

Qhov siab ntawm roj (h ₁ ) = 8 cm

Xav tau: qhov ceev ntawm cov roj

Tshuaj:

ρ ₁ gh ₁ =ρ ₂ gh ₂

ρ ₁ h ₁ =ρ ₂ h ₂

(1000)(5) = (ρ ₂ )(8)

5000 = (ρ ₂ )(8)

ρ ₂ = 625 kg.m ^-3

3. Cov yeeb nkab AU raug muab roj kerosene tso rau hauv ua ntej ces mam li ntxiv dej. Yog tias qhov hnyav ntawm roj kerosene yog 0.8 grams/cm3 ^thiab qhov ceev ntawm dej yog 1 gram/cm3 ^thiab thaj tsam hla yog 1.25 cm2 ^. Txheeb xyuas seb yuav tsum ntxiv dej ntau npaum li cas kom qhov siab sib txawv ntawm qhov chaw roj kerosene yog 15 cm.

A. 9 ml

B. 12 ml

C. 15 ml Cov kua dej zoo li qub - teeb meem thiab kev daws teeb meem 11

D. 18 ml

Paub:

Qhov ceev ntawm kerosene (ρ ₁ ) = 0.8 gram/ ^cm3

Qhov Ceev ntawm dej (ρ ₂ ) = 1 gram/ ^cm3

Thaj tsam seem ntawm lub raj e = 1.25 cm ²

Qhov siab sib txawv ntawm qhov chaw ntawm kerosene (h ₁ ) = 15 cm

Xav tau: Qhov ntim dej

Tshuaj:

Qhov siab ntawm dej (h ₂ ):

ρ ₁ gh ₁ = ρ ₂ gh ₂

(0,8)(15)(1)(h ₂ )

h ₂ = 12 cm

Qhov ntim dej:

V = ( Cheeb tsam seem ntawm lub kav dej e ) (qhov siab ntawm dej)

V = (1.25 cm2 ⁾ (12 cm)

V = 15 ^cm3

1 liv = 1 dm ³ = 10 ³ cm ³

1 milliliter = 10 ^-3 liv s = (10 ^-3 )(10 ³ ) cm ³ = 1 cm ³

Qhov ntim dej yog 15 cm ³ = 15 milliliters

Cov lus teb yog C.

4. Ib lub yeeb nkab U puv nrog dej nrog qhov ceev ntawm 1000 kg/m3 ^. Ib kem ntawm lub yeeb nkab U puv nrog glycerin nrog qhov ceev ntawm 1200 kg/m3 ^. Yog tias qhov siab ntawm glycerin yog 4 cm, txiav txim siab qhov siab sib txawv ntawm ob kem ntawm lub yeeb nkab.

A. 0.8 cm

B. 4 cm

C. 8 cm

D. 12 cm

Paub:

Qhov Ceev ntawm dej (ρ ₁ ) = 1000 kg/ ^m3

Qhov ceev ntawm glycerin (ρ ₂ ) = 1200 kg/ ^m3

Qhov siab ntawm glycerin (h2 ₎ = 4 cm

Xav tau: Qhov siab sib txawv ntawm ob kab ntawm cov yeeb nkab.

Tshuaj:

Qhov siab ntawm kem ntawm cov yeeb nkab (h ₁ ):

ρ ₁ h ₁ = ρ ₂ h ₂

(1000)(h1 ₎ = (1200)(4)

(1000)(h1 ₎ = 4800

h ₁ = 4.8 cm

Qhov siab sib txawv ntawm ob kab ntawm cov yeeb nkab U = h ₁ – h ₂ = 4.8 cm – 4 cm = 0.8 cm

Cov lus teb yog lawm yog A.

5. Ib lub yeeb nkab U muaj ob qhov kawg qhib puv nrog dej nrog qhov hnyav ntawm 1 g/cm3 ^. Thaj tsam ntu ntawm lub yeeb nkab yog tib yam, uas yog 1 cm2 ^. Ib tug neeg tshuab rau ib kawg ntawm ko taw ntawm lub yeeb nkab kom qhov saum npoo ntawm dej ntawm ko taw tod nce 10 cm ntawm nws qhov chaw qub. Yog tias qhov kev nrawm vim lub ntiajteb txawj nqus yog s 10 m/s2 ces txiav txim siab lub zog uas tus neeg ntawd ua.

A. 20 kilodynes

B. 10 kilodynes

C. 2 kilodynes

D. 1 kilodyne

Paub:

Hloov txhua chav mus rau lub kaw lus thoob ntiaj teb.

Qhov Ceev ntawm dej (ρ ₁ ) = 1 gr/cm3 ⁼¹⁰ -3 ^kg / 10 ^-6 m3 = 10 ³ kg/ ^m3

Thaj tsam hla ntawm cov yeeb nkab (A) = 1 cm ² = 10 ^-4 m ²

Qhov kev hloov ntawm kem ntawm cov yeeb nkab (h) = 10 cm = 1 dm = 10 ^-1 m

Kev nrawm vim lub ntiajteb txawj nqus (g) = 10 ms ^-2 = 10 ¹ ms ^-2

Qhov ntim ntawm cov dej txav (V) = (A)(h) = (1 cm ² )(10 cm) = 10 cm ³ = (10 ¹ )(10 ^-6 m ³ ) = 10 ^-5 m ³

Xav tau: Lub zog (F) ua los ntawm tus neeg.

Tshuaj:

Lub zog uas tus neeg ntawd ua = qhov hnyav ntawm dej uas siab li 10 cm

F = w

F = mg —–> Kab zauv ntawm qhov ceev: m = ρ V

F = ρ V g

F = (10 ³ )(10 ^-5 )(10 ¹ )

F = (10 ⁴ )(10 ^-5 )

F = 10 ^-1 Newton —–> 1 Newton = 10 ⁵ dynes

F = (10 ^-1 )(10 ⁵ dyne)

F = 10 ⁴ dynes

F = 10 kilodynes

Cov lus teb yog B.

6. Muab ib lub raj zoo li tus Y ntxig rau sab saud kom ob txhais taw sab laug thiab sab xis raug muab tso rau hauv ob hom kua. Tom qab ob txhais taw raug muab tso rau hauv cov kua, ces sab saum toj ntawm lub yeeb nkab Y raug kaw nrog tus ntiv tes thiab rub mus rau saum toj, kom ob ceg ntawm lub yeeb nkab Y puv nrog ib kem ntawm cov kua dej sib txawv. Yog tias qhov ceev ntawm thawj cov kua yog 0.80 gram.cm ^-3 thiab qhov ceev thib ob yog 0.75 gram.cm ^-3 , thiab kem kua qis dua yog 8 cm, ces txiav txim siab qhov siab sib txawv ntawm ob kem kua ntawm lub yeeb nkab U.

A. 1.0666 cm Cov kua dej zoo li qub - teeb meem thiab kev daws teeb meem 12

B. 0.9375 cm

C. 0.3533 cm

D. 0.5333 cm

Paub:

Qhov ceev ntawm cov kua thawj zaug (ρ ₁ ) = 0,80 gram.cm ^-3

Qhov ceev ntawm cov kua thib ob (ρ ₂ ) = 0,75 gram.cm ^-3

Qhov siab ntawm cov kua qis dua (h ₁ ) = 8 cm

Xav tau: Qhov siab sib txawv ntawm ob kab kua ntawm U pip e

Tshuaj:

Qhov siab ntawm cov kua dej siab dua (h ₂ ):

ρ ₁ h ₁ = ρ ₂ h ₂

(0.80)(8) = (0.75)( _h2 )

6.4 = 0.75 ( _h2 )

h2 = 6.4 / _0.75

h ₂ = 8.5 cm

Qhov sib txawv ntawm qhov siab ntawm cov kua = h ₂ - h ₁ = 8.5333 cm - 8 cm = 0.5333 cm

Cov lus teb yog D.

Lub zog ua kom muaj zog

7. Ib lub pob zeb uas muaj qhov loj li 0.5 m3 ^muab tso rau hauv cov kua uas muaj qhov ceev li 1.5 gr cm ^-3 . Kev nrawm vim lub ntiajteb txawj nqus yog 10 ms ^-2 . Lub zog ntab yog dab tsi?

Paub:

Ntim ntawm pob zeb (V) = 0.5 ^m3

Qhov Ceev ntawm dej (ρ) = 1.5 gr cm ^–3 = 1500 kg m ^-3

Kev nrawm vim yog lub ntiajteb txawj nqus (g) = 10 ms ^-2

Xav tau: lub zog ntab ( _FA )

Tshuaj:

Qhov sib npaug ntawm lub zog buoyant:

F _A = ρ g V = (1500 kg m ^-3 ) (10 ms ^-2 ) (0.5 m ³ ) = 7500 kg m/s ² = 7500 Newtons

Ntab

8. Ib daim dej khov ntab hauv hiav txwv raws li pom hauv daim duab hauv qab no. Qhov ceev ntawm dej hiav txwv yog 1.2 gr cm ^-3 thiab qhov ceev ntawm dej khov yog 0.9 gr c ^-3 . Qhov ntim ntawm dej khov hauv dej hiav txwv = ……. x qhov ntim ntawm dej khov hauv huab cua.

Paub: Cov kua dej zoo li qub - teeb meem thiab kev daws teeb meem 2

Qhov ceev ntawm dej hiav txwv (ρ _{dej hiav txwv} ) = 1.2 gr cm ^–3

Qhov ceev ntawm dej khov (ρ _{dej khov} ) = 0.9 gr c ^–3

Xav tau: Qhov ntim ntawm dej khov hauv dej hiav txwv = ……. x qhov ntim ntawm dej khov hauv huab cua.

Tshuaj:

Cov kua dej zoo li qub - teeb meem thiab kev daws teeb meem 3

Qhov ntim ntawm dej khov hauv hiav txwv = 0.75

Qhov ntim ntawm dej khov hauv huab cua = 0.25

Qhov ntim ntawm cov dej khov hauv dej hiav txwv = 3 x qhov ntim ntawm cov dej khov hauv huab cua (3 x 0.25 = 0.75).

9. Ib yam khoom ntab hauv cov kua uas muaj 2/3 ntawm cov khoom nyob hauv cov kua. Yog tias qhov ceev ntawm cov khoom yog 0.6 gr cm3 ^, ces qhov ceev ntawm dej yog dab tsi.

Paub:

Qhov feem ntawm cov khoom hauv kua = 2/3

Qhov ceev ntawm yam khoom = 0.6 gr cm3 ⁼ 600 kg ^m3

Xav tau: qhov ceev ntawm cov kua (x)

Tshuaj:

Cov kua dej zoo li qub - teeb meem thiab kev daws teeb meem 4

Qhov ceev ntawm cov kua yog 900 kg ^m3

10. Ib tug ntoo ntab hauv dej, qhov twg 3/5 ntawm cov ntoo nyob hauv dej. Yog tias qhov ceev ntawm dej yog 1 × 10 ³ kg/m3 ^, qhov ceev ntawm ntoo yog dab tsi?

Paub:

Ib feem ntawm yam khoom hauv dej = 3/5

Qhov Ceev ntawm dej = 1 × 10 ³ kg/m3 ⁼ 1000 kg/ ^m3

Xav tau: Qhov ceev ntawm ntoo (x)

Tshuaj:

Cov kua dej zoo li qub - teeb meem thiab kev daws teeb meem 5

Qhov ceev ntawm ntoo yog 600 kg/m3 ⁼ 6 x 10 ² kg/ ^m3

Cov kua dej static yog dab tsi?
- teb: Kev kawm txog cov kua dej zoo li qub, tseem hu ua hydrostatics, yog ceg ntawm cov txheej txheem kua dej uas kawm txog cov kua dej thaum so thiab cov zog uas cov kua dej zoo li qub siv rau ntawm cov khoom uas tau muab tso rau hauv dej thiab phab ntsa thawv.
Lub siab nyob rau hauv cov kua dej sib txawv li cas nrog qhov tob?
- teb: Hauv cov kua dej uas tsis txav mus los, qhov siab nce linearly nrog qhov tob vim qhov hnyav ntawm cov kua dej saum toj no txhua qhov tob. Qhov kev hloov pauv ntawm qhov siab nrog qhov tob yog muab los ntawm $Δ P = ρ g h$ , qhov twg $ρ$ yog qhov ceev ntawm cov kua dej, $g$ yog qhov kev nrawm ntawm lub ntiajteb txawj nqus, thiab $h$ yog qhov tob.
Pascal txoj cai yog dab tsi?
- teb: Txoj cai Pascal hais tias qhov kev hloov pauv ntawm lub zog siv rau cov kua dej kaw yog xa mus rau txhua qhov ntawm cov kua dej thiab rau phab ntsa ntawm nws lub thawv.
Lub tshuab nqa hydraulic ua haujlwm li cas raws li cov ntsiab cai ntawm cov kua dej static?
- teb: Lub tshuab nqa hydraulic siv Pascal txoj cai. Thaum lub zog me me raug siv rau lub piston me me, nws tsim lub zog siab hauv cov kua dej. Lub zog no raug xa mus tsis tu ncua thoob plaws hauv cov kua dej, ua rau lub zog loj dua rau lub piston loj dua, ua rau lub tshuab nqa tuaj yeem tsa cov khoom hnyav nrog kev siv zog me ntsis.
Lub zog ntab yog dab tsi thiab nws muaj feem cuam tshuam li cas rau cov kua dej static?
- teb: Lub zog ntab yog lub zog uas cov kua dej tso rau saum toj ntawm txhua yam khoom uas nyob hauv dej. Raws li Archimedes txoj cai, lub zog ntab rau ntawm ib yam khoom yog sib npaug rau qhov hnyav ntawm cov kua dej uas cov khoom raug tshem tawm.
Vim li cas cov khoom ntab los yog tog hauv cov kua dej?
- teb: Seb ib yam khoom ntab los yog poob rau hauv dej nyob ntawm seb lub zog ntab thiab qhov hnyav ntawm yam khoom ntawd muaj feem cuam tshuam li cas. Yog tias lub zog ntab (vim yog cov kua dej uas raug tshem tawm) loj dua qhov hnyav ntawm yam khoom, nws yuav ntab. Yog tias yam khoom ntawd hnyav dua, nws yuav poob rau hauv dej.
Lub tswv yim ntawm hydrostatic siab yog dab tsi?
- teb: Lub zog hydrostatic yog lub zog uas cov kua dej tso tawm thaum so vim yog lub zog ntawm lub ntiajteb txawj nqus. Nws nce linearly nrog qhov tob hauv cov kua dej, thiab suav ua $P = P_{0} + ρ g h$ , qhov twg $P_{0}$ yog lub siab nyob rau saum npoo av, $ρ$ yog qhov ceev ntawm cov kua dej, $g$ yog qhov kev nrawm ntawm lub ntiajteb txawj nqus, thiab $h$ yog qhov tob.
Lub zog ntawm huab cua cuam tshuam li cas rau cov kua dej static?
- teb: Lub huab cua tuaj yeem xav tias yog cov kua dej. Lub zog siab ntawm huab cua yog lub zog siab uas lub zog ntawm huab cua tso rau saum ib qho chaw. Nws txo qis nrog qhov siab, zoo ib yam li lub zog siab hauv cov kua dej txo qis thaum ib qho txav mus rau sab saud hauv cov kua dej.
Lub luag haujlwm ntawm lub thawv ua lub luag haujlwm li cas rau kev faib siab ntawm cov kua dej uas nyob hauv nws?
- teb: Hauv kev ntsuas dej ntws, qhov siab ntawm qhov tob uas muab tsuas yog nyob ntawm qhov siab ntawm cov kua dej saum qhov tob ntawd xwb, tsis yog nyob ntawm cov duab ntawm lub thawv. Yog li, qhov siab ntawm qhov tob tshwj xeeb yog tib yam txawm tias lub thawv zoo li cas los xij.
Qhov tseem ceeb ntawm qhov hydrostatic paradox yog dab tsi?

teb: Qhov kev sib cav sib ceg ntawm hydrostatic qhia tau hais tias hauv cov kua dej static, lub zog uas cov kua dej static tso rau hauv qab ntawm lub thawv tsuas yog nyob ntawm qhov siab ntawm cov kua dej, tsis yog nws qhov ntim lossis cov duab ntawm lub thawv. Yog li, cov thawv sib txawv heev nrog tib qhov siab ntawm cov kua dej tso tawm tib lub siab ntawm lawv lub hauv paus, txawm tias lawv tuav cov kua dej sib txawv.