Tauira o te whakaterenga ā-papa

4 Ngā Tauira o ngā Raru Whakaterenga Ā-papa

1. E hia te tere o te whakaterenga ā-papa i runga i te mata o te marama? Ko te papatipu o te marama = 7,35 x 10²² kg, te radius o te marama = 1.740.000 mita, te pūmau ā-papatipu ao (G) = 6,67 x 10^-11 N m² /kg²
Kōrero
Te tātai ture tuarua a Newton:

Whakaahuatanga: G = te pūmau ā-papatipu ao, M = te papatipu o te whenua, m = te papatipu o te mea, r = te tawhiti mai i waenganui o te whenua ki te mea. Mena kei runga i te mata o te whenua te mea, kei te taha rānei o te mata o te whenua, ko r = te pūtoro o te whenua.

Whakamahia tēnei tātai hei tatau i te whakaterenga nā te kaha ā-papatipu (g) ​​i runga i te mata o tētahi aorangi, ko M = te papatipu o te aorangi, te amiorangi, te whetu me ētahi atu, ā, ko r = te pūtoro o te aorangi, te amiorangi, te whetu me ētahi atu.
He aha te rahi o te whakaterenga ā-papa i runga i te mata o te marama?

2. Ko te tere ā-papa ā-papa toharite i runga i te mata o te Ao he ōrite ki g. I te teitei o R (R = te radius o te whenua) mai i te mata o te whenua, ko te rahi o te whakaterenga ā-papa o te whenua... e whakaatuhia ana i roto i g.
Kōrero
He rite whakamuri te tere o te kaha ā-papa ki te tapawhā o te tawhiti:

R = te pūtoro o te whenua. I te teitei o R mai i te mata o te whenua = i te teitei o 2R mai i waenganui o te whenua. Mena ka kiia ko R he 1, ko 2R = 2(1) = 2.
I te teitei R mai i te mata o te whenua, ko te uara o te whakaterenga nā te kaha ā-papa he ¼ karamu. Mena ko te karamu = 9,8 m/s² Nō reira, i te teitei R mai i te mata o te whenua, ko te uara o te whakaterenga nā te kaha ā-papa he 2,45 m/s².

3. Ko te tere ā-papa ā-papa toharite i runga i te mata o te Ao ko gI te teitei o te 2D (D = te whānui o te whenua) mai i te mata o te whenua, ko te rahi o te whakaterenga ā-papa ko...
A. g
B. 1/2 karamu
C. 1/4 karamu
D. 1/8 karamu
E. 1/16 karamu
Kōrero:

He rite te kaha ā-papa ki te whakaterenga nā te kaha ā-papa. He rite whakamuri te kaha ā-papa ki te tapawhā o te tawhiti, nō reira he rite whakamuri anō hoki te whakaterenga nā te kaha ā-papa ki te tapawhā o te tawhiti.
Whakaahuatanga: g = whakaterenga ā-papa, r = tawhiti o tētahi wāhi mai i te pokapū o te whenua.
Kei te tawhiti R te mata o te Ao mai i te pokapū o te Ao, ko R = te radius o te Ao. Mena ko R te 1, ko te whakaterenga nā te kaha ā-papa i runga i te mata o te Ao ko:
E whakaatu ana tēnei hua i runga i te mata o te Ao, ko te whakaterenga ā-papa he g. He aha te whakaterenga ā-papa i te teitei 2D?
D = 2R. 2D = 2(2R) = 4R. Ko R he 1, nō reira ko 4R = 4
Ko te whakautu tika ko E.

4. Mena ko te tūranga o te mea A he 2R i runga ake i te mata o te whenua, ko te tūranga o te mea B he 3R 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 : 9
E. 9 : 4
Kōrero:
R = te pūtoro o te whenua. Ko te uara o R he 1, nō reira ko 2R = 2, ā, ko 3R = 3.
Ko te kaha o te papa tōpana (g) i te teitei o te 2R i runga ake i te mata o te whenua ko:
Ko te kaha o te papa tōpana (g) i te teitei o te 3R i runga ake i te mata o te whenua ko:

Ko te ōwehenga o te karamu i ngā teitei 2R me te 3R ko:

Ko te whakaterenga nā te kaha ā-papa i te teitei o te 2R he 2,25 ngā wā nui ake i te whakaterenga nā te kaha ā-papa i te teitei o te 3R.
Ko te whakautu tika ko E.

Ngā Pātai Whakaterenga Ā-Toi

1. Tātaihia te rahi o te whakaterenga ā-papa i runga i te mata:
(a) Rā (b) Mercury (c) Venus (d) Mars (e) Jupiter (f) Saturn (g) Uranus (h) Neptune
Ngā raraunga e hiahiatia ana:
Pūmau ā-papatipu ao (G) = 6,67 x 10^-11 N m² /kg²
Papatipu o te rā = 1,99 x 10³⁰ kg, te pūtoro o te rā = 2,44 x 10⁶ m
Papatipu o Mercury = 3,30 x 10²³ kg, te pūtoro o Mercury = 6,96 x 10⁸ m
Papatipu o Hine-ā-rangi = 4,87 x 10²⁴ kg, te pūtoro o Hine-tū = 6,05 x 10⁶ m
Papatipu o Mātaota = 6,42 x 10²³ kg, te pūtoro o Mātaota = 3,40 x 10⁶ m
Papatipu o Hūpiter = 1,90 x 10²⁷ kg, te pūtoro o Hūpiter = 6,91 x 10⁷ m
Papatipu o Hānuere = 5,69 x 10²⁶ kg, te pūtoro o Hānuere = 6,03 x 10⁷ m
Papatipu o Uranus = 8,66 x 10²⁵ kg, te radius o Uranus = 2,56 x 10⁷ m
Papatipu o Neptun = 1,03 x 10²⁶ kg, te pūtoro o Neptune = 2,48 x 10⁷ m
Pūtake raraunga mō te papatipu me te radius o te rā me ngā aorangi

2. Ko te tere ā-papa ā-papa toharite i runga i te mata o te Ao he ōrite ki g. Tātaihia te whakaterenga nā te kaha ā-papa i te teitei o ……. mai i te mata o te whenua:
(a) 2R (b) 3R (c) 4R (d) 5R (e) 6R (f) 7R (g) 8R (h) 9R (i) 10 R
Āhua i roto g me ngā tau!