Te pūmau o te wai – ngā raruraru me ngā otinga

Te pūmau o te wai – ngā raruraru me ngā otinga

Pēhanga wai

1. He aha te dte rerekētanga i waenga i te pēhanga hydrostatic o te toto i waenganui in te roro me te kapus of ngā waewae o he tangata e 165 henemita te roa (me kī te kiato o te toto = 1.0 × 10³ kg / m³, te whakaterenga nā te kaha ā-papa = 10m/s²)

Mōhiotia:

Teitei (h) = 165 henimita = 165/100 m = 1.65 mita

Te mātotoru o te toto (ρ) = 1.0 × 10³ kg / m³

Te whakaterenga nā te kaha ā-papa (g) = 10 m/s²

Hiahia: pēhanga wai

Rongoā:

P = ρ gh

P = (1.0 × 10³)(10)(1.65)

P = (1.0 × 10⁴)(1.65)

P = 1.65 x 10⁴ N / m²

Paipa-U

2. I te tīmatanga, ka whakakīia te paipa AU ki te wai, kaua ki te kotahi paipa kua whakakīia ki te hinu, e whakaaturia ana i te pikitia i raro nei. Ko te mātotoru o te wai he 1000 kg/m³Mena he 8 henimita te teitei o te hinu, ā, he 5 henimita te teitei o te wai, he aha te mātotoru o te hinu?

Mōhiotia:

Te mātotoru o te wai = 1000 kg.m^-3

Te teitei o te wai (h₂) = 5 henemita

Te teitei o te hinu (h₁) = 8 henemita

E hiahiatia ana: te matotoru o te hinu

Rongoā:

ρ₁ gh₁ =ρ₂ gh₂

ρ₁ h₁ =ρ₂ h₂

(1000)(5) = (ρ₂)(8)

5000 = (ρ₂)(8)

ρ₂ = 625 kg.m^-3

3. I whakakīia tuatahitia te paipa AU ki te hinu kātahi ka tāpirihia he wai. Mena papatipu o he 0.8 karamu/cm te hinu kakara³ me te te matotoru o te wai he 1 karamu/cm³ ā, ko te horahanga whakawhiti he 1.25 cm². Whakatauhia te nui me tāpiri he wai kia te rerekētanga teitei o te he 15 cm te mata o te hinu

A. 9 ml

B. 12 ml

C. 15 ml

D. 18 ml

Mōhiotia:

Te mātotoru o te hinu (ρ₁) = 0.8 karamu/cm³

Te mātotoru o te wai (ρ₂) = 1 karamu/cm³

Te horahanga wāhanga o te paipae = 1.25cm²

Te rerekētanga teitei o te mata o te hinu kakara (h₁) = 15 henemita

E hiahiatia ana: Te rahi o te wai

Rongoā:

Te teitei o te wai (h₂):

ρ₁ gh₁ = ρ₂ gh₂

(0,8)(15)(1)(h)₂)

h₂ = 12cm

Te rahinga o te wai:

V = (Te horahanga wāhanga o te paipae)(teitei o te wai)

V = (1.25 henimita²)(12 henimita)

V = 15 henimita³

1 rita = 1 dm³ = 10³ cm³

1 miririta = 10^-3 ritas = (10^-3)(10³) henimita³ = 1cm³

Ko te rōrahi o te wai he 15 cm³ = 15 miririta

Ko te whakautu tika ko C.

4. He paipa U kua kī tonu i te wai, ko te mātotoru o te 1000 kg/m³Kotahi te pou o te paipa U kua whakakīia ki te karisērine me te mātotoru o te 1200 kg/m³Mena he 4 cm te teitei o te karisēneti, tātaihia te rerekētanga teitei o ngā pou e rua o te paipa.

A. 0.8 henemita

B. 4 henemita

C. 8 henimita

D. 12 henimita

Mōhiotia:

Te mātotoru o te wai (ρ₁) = 1000 kg/m³

Te mātotoru o te glycerin (ρ₂) = 1200 kg/m³

Teitei o te glycerin (h₂) = 4 henemita

Hiahia: Te rerekētanga teitei o ngā pou e rua o te paipa.

Rongoā:

Te teitei o te pou o te paipa (h₁):

ρ₁ h₁ = ρ₂ h₂

(1000)(h₁) = (1200)(4)

(1000)(h₁) = 4800

h₁ = 4.8cm

Te rerekētanga teitei o ngā pou e rua o te paipa U = h₁ – h₂ = 4.8 henimita – 4 henimita = 0.8 henimita

Ko te whakautu tika ko A.

5. He paipa Kei a koe e rua ngā pito e tuwhera ana, kī tonu i te wai mā te he puranga of 1 g / cm³He rite tonu te horahanga wāhanga i te taha o te paipa, arā, 1 cm²Ka pupuhi tetahi on tetahi pito o te waewae o te paipa kia mata o ka piki te wai i te waewae kē atu i te 10 cm mai i tōna tūranga taketake. Mena te whakatere nā te kaha ā-papa is 10 m/s2 kātahi whakatau ko te pakari i mahihia e taua tangata.

A. 20 kirodina

B. 10 kirodina

C. 2 kirodina

D. 1 kirodina

Mōhiotia:

Hurihia ngā waeine katoa ki te pūnaha Ao Whānui.

Te mātotoru o te wai (ρ₁) = 1 karamu/henitimi³ = 10^-3 kg / 10^-6 m³ = 10³ kg / m³

Te horahanga whakawhiti o te paipa (A) = 1 cm² = 10^-4 m²

Ko te huringa o te pou o te paipa (h) = 10 cm = 1 dm = 10^-1 m

Te whakaterenga nā te kaha ā-papa (g) = 10 ms^-2 = 10¹ Whaea^-2

Te rōrahi o te wai i nekehia (V) = (A)(h) = (1 cm²)(10 henimita) = 10 henimita³ = (10¹)(10^-6 m³) = 10^-5 m³

E hiahiatia ana: Te kaha (F) i mahia e te tangata.

Rongoā:

Ko te kaha i pā ki taua tangata = te taumaha o te wai me te teitei o te 10 cm

F = w

F = mg —–> Whārite o te mātotorutanga: m = ρ V

F = ρ V g

F = (10³)(10^-5)(10¹)

F = (10⁴)(10^-5)

F = 10^-1 Nūtene —–> 1 Newton = 10⁵ mimi

F = (10^-1)(10⁵ tāne)

F = 10⁴ mimi

F = 10 kirodina

Ko te whakautu tika ko B.

6. Ka whakauruhia he ngongo āhua-Y ki raro, kia rumakina ai te waewae maui me te waewae matau ki roto i ngā momo wai e rua. Kia rumakina ngā waewae e rua ki roto i te wai, ka katia te tihi o te paipa Y ki te maihao, ka tōia ki runga, kia whakakīia ai ngā waewae e rua o te paipa Y ki tētahi pou o ngā wai matotoru rerekē. Mena ko te matotoru o te wai tuatahi he 0.80 karamu.cm^-3 me te tuarua o ngā mātotorutanga is 0.75 karamu/cm^-3, ā, ko te pou wai o raro he 8 cm, kātahi whakatau te rerekētanga teitei i waenga i ngā pou wai e rua i runga i te paipa Ue.

A. 1.0666 henemita

B. 0.9375 henemita

C. 0.3533 henimita

D. 0.5333 henimita

Mōhiotia:

Te mātotoru o te wai tuatahi (ρ₁) = 0,80 karamu.cm^-3

Te mātotoru o te wai tuarua (ρ₂) = 0,75 karamu.cm^-3

Te teitei o te wai o raro (h₁) = 8 henemita

E hiahiatia ana: Tte rerekētanga teitei i waenga i ngā pou wai e rua i runga i te paipa Ue

Rongoā:

Tte teitei o te ngā wai teitei ake (h₂):

ρ₁ h₁ = ρ₂ h₂

(0.80)(8) = (0.75)(h)₂)

6.4 = 0.75 (h₂)

h₂ = 6.4/0.75

h₂ = 8.5cm

Te rerekētanga teitei o ngā wai = h₂ – h₁ = 8.5333 henimita – 8 henimita = 0.5333 henimita

Ko te whakautu tika ko D.

Te kaha pōuri

7. He kōhatu he 0.5 m te rōrahi³ whakanohoia ki roto i tētahi wai he 1.5 karamu henimita te matotoru^-3. Ko te whakaterenga nā te kaha ā-papa he 10 ms^-2He aha te kaha pōrewarewa?

Mōhiotia:

Te rōrahi o te kōhatu (V) = 0.5 m³

Te mātotoru o te wai (ρ) = 1.5 karamu henimita^-3 = 1500 kg m^-3

Te whakaterenga nā te kaha ā-papa (g) = 10 ms^-2

Hiahia: te kaha pōturi (F_A)

Rongoā:

Te whārite o te kaha pōrewarewa:

F_A = ρ g V = (1500 kg m^-3)(10 ms^-2)(0.5 mita³) = 7500 kg m/s² = 7500 Niutona

Tuhinga o mua

8. Kei te mānu tetahi poraka hukapapa i te moana e whakaaturia ana i te pikitia i raro nei. Ko te mātotoru o te moana he 1.2 karamu henimita^-3 ā, ko te mātotoru o te huka he 0.9 gr c^-3Te rōrahi o te hukapapa i roto i te wai moana = ……. x te rōrahi o te hukapapa i te rangi.

Mōhiotia:

Te mātotoru o te moana (ρ_Moana) = 1.2 karamu henimita^-3

Te mātotoru o te huka (ρ_tio) = 0.9 karamu c^-3

Hiahia: Te rōrahi o te hukapapa i roto i te wai moana = ……. x te rōrahi o te hukapapa i te rangi.

Rongoā:

Te rōrahi o te hukapapa i te moana = 0.75

Te rōrahi o te hukapapa i te hau = 0.25

Ko te rahinga o te hukapapa i roto i te wai moana = 3 x te rahinga o te hukapapa i te rangi (3 x 0.25 = 0.75).

9. Ka mānu tētahi mea i roto i tētahi wai, kei roto i te wai te 2/3 o te mea. Mena ko te mātotoru o te mea he 0.6 karamu henimita³, kāti he aha te mātotoru o te wai.

Mōhiotia:

Te wāhanga o te mea i roto i te wai = 2/3

Te mātotoru o te mea = 0.6 karamu cm³ = 600 kg m³

Hiahia: te mātotoru o te wai (x)

Rongoā:

Ko te mātotoru o te wai he 900 kg m³

10. Ka mānu te rakau i roto i te wai, ā, kei roto i te wai te 3/5 o te wahi o te rakau. Mena ko te mātotoru o te wai he 1 × 10³ kg / m³, he aha te matotoru o te rakau?

Mōhiotia:

Wāhanga o te mea i roto i te wai = 3/5

Te mātotoru o te wai = 1×10³ kg / m³ = 1000 kg/m³

E hiahiatia ana: Te mātotoru o te rakau (x)

Rongoā:

Ko te matotoru o te rakau he 600 kg/m³ = 6x10² kg / m³

1. He aha te pūmautanga wai?
   • whakahoki: Ko te pūtaiao wai pūmau, e mōhiotia ana ko te pūtaiao wai pūmau, te peka o te hangarau wai e ako ana i ngā wai e okioki ana me ngā kaha e pā ana ki ngā wai pūmau ki runga i ngā mea e rumakina ana ki roto i te wai me ngā pakitara ipu.
2. He pēhea te rerekētanga o te pēhanga i roto i te wai i runga i te hohonutanga?
   • whakahoki: I roto i te wai pūmau, ka piki haere te pēhanga i runga i te āhua rārangi me te hohonu nā te taumaha o te pou wai i runga ake i tētahi hohonutanga kua hoatu. Ko te huringa o te pēhanga me te hohonutanga ka hoatu e $\Delta P=\rho gh$, i reira $\rho$ ko te mātotoru wai, $g$ ko te whakaterenga ā-papa, me $h$ ko te hohonutanga.
3. He aha te mātāpono a Pascal?
   • whakahoki: E ai ki te mātāpono a Pascal, ko te huringa o te pēhanga e pā ana ki tētahi wai kua kati, ka tukuna tonutia ki ngā wāhanga katoa o te wai, tae atu ki ngā pakitara o tōna ipu.
4. Me pēhea te mahi a te pūwero waipēhi i runga i ngā mātāpono o te pūmautanga wai?
   • whakahoki: Ka whakamahia e te ararewa waipēhi te mātāpono a Pascal. Ina pāngia he kaha iti ki tētahi piston iti, ka hangaia he pēhanga i roto i te wai. Ka tukuna tēnei pēhanga puta noa i te wai, ka nui ake te kaha e tukuna ana ki tētahi piston nui ake, ka taea ai e te ararewa te hiki i ngā mea taumaha me te iti o te kaha.
5. He aha te kaha pōrewarewa, ā, he aha tōna hononga ki te āhua pumau o te wai?
   • whakahoki: Ko te kaha pōrewarewa ko te kaha whakarunga e pā ana ki tētahi mea e rumakina ana ki roto i te wai. E ai ki te mātāpono a Archimedes, ko te kaha pōrewarewa i runga i tētahi mea he ōrite ki te taumaha o te wai kua nekehia e te mea.
6. He aha i mānu ai, i totohu ai rānei ngā mea i roto i ngā wai?
   • whakahoki: Ko te mana o te mea ka mānu, ka totohu rānei, e whakawhirinaki ana ki te whanaungatanga i waenga i te kaha pōtae me te taumaha o te mea. Mēnā he nui ake te kaha pōtae (nā te wai i nekehia) i te taumaha o te mea, ka mānu. Mēnā he nui ake te taumaha o te mea, ka totohu.
7. He aha te ariā o te pēhanga waipū?
   • whakahoki: Ko te pēhanga waipūmau te pēhanga e pā ana ki te wai e takoto kau ana nā te kaha o te ā-papa. Ka piki haere i runga i te rārangi me te hohonutanga o te wai, ā, ka tatauhia pēnei P=P₀​+ρgh, i reira P₀​ ko te pēhanga i te mata, $\rho$ ko te mātotoru wai, $g$ ko te whakaterenga ā-papa, me $h$ ko te hohonutanga.
8. He aha te hononga o te pēhanga o te āhuarangi ki te pumau o te wai?
   • whakahoki: Ka taea te whakaaro ki te āhuarangi he wai. Ko te pēhanga āhuarangi te pēhanga e pā ana ki te taumaha o te hau i runga ake i tētahi pūwāhi. Ka heke iho i te teitei, he rite ki te hekenga o te pēhanga i roto i te wai i a te tangata e neke ake ana i roto i te pou wai.
9. He aha te tūranga o te āhua o te ipu i roto i te tohatoha pēhanga o te wai pūmau i roto i taua ipu?
   • whakahoki: I roto i te pūtaiao wai pūmau, ko te pēhanga i tētahi hohonutanga kua whakaritea ka whakawhirinaki noa ki te teitei o te pou wai i runga ake i taua hohonutanga, kaua ki te āhua o te ipu. Nō reira, he rite tonu te pēhanga i tētahi hohonutanga motuhake ahakoa te āhua o te ipu.
10. He aha te hiranga o te paradox hydrostatic?

• whakahoki: E whakaatu ana te paradox hydrostatic i roto i te fluid statics, ko te kaha e pā ana ki te wai static i raro i te ipu ka whakawhirinaki anake ki te teitei o te pou wai, ehara i te rōrahi, i te āhua rānei o te ipu. Nō reira, ko ngā ipu tino rerekē me te teitei wai kotahi ka pā te pēhanga kotahi ki tō rātou turanga, ahakoa he rerekē te nui o te wai e pupuri ana i roto.