Ngā tauira pātai mō te kaha ā-papa

9 Ngā Tauira o ngā Pātai mō te Āhua Ā-Toi

1. Ko te ōwehenga o ngā papatipu o ngā aorangi A me B he 2:3, ko te ōwehenga ia o ngā radius o ngā aorangi A me B he 1:2. Mēnā ko te taumaha o tētahi mea i runga i te aorangi A he w, ko te taumaha o te mea i runga i te aorangi B he….

A. 3/8 w

B. 3/4 w

C. 1/2 w

D. 4/3 w

E. 8/3 w

Kōrero

E mōhiotia ana :

Papatipu o te aorangi A (m _A ) = 2

Papatipu o te aorangi B (m _B ) = 3

Te whānui o te aorangi A (r _A ) = 1

Te whānui o te aorangi B (r _B ) = 2

Papatipu o te mea = m

Taumaha o tētahi mea i runga i te aorangi A = w

I pātaihia : te taumaha o te mea i runga i te aorangi B

Whakautu :

Ko te tātai mō te kaha ā-papa i ahu mai i te ture kaha ā-papa a Newton ko:

Whakaahuatanga: w = taumaha, G = pūmau ā-papatipu ao, M = papatipu o te aorangi, m = papatipu o te mea, r = tawhiti o te mea mai i te pokapū o te aorangi. Mena kei runga te mea i te mata o te aorangi, ko r = te pūtoro o te aorangi.

He rite tonu te taumaha o te mea, nō reira whakakapia te m ki te w/2G

Ko te whakautu tika ko A.

2. Ka whakarewaina poutū ake tētahi rōkete, ko tōna taumaha he w, mai i te mata o te whenua. Mena ko D te whānui o te whenua, kāti, i te wā e 0,5 D te teitei o te rōkete mai i te mata o te whenua, ko te taumaha o te rōkete ko...

A. 4 w

B. 2 w

C. w

D. 0,5 w

E. 0,25 w

Kōrero

E mōhiotia ana:

Taumaha rōkete = w

Te pūtoro o te whenua = te tawhiti mai i te pokapū o te whenua = R

Te whānui o te Ao = D = 2R

Pātai: Te taumaha o te rōkete ina eke te rōkete ki te teitei o te 0,5 D mai i te mata o te whenua.

Whakautu:

0,5 D = 0,5 (2R) = R

Ko te tawhiti o te rōkete mai i waenganui o te whenua = te pūtoro o te whenua + te tawhiti o te rōkete mai i te mata o te whenua = R + R = 2R

Ko te taumaha te kaha ā-papa e pā ana ki tētahi mea. He rite whakamuri te kaha ā-papa (F) ki te tapawhā o te tawhiti mai i te pokapū o Papatūānuku (R), nō reira he rite whakamuri te taumaha ki te tapawhā o te tawhiti.

Ko te whakautu tika ko E.

3. Ripanga raraunga ā-tinana mō te mea A me te mea B e pā ana ki te mata o te whenua, ko te radius he R. Ko te whakatairite i te kaha o te papa tōpana o te mea A ki te mea B ko...

A. 2 : 1

B. 4 : 1

C. 1 : 4

D. 9 : 4

E. 4 : 9

Kōrero

E mōhiotia ana :

Papatipu o te mea A (m _A ) = 1

Papatipu o te mea B (m _B ) = 2

Ko te tawhiti o te mea A mai i te aorangi o Papatūānuku (r _A ) = 1

Ko te tawhiti o te mea B mai i te aorangi o Papatūānuku (r _B ) = 2

Pātai : te whakatairite i te kaha o te papa tōpana o te mea A (g _A ) me te mea B (g _B )

Whakautu :

Ko te tātai mō te kaha o te papa tōpana o te Ao:

Whakaahuatanga: g = te kaha o te papa tōpana o te whenua, G = te pūmau tōpana ao, m _B = te papatipu o te whenua, r _B = te pūtoro o te whenua

Te whakataurite i te kaha o te papa tōpana o te mea A (g _A ) me te mea B (g _B )

karamu _A : karamu _B

G: G/2

1: 1/2

2: 1

Ko te whakautu tika ko A.

4. Mena ko te tūranga o te mea A he 1/2 R i runga ake i te mata o te whenua, ko te tūranga o te mea B he 2R i runga ake i te mata o te whenua (R = te radius o te whenua), ko te ōwehenga o ngā kaha o te papa tōpana e pāngia ana e ngā mea A me B ko...

A. 1 : 8

B. 1 : 4

C. 2 : 3

D. 4 : 1

E. 8 : 1

Kōrero

E mōhiotia ana :

Te tawhiti o te mea A mai i te pokapū o te whenua = 0,5R + R = 1,5R = 1,5

Te tawhiti o te mea B mai i te pokapū o te whenua = 2R + R = 3R = 3

Pātai : Te whakataurite i te kaha o te papa tōpana e pāngia ana e ngā mea A me B

Whakautu :

Te whakataurite i te kaha o te papa tōpana e pāngia ana e ngā mea A me B :

Ko te whakautu tika ko D.

5. Ka pāngia te kairangi moana i runga i te mata o te whenua e te papa tōpana o te g, nō reira, ina tae ia ki te teitei o te 1,5 R mai i te mata o te whenua, ka pāngia ia e te papa tōpana o te …. (R = te pūtoro o te whenua).

A. karamu/0,50

B. g/2,25

C. g/6,25

D. g/7,50

Hei tauira/6,00

Kōrero

He rite tonu te kaha ā-papa (F) ki te papa ā-papa (g). Ka nui ake te kaha ā-papa, ka nui ake te papa ā-papa. He rite tonu te kaha ā-papa (F) e pāngia ana e tētahi mea ki te 1/r₂ ^, ko r = te tawhiti o tētahi mea mai i te pokapū o te whenua. Nā te mea he rite tonu te kaha ā-papa ki te 1/r₂ ^, he rite tonu hoki te papa ā-papa (g) ki te 1/ ^r₂.

Ina kei runga i te mata o te whenua te kairangi moana i te tawhiti R (R = te radius o te whenua) mai i te pokapū o te whenua, ko te papa tōpana e pā ana ki a ia ko g. Ka taea tēnei te whakamārama mā te tātaitanga e whai ake nei:

He ōrite te āpure tōpana (g) ki te 1/R₂ ^. Mēnā ko R = 1, ko 1 / R₂ ⁼ 1 / 1₂ ⁼ 1 / 1₂ = 1. Mēnā ko te tawhiti o te kairangi moana mai i te pokapū o te whenua = 1, ka pāngia ia e te āpure tōpana o = (g)(1) = g.

Ko te tawhiti o te kairangi i te pokapū o te whenua he 1,5R = 1,5(1) = 1,5 kātahi ka pāngia ia e te papa tōpana o: 1 / R2 ⁼ 1 / 1.52 ⁼ 1 / 2,25. Nō reira, ki te mea ko te tawhiti o te kairangi i te pokapū o te whenua he 1,5 kātahi ka pāngia ia e te papa tōpana o = (g)(1 / 2,25) = g / 2,25

Ko te whakautu tika ko B.

6. Ko te whakatairite i te kaha o te papa tōpana o te whenua mō ngā mea e rua, ko tētahi kei runga i te mata o te whenua, ko tētahi kei te teitei o te ½ R mai i te mata o te whenua (R = te pūtoro o te whenua) ko....

A. 1 : 2

B. 2 : 3

C. 3 : 2

D. 4 : 9

E. 9 : 4

Kōrero

E mōhiotia ana :

Te tawhiti o te mea A mai i te pokapū o te whenua (r _A ) = R = 1

Ko te tawhiti o te mea B mai i te pokapū o te whenua (r _B ) = 0,5R + R = 1,5R = 1,5

Pātai : Te whakataurite i te kaha o te papa tōpana e pāngia ana e ngā mea A me B

Whakautu :

Te whakataurite i te kaha o te papa tōpana e pāngia ana e ngā mea A me B :

Ko te whakautu tika ko E.

7. E hia te kaha o te kaha ā-papa i waenganui i te whenua me tētahi mea kei runga ake i te mata o te whenua? Papatipu o te whenua = 5,97 x 10²⁴ kg, te papatipu o te mea = 1000 kg, te radius o te whenua = 6,38 x 10⁶ mita. He aha te taumaha, te kaha ā-papa rānei o te whenua e pā ana ki te mea mēnā ka tatauhia mā te whakamahi i te tātai ture tuarua a Newton, ko te whakaterenga ā-papa (g) = 9,8 m/s² ?
Kōrero
E mōhiotia ana:
Te taumaha o te whenua (m_B) = 5,97 x 10²⁴ kg
Papatipu o te mea (m_b) = 10³ kg
Te pūtoro o te Ao (r) = 6,38 x 10⁶ mita
Pūmau ā-papatipu ao (G) = 6,67 x 10^-11 N m² /kg²
Te whakaterenga nā te kaha ā-papa (g) = 9,8 m/s²
I pātaihia: e hia te rahi o te kaha ā-papa?
Whakautu:

Te rahi o te kaha ā-papa i waenganui i te whenua me tētahi mea (mā te whakamahi i te tātai ture ā-papa a Newton):
Whakaahuatanga w = F = te kaha ā-papatipu, G = te pūmau ā-papatipu whānui, mB = te papatipu o te whenua, mb = te papatipu o te mea, r = te tawhiti i waenganui i te pokapū o te whenua me te pokapū o te mea. Kei runga i te mata o te whenua te mea, ko r = te radius o te whenua.
Taumaha o tētahi mea (mā te whakamahi i te tātai ture tuarua a Newton):
w = mg = (1000)(9,8) = 9800 Ngā Niutona
Whakatauritea tēnei hua tātaitanga ki te mea o mua. He tata rite ngā uara nā te whakaawhiwhi. Ka taea te whakatau ko te taumaha o tētahi mea i runga i te mata o te Ao ko te kaha o te kaha ā-papa o te Ao e pā ana ki tētahi mea i runga i te mata o te Ao.

8. He aha te kaha ā-papa i waenganui i te whenua me tētahi mea kei te teitei o te 10.000 mita i runga ake i te whenua? Papatipu o te whenua = 5,97 x 10²⁴ kg, te papatipu o te mea = 1000 kg, te radius o te whenua = 6,38 x 10⁶ mita.
Kōrero:

Whakatauritea ki te whakautu nama 1. Ko te tawhiti atu i te whenua, ko te iti iho o te taumaha o te mea.

9. He taumaha te rōkete w i whakarewaina poutū ake i te mata o te whenua. Mena ko D te whānui o te whenua, tātaihia te taumaha o te rōkete ina eke te rōkete ki te teitei o te 2D mai i te mata o te whenua.
Kōrero
E mōhiotia ana:
D = te whānui o te whenua, R = te pūtoro o te whenua, 1 D = 2 R, 2 D = 4 R
Pātai: He aha te taumaha o te rōkete ina kei te teitei o te 2D?
Whakautu:
He rite whakamuri te kaha o te taumaha, te kaha ā-papa rānei, ki te tapawhā o te tawhiti. Mā te pāngarau:

Ngā pātai mō te kaha ā-papa

1. E hia te kaha o te kaha ā-papa i waenganui i te whenua me tētahi mea kei runga ake i te mata o te whenua? Papatipu o te whenua = 5,97 x 10²⁴ kg, te papatipu o te mea = 2000 kg, te radius o te whenua = 6,38 x 10⁶ mita. He aha te taumaha, te kaha ā-papa rānei o te whenua e pā ana ki te mea mēnā ka tatauhia mā te whakamahi i te tātai ture tuarua a Newton, ko te whakaterenga ā-papa (g) = 9,8 m/s² ?
2. He aha te kaha ā-papa i waenganui i te whenua me tētahi mea kei te teitei o te 100.000 mita i runga ake i te whenua? Papatipu o te whenua = 5,97 x 10²⁴ kg, te papatipu o te mea = 2000 kg, te radius o te whenua = 6,38 x 10⁶ mita.
3. He taumaha te rōkete w i whakarewaina poutū ake i te mata o te whenua. Mena ko D te whānui o te whenua, tātaihia te taumaha o te rōkete ina kei te teitei 3D te rōkete mai i te mata o te whenua.