Te kaha ā-papatipu Taumaha – Ngā Raru me ngā Otinga

5 Te kaha ā-papatipu Taumaha – Ngā Raru me ngā Otinga

1. He aha te te kaha o te kaha ā-papa e pā ana ki tētahi mea i te mata o te Ao? papatipu = 5.98x10²⁴ kg, te papatipu o te mea = 1000 kg, ko te radius o te Ao he 6.38 x 10⁶ m.

Mōhiotia:

Te taumaha o te whenua (m_E) = 5.98 x 10²⁴ kg

Papatipu o te mea (m_o) = 1000 kirokaramu

Te radius o te Ao (r_E) = 6.38 x 10⁶ m

Pūmau whānui (G) = 6.67 x 10^-11 N m² /kg²

Whakaterenga na te kaha o te kaha (g) = 9.8 m/s²

E hiahiatia ana: te kaha o te kaha ā-papa

Rongoā:

w = taumaha, F = kaha, G = pūmau whānui, m_E = Te papatipu o te whenua, m_o = ote papatipu o te mea, r = te tawhiti i waenganui i te pokapū o Papatūānuku me te mea.

Kei te mata o Papatūānuku te mea, nō reira ko r = tte radius o te Ao

Te taumaha o te mea (Te ture tuarua o te nekehanga a Newton):

w = mg

w = (1000 kg)(9.8 m/s²)

w = 9800 N

2. He aha te kaha o te kaha ā-papa e pā ana ki tētahi mea i te 10,000 mita i runga ake i te mata o te Ao? Papatipu o te Ao = 5.98 x 10²⁴ kg, te papatipu o te mea = 1000 kg, ko te radius o te Ao he 6.38 x 10⁶ m.

Rongoā:

3. Ko te taumaha o tētahi waka mokowhiti ko w. Mena ko D te whānui o Papatūānuku, tātaihia te taumaha o te waka mokowhiti ina kei te 2D te teitei o te waka mokowhiti i runga ake i te mata o Papatūānuku.

Mōhiotia:

D = te whānui o te Ao,

R = te pūtoro o te Ao

1 D = 2 R, 2 D = 4 R

Hiahia: te taumaha o te waka mokowhiti i te 2D i runga ake i te mata o te Ao?

Rongoā:

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

Mōhiotia:

Te taumaha o te aorangi A (m_A) = 2

Te taumaha o te aorangi B (m_B) = 3

Te pūtoro o te aorangi A (r_A) = 1

Te whānui o te aorangi B (r)_B) = 2

Papatipu o te mea = m

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

Hiahia: Te taumaha o te mea i runga i te aorangi B

Rongoā:

Ko te whārite o te kaha o te taumaha mai i te ture ā-papatipu a Newton:

w = taumaha, G = pūmau ā-papa, M = papatipu o te aorangi, m = papatipu o te mea, r = te tawhiti i waenga i te mea me te aorangi. Mena kei runga te mea i te mata o te aorangi, ko te r = te radius o te aorangi.

Te taumaha o te mea i runga i te aorangi A:

Te taumaha o te mea i runga i te aorangi B:

He rite te papatipu o te mea, nō reira me whakakapi te m ki te w/2G.

5. Ka whakarewaina poutū mai i te mata o Papatūānuku tētahi rōkete, ko tōna taumaha he w. Ko D te whānui o Papatūānuku. Ina eke te rōkete ki te teitei o te 0.5 D i runga ake i te mata o Papatūānuku, he aha te taumaha o te rōkete?

Mōhiotia:

Taumaha o te rōkete = w

Ko te radius o Papatūānuku = te tawhiti mai i te pokapū o Papatūānuku = R

Te whānui o te whenua = D = 2R

Hiahia: Te taumaha o te rōkete i te teitei o te rōkete i te 0.5 D i runga ake i te mata o te Ao.

Rongoā:

0.5 D = 0.5 (2R) = R

Ko te tawhiti o te rōkete mai i te pokapū o Papatūānuku = te radius o Papatūānuku + te radius o te rōkete mai i te mata o Papatūānuku = R + R = 2R

Ko te taumaha te kaha o te papatipu e pā ana ki tētahi mea. He rite whakamuri te kaha o te papatipu (F) ki te tapawhā o te tawhiti mai i te pokapū o te whenua (R) kia rite whakamuri ai te taumaha ki te tapawhā o te tawhiti.

1. Ngā raruraru me ngā otinga o te ture a Newton mō te kaha ā-ao
2. Ngā kaha ā-papa, ngā raruraru taumaha, me ngā otinga
3. Te whakaterenga nā ngā raruraru ā-papa me ngā otinga
4. Ngā raruraru me ngā otinga o te amiorangi tukutahi-whenua
5. Ngā raruraru me ngā otinga o te ture a Kepler ngā raruraru me ngā otinga