He tauira o te ture a Pascal

9 Ngā Tauira o te Ture a Pascal

1. Ko te horahanga whakawhiti-wāhanga o ia tīki waipēhi he 0,04 m² me te 0,10 m²Mena he 5 Newton te kaha whakauru, he aha te kaha whakaputa mōrahi?
Kōrero:
E mōhiotia ana:
A₁ = 0,04 m²
A₂ = 0,10 m²
F₁ = 5 N
I pātaihia: F₂ ?
Whakautu:

F₁/A₁ =F₂/A₂
5/0,04 = F₂/ 0,10
125 = F₂/ 0,10

F₂ = (125)(0,10) = 12,5 N

2. Ko te radius o te tapahanga iti o te tīki waipēhi he 2 cm, ā, ko te radius o te tapahanga nui he 25 cm. E hia te kaha e pā ana ki te tapahanga iti hei hiki i tētahi motuka he 2000 kg te taumaha?
Kōrero:
E mōhiotia ana:
r₁ = 2 henimita = 0,02 mita
r₂ = 25 henimita = 0,25 mita
A₁ = (3,14)(0,02)² = 0,001256 m²
A₂ = (3,14)(0,25)² = 0,19625 m²
F₂ = w = mg = (2000)(9,8 m/s)²) = 19600 N
I pātaihia: F₁ ?
Whakautu:
F₁/A₁ =F₂/A₂
F₁/0,001256 = 19600/0,19625
F₁/0,001256 = 99.872,6

F₁ = 125,44 N

3. Ko te pēhanga mōrahi o te hū waipēhi he 10 atm. He aha te taumaha mōrahi (kg) ka taea te hiki mena he 20 cm te whānui o te putanga?
Kōrero:
E mōhiotia ana:
1 atm = 1,013 x 10⁵ N / m²
p _ine = 10 atm = (10)(1,013 x 10⁵ N / m²) = 10,13 x 10⁵ N / m²
F₁ = 10,13x10⁵ N / m²
A₁ = 1 m²
A₂ = (3,14)(0,10 mita)² = 0,0314 m²
I pātaihia: F₂ ?
Whakautu:
p = F/A, F rānei₁/A₁ =F₂/A₂
1013000/1 = F₂/ 0,0314
1.013.000 = F₂/ 0,0314

F₂ = 31.808 N

Papatipu mōrahi:
w = mg
31.808 = mita (9,8)
m = 3.245,7 kg

4. Tirohia te pikitia e whai ake nei!

Horahanga whakawhiti-wāhanga A₁ = 10cm²

Horahanga whakawhiti-wāhanga A₂ = 100cm²

Kāhua (F₁) me hoatu hei pupuri i te F₂ = 100 N kia taurite ai te pūnaha...

A. 1.000 Newton

B. 100 Newton

C. 10 Newton

D. 1 Newton

Kōrero

E mōhiotia ana:

Horahanga whakawhiti-wāhanga 1 (A₁) = 10 henemita²

Horahanga whakawhiti-wāhanga 2 (A₂) = 100cm²

Kāhua 2 (F₂) = 100 Niutona

I pātaihia: Kāhua 1 (F₁)

Whakautu:

Ko te taputapu kei te ahua i runga ake nei he tīki waipēhi. Ko te mahi a te tīki waipēhi e ahu mai ana i te ture a Pascal. E ai ki te ture a Pascal, ko te pēhanga e pā ana ki te wai ka tukuna e te wai ki ngā taha katoa, me te pēhanga ōrite e pā ana ki ngā wāhanga katoa o te wai.

Tātai pēhanga:

P = F / A

Whakaahuatanga tātai: P = pēhanga, F = kaha, A = horahanga mata.

Ko te pēhanga e pā ana ki te wai i roto i te ngongo iti (P₁) = F₁ / TO₁.
Ko te pēhanga e pā ana ki te wai i roto i te ngongo nui (P₂) = F₂ / TO₂

Te pēhanga o te wai i roto i te ngongo iti (P₁) he ōrite ki te pēhanga o te wai i roto i te ngongo nui (P₂).
P₁ =P₂
F₁ / TO₁ =F₂ / TO₂

F₁ / 10 cm²  = 100 N / 100 henemita²

F₁ / 10 = 1 N

F₁ = (10)(1 N)

F₁ = 10 Niutona

Ko te whakautu tika ko C.

5. Tirohia te pikitia i raro nei!

Mena ko te horahanga whakawhiti-wāhanga ko A₁ = 0,001 m² me A₂ = 0,1 m² , kātahi ka nui te kaha pēhanga i A₂ ko …

A. 100 N

B. 1.000 N

C. 10.000 N

D. 100.000 N

Kōrero

E mōhiotia ana:

Horahanga whakawhiti-wāhanga 1 (A₁) = 0,001 mita²

Horahanga whakawhiti-wāhanga 2 (A₂) = 0,1 mita²

Te kaha i runga i te horahanga whakawhiti-wāhanga 1 (F₁) = 100 Niutona

I pātaihia: Te kaha i runga i te horahanga whakawhiti-wāhanga 2 (F₂)

Whakautu:

E ai ki te Ture a Pascal, ko te pēhanga e pā ana ki te wai ka tukuna e te wai ki ngā taha katoa, ā, ko te nui o te pēhanga ka pā ki ngā wāhanga katoa o te wai.

P₁ =P₂
F₁ / TO₁ =F₂ / TO₂

100 N / 0,001 m² = F₂ / 0,1 m²

100 N / 0,001 = F₂ / 0,1

100.000 N = F₂ / 0,1

F₂ = (0,1)(100.000 N)

F₂ = 10.000 N

Ko te whakautu tika ko C.

6. Tirohia te pikitia!

Kei runga i te piston B tētahi waka, e 16.000 N te taumaha, e whakaaturia ana i te pikitia. Hei hiki i te waka, me whakamahi he kaha F o….

A. 50 N

B. 80 N

C. 200 N

D. 400 N

Kōrero

Whakaaturia ngā waeine katoa ki ngā waeine o te ao

E mōhiotia ana:

Taumaha waka (w) = 16.000 N

Horahanga mata B (A)_B) = 4000 henemita² = 4000 / 10.000 mita² = 4 / 10 mita² = 0,4 m²

Horahanga mata A (A_A) = 50 henemita² = 50 / 10.000 mita² = 0,005 m²

I pātaihia: Kāhua F

Whakautu:

Ka tatauhia te kaha F mā te whakamahi i te tātai ture a Pascal.

F/A_A = w / A_B

F / 0,005 m² = 16.000 N / 0,4 m²

F / 0,005 = 16.000 N / 0,4

F / 0,005 = 40.000 N

F = (40.000 N)(0,005)

F = 200 Newton

Ko te whakautu tika ko C.

7. Tirohia te pikitia o te taputapu waipēhi āhua-U i raro nei!
Ko te taumaha o te poraka X i runga i te ngongo iti hei pupuri i te taurite o te taputapu waipēhi ko….

A. 5 N
B. 25 N
C. 10.000 N
D. 25.000 N

Kōrero

E mōhiotia ana:
Ko te horahanga mata o te rango iti (A₁) = 5 henemita²
Ko te horahanga mata o te rango nui (A₂) = 100 henemita²
Te kaha o te taumaha o te poraka i runga i te rango nui (F₂) = 500 Niutona
Pātai: Te kaha o te kaha ā-papa o te poraka i runga i te ngongo iti (F₁)
Whakautu:

Ko te taputapu kei te ahua i runga ake nei he tīki waipēhi. Ko te mahi a te tīki waipēhi e ahu mai ana i te ture a Pascal. E ai ki te ture a Pascal, ko te pēhanga e pā ana ki te wai ka tukuna e te wai ki ngā taha katoa, me te pēhanga ōrite e pā ana ki ngā wāhanga katoa o te wai.

Ina pēhia te mata o te ngongo iti ki raro, ka pēhia hoki te wai i roto i te ngongo iti. Ka tukuna te pēhanga e pā ana ki te wai i roto i te ngongo iti ki te wai i roto i te ngongo nui. Ka pā te pēhanga ki te wai i roto i te ngongo nui ki te pēhanga o te wai i roto i te ngongo iti. Waihoki, ka tukuna te pēhanga e pā ana ki te wai i roto i te ngongo nui ki te wai i roto i te ngongo iti. Ka pā te pēhanga o te wai i roto i te ngongo iti ki te pēhanga e pā ana ki te wai i roto i te ngongo nui.

Tātai pēhanga:
P = F / A
Whakaahuatanga tātai: P = pēhanga, F = kaha, A = horahanga mata.

Ko te pēhanga e pā ana ki te wai i roto i te ngongo iti (P₁) = F₁ / TO₁.
Ko te pēhanga e pā ana ki te wai i roto i te ngongo nui (P₂) = F₂ / TO₂

Te pēhanga o te wai i roto i te ngongo iti (P₁) he ōrite ki te pēhanga o te wai i roto i te rango nui P₂).
P₁ =P₂
F₁ / TO₁ =F₂ / TO₂
F₁ / 5 henemita² = 500 N / 100 cm²
F₁ / 5 = 500 N / 100
F₁ / 5 = 5 N
F₁ = (5)(5) N
F₁ = 25 N
Ko te whakautu tika ko B.

8.
Kia aro ki te kaupapa paipa Pascal e whai ake nei!

Mena ko te kaha pēhi F₁ = 300 N. Te rahi o te kaha F₂ kia taurite ai te āhua….
A. 72 N
B. 1250 N
C. 1500 N
D. 3600 N
Kōrero
E mōhiotia ana:
Ko te horahanga mata o te rango iti (A₁) = 12 henemita²
Ko te horahanga mata o te rango nui (A₂) = 50 henemita²
Te rahi o te kaha pēhanga i runga i te ngongo iti (F₁) = 300 Niutona
Pātai: Te rahi o te kaha pēhanga i runga i te ngongo nui (F₂)

Whakautu:

Te pēhanga o te wai i roto i te ngongo iti (P₁) he ōrite ki te pēhanga o te wai i roto i te ngongo nui (P₂).
P₁ =P₂
F₁ / TO₁ =F₂ / TO₂
300 N / 12 henimita² =F₂ / 50 henemita²
300 N / 12 = F₂ / 50
25 N = F₂ / 50
F₂ = (50)(25) N
F₂ = 1250 N
Ko te whakautu tika ko B.

9.
Tirohia te pikitia e whai ake nei o te taputapu a Pascal!

Ko te rahi o te kaha (F) me whakamahi hei pupuri i te taputapu kia taurite ko….
A. 100 Newton
B. 250 Newton
C. 600 Newton
D. 4800 Newton
Kōrero
E mōhiotia ana:
Ko te horahanga mata o te rango iti (A₁) = 4 henemita²
Ko te horahanga mata o te rango nui (A₂) = 16 henemita²
Te rahi o te kaha ā-papa i runga i te ngongo nui (F₂) = 1000 Niutona
Pātai: Te rahi o te kaha i runga i te ngongo iti (F₁)
Whakautu:
Te pēhanga o te wai i roto i te ngongo iti (P₁) he ōrite ki te pēhanga o te wai i roto i te ngongo nui (P₂).
P₁ =P₂
F₁ / TO₁ =F₂ / TO₂
F₁ / 4 henemita² = 1000 N / 16 cm²
F₁ / 4 = 1000 N / 16
F₁ / 1 = 1000 N / 4
F₁ = 1000 N / 4
F₁ = 250 N
Ko te whakautu tika ko B.

Pūtake pātai:

Ngā Pātai Whakamātautau Pūtaiao ā-Motu mō te Kura Tuarua/Kura Tuarua Ihirama

Pātai Te ture a Pascal

1. Ko te horahanga whakawhiti-wāhanga o ia tīki waipēhi he 0,03 m² me te 0,12 m²Mena he 6 Newton te kaha whakauru, he aha te kaha whakaputa mōrahi?
(24 N)
2. Ko te radius o te tapahanga iti o te tīki waipēhi he 1,5 cm, ā, ko te radius o te tapahanga nui he 20 cm. E hia te kaha e pā ana ki te tapahanga iti hei hiki i tētahi motuka he 2200 kg te taumaha?
(121,3 N)

3. Ko te pēhanga mōrahi o te hū waipēhi he 14 atm. He aha te taumaha mōrahi (kg) ka taea te hiki mena he 30 cm te whānui o te putanga?
(10.224 kg)