Te ture a Newton mō te kaha ā-ao

He tuhinga mō te ture ā-papatipu a Newton

I roto i te kaupapa o te ture a Newton, i akohia ko ia mea e okioki ana i te tīmatanga ka neke, ko ia mea rānei e neke ana i te tīmatanga ka okioki mēnā he "mea" e neke ana, e aukati ana rānei i te mea. Ka kiia tetahi mea he "kaha". He aha te take e taka ai, e neke ai rānei te hua ki te mata o te whenua i muri i te tukunga mai i te kakau? E kī ana te ture a Newton mēnā ka neke te hua, me whai kaha te hua. Ko te kaha e taka ai te hua, tetahi mea rānei ki te mata o te whenua ka kiia ko te te kaha o te kaha ā-papa.

Ko te raruraru o ngā mea e hinga ana e pā ana ki te kaha o te papatipu, e akohia ana e koe i tēnei wā, kua whakaarohia, kua akohia hoki e Isaac Newton, he kaipūtaiao Piritana. Ko tēnei take i whakaarohia e Newton kua noho mai i Kariki Tawhito. E rua ngā take matua kua rangahaua e ngā Kariki, i mua noa atu i te whānautanga o Newton. Ko te pātai e pātaihia tonutia ana ko te take e hinga tonu ai ngā mea ki te mata o te whenua me te pehea e neke ai ngā aorangi, tae atu ki te rā me te marama. I kite ngā Kariki i taua wā i te āwangawanga mō ngā mea e hinga ana me ngā nekehanga o ngā aorangi he mea rerekē e rua. Nō reira, i haere tonu tae noa ki te wā o Newton. Nō reira, ko tā Newton i hanga i runga i te mahi a ngā tāngata i mua i a ia. Ko te mea e wehewehe ana i a Newton me ngā tāngata i mua i a ia, ko te kitenga o Newton i te uaua o ngā mea e hinga ana me te nekehanga o ngā aorangi i puta mai i te mea kotahi anake, ā, me whakarongo ki te ture kotahi. Arā, i tautohe a Newton ko te kaha e meinga ai ngā mea kia hinga ki te mata o te whenua ko te kaha kotahi, e meinga ai te marama kia neke haere i te whenua.

Te whanaungatanga i waenga i te kaha o te papatipu ki te tawhiti me te papatipu

I te whakatakoto i te ture o te kaha ā-papa, i whakaritea e Newton te tere o te hinganga o ngā hua ki te mata o te whenua me te tere pūtahi o te marama i te wā e huri ana i te whenua. E ai ki a Newton, ko te tere e pā ana ki te hinganga o ngā hua me te tere pūtahi o te marama e huri ana i te whenua, i puta mai i te kaha kotahi, arā, te kaha ā-papa o te whenua. E kī ana a Newton ko te tere o te marama i te wā e huri ana i te whenua he rite ki te 1/r2, ko r = te tawhiti i waenganui i te pokapū o te whenua me te pokapū o te marama = 3.84 x 108 m. Ko te tere o te hinganga o ngā hua he rite ki te 1/R.², ko R = te tawhiti i waenganui i te pokapū o te whenua me te pokapū hua. Kei te tata te hua ki te mata o te whenua, nō reira ko R = R_F, kei hea a R_E = te pūtoro o te whenua = 6.37 x 10⁶ m. Nō reira, ko te whakataurite i waenga i te whakaterenga o te marama (a_M) me te whakaterenga hua (g):

Nā, ko te whakaterenga ā-pokapū o te marama:

a_M = (2.75 x 10^-4)(g) = (2.75 x 10^-4)(9.8 m/h²) = 2.7 x 10^-3 m / s²

I rerekē anō te tatau a Newton i te whakaterenga ā-pokapū o te marama. E mōhiotia ana ko te wā porowhita o te marama, ko te wā rānei o te marama hei mahi i te hurihanga kotahi = 27.3 rā = 2.36 x 10⁶ hēkona. Ko te roa o te ara e haerehia ana e te marama = te porowhita o te porowhita o te marama = 2 (3.14) (r) ko r = te tawhiti i waenganui i te pokapū o te marama me te pokapū o te whenua. Ko te whakaterenga pokapū o te Marama:

Ko te whakaterenga ā-pokapū o te marama i whiwhihia i roto i tēnei tātaitanga he rite tonu ki ngā hua o ngā tātaitanga o mua. E kī ana te Ture Tuarua a Newton he rite te kaha ki te whakaterenga (F = ma). E whakaatu ana ngā tātaitanga o runga ake nei he rite te whakaterenga ki te 1/r² he rite whakamuri rānei te whakaterenga ki te tapawhā o te tawhiti (r²Nō reira, ka taea te whakatau ko te kaha ā-papa he rite ki te 1/r² he rite whakamuri rānei te kaha ā-papa ki te tapawhā o te tawhiti. Mā te pāngarau:

Haunga te tirotiro i te whanaungatanga i waenga i ngā kaha ā-pū me te tawhiti i waenga i ngā mea, i tirotirohia anō hoki e Newton te whanaungatanga i waenga i ngā kaha ā-pū me te papatipu o ngā mea. E kī ana te Ture Tuatoru a Newton, mēnā he kaha mahi, he kaha tauhohenga anō hoki. He rite te rahi o te kaha mahi me te kaha tauhohenga, ā, he rerekē te ahunga (mahi-F = tauhohenga -F, he tohu kino e tohu ana he rerekē te ahunga o te kaha). Mēnā ka kukume te kaha ā-pū o te whenua i te hua, ka kukume anō hoki te kaha ā-pū o te hua i te whenua. Ka mahi te kaha ā-pū o te whenua ki te hua, engari ka mahi te kaha ā-pū o te hua ki te whenua. Waihoki, ko te kaha ā-pū i waenga i te whenua me te marama. Ko te kaha ā-pū o te whenua me te kaha ā-pū o te hua, te kaha ā-pū rānei me te kaha ā-pū o te marama, he kaha tauhohenga. Nā te mea he rite te kaha ki te papatipu (F = ma) ā, nā te mea he rite te rahi o te kaha mahi me te kaha tauhohenga, me rite te kaha ā-pū i waenga i ngā mea e rua ki te papatipu o ngā mea e rua. I roto i te pāngarau:

Te ture a Newton mō te kaha ā-ao

E ai ki te ture ā-papatipu a Newton, ka kukume tetahi i tetahi i roto i ngā mea katoa o te ao whānui, ā, he rite te kukume i waenga i ngā mea ki tō rātou papatipu, ā, he rite whakamuri ki te tapawhā o tō rātou tawhiti. Mēnā he m ngā papatipu e rua o ngā mea₁ me te m₂ e wehea ana e te tawhiti r, ko te rahi o te kaha ā-papa i waenganui i ngā mea e rua ko:

G = te pūmau ā-papatipu (6.673 x 10^-11 Nm²/kg²). Ka inehia a G mā te whakamātautau.

F₁₂ ko te kaha ā-papa e pā ana ki a m₁ i te m₂ i a F₂₁ ko te kaha ā-papa e pā ana ki a m₂ i te m₁. F₁₂ e mahi ana ki m₂ ā, ka kumea a m₂ ki te taha m₁, ko F ia₂₁ e mahi ana ki m₁ ā, ka kumea a m₁ ki te taha m₂. F₂₁ me F₁₂ he rite te rahi, he rite te ahunga. Nō reira, ko F₂₁ me F₁₂ he takirua mahi-tauhohenga. ko r te tawhiti i waenga i ngā pokapū o m₁ me te pokapū o m₂. Te pokapū o m₁ kei waenganui o te mea, pērā anō hoki te pokapū o m₂. Mena ka whakahuatia a r i roto i te km, ka hurihia tuatahitia ki ngā mita (waeine pūnaha ā-ao).

Tauira raruraru 1 (te kaha ā-papa i waenga i ngā matūriki e 2)

Tātaihia te kaha ā-papatipu i waenganui i ngā ākonga e rua, he 30 kg te taumaha o ia ākonga, he 40 kg te taumaha, ā, he 1 mita te tawhiti.

otinga

He iti rawa te rahi o te kaha ā-papa, ā, kāore ngā mea e rua e kukume tetahi ki tetahi.

Tauira raruraru 2 (te kaha ā-papa i waenga i ngā matūriki e 2)

Tātaihia te kaha ā-papatipu katoa e pāngia ana e m² nā te kaha ā-papa e pā ana ki te m1 i te m² me te kaha ā-papa i pā ki a m³ i te m². Te tawhiti i waenga i ngā pokapū m¹ me te m² he 2 mita, ā, ko te tawhiti i waenga i ngā pokapū he m² me te m³ he 1 mita.

Rongoā:

Te kaha o te taumaha o m₁ i te m₂:

Te kaha o te taumaha o m₃ i te m₂:

Ko te kaha ā-papatipu katoa e pāngia ana e m₂:

Tapeke fg = (6.673 – 1.668) x 10^-11 N = 5.005 x 10^-11 N. I te ahua i raro nei, ko te F₃₂ he roa ake te pere i te F₁₂ ngā pere. Nō reira, ka haere te ahunga o te kaha ā-papatipu katoa ki te m₃.

Tauira raruraru 3 (kaha katoa o te taumaha = kore):

E rua ngā pōro A me B, ko te taumaha o ia pōro he m me te 5 m. He rite te whānui o ngā pōro e rua. Mena he kore te kaha ā-papa i waenganui i te pōro A me te pōro B, ko te tawhiti o taua pūwāhi mai i te mata o te pōro A ko …

Rongoā:

Ko te whānui o ngā pōro A me B he 1 mita, nō reira ko te pūtoro o ngā pōro A me B he 0.5 mita. Ko te tawhiti i waenganui i ngā pokapū o ngā pōro A me B he 6 mita.

Ka whakatakotoria e mātou he matūriki whakamātautau he papatipu m tōna ki tētahi pūwāhi kei waenganui i te pōro A me te pōro B.

F_A = te kaha ā-papatipu e pā ana ki te pōro A ki te matūriki whakamātautau (te ahunga o te ā-papatipu ki te pōro A).

F_B = te kaha ā-papa e pā ana ki te pōro B ki te matūriki whakamātautau (te ahunga o te ā-papa ki te pōro B).

Nō reira, ko te kaha ā-papa e pāngia ana e te matūriki whakamātautau he kore, kāti ko F_A =F_B (F_A me F_B he ahunga whakahāwea).

Whakamahia te tātai tapawhā hei whakatau i te uara o x

Nō reira x = 4.88 mita

4.88 m – 0.5 m = 4.38 m. Kore te kaha ā-papa, 4.38 mita mai i te mata o te pōro A. He aha te tawhiti mai i te mata o te pōro B?

Te ine i te pūmau taumaha ā-ao (G)

Hei kimi i te taumaha o tō tinana, me tū noa koe i runga i tētahi tauine, kātahi ka pānui i te tauine o tō taumaha tinana. He māmā noa te ine i tō taumaha tinana. Āe, me pēhea te ine i te taumaha o te whenua? Kāore he tauine nunui e whakamahia ana hei ine i te taumaha o te whenua. Ki te kore he tauine, kāore e taea te ine i te taumaha o te whenua mā te whakamahi i ēnei tauine nā te mea kei te neke tonu te whenua i ngā wā katoa. Ka mōhiotia te taumaha o te whenua mā roto i ngā tātaitanga i muri i te ine i te pūmau ā-papatipu ao (G) mā te whakamātautau.

Taumaha

Ko te taumaha o tētahi mea ko te kaha tōpana katoa e pā ana ki tētahi mea nā te kaha tōpana e pā ana ki taua mea. Mēnā kei runga ake i te mata o te whenua, i te mata rānei o te whenua te mea, kāti ka warewarehia e tātou te kaha tōpana e haria ana e ētahi atu mea o te ao. Whakaarohia te taumaha o tētahi mea hei kaha tōpana o te whenua e pā ana ki taua mea.

w = te taumaha o te mea, m_E = te papatipu o te whenua, m = te papatipu o te mea, R_E = te pūtoro o te whenua.

Mena kei runga ake te teitei o te mea i te mata o te whenua i te teitei h (kei runga ake ngā mea i tētahi teitei pēnei i te papa, hei tauira), kei runga ake rānei i te mata o te whenua i te tawhiti r, ko r = R_E + h,

ko te kaha ā-papa e pā ana ki te mea, ki te taumaha rānei o te mea, koia tēnei:

E whakaatu ana tēnei whārite ka heke te taumaha o tētahi mea ki te tapawhā o te tawhiti mai i te pokapū o te whenua. Nō reira, ka heke te taumaha o ngā mea i te tawhiti atu i te mata o te whenua.

Te whakaterenga o te kaha ā-papa

I runga i te ture tuarua a Newton, e mōhio ana tātou ko te taumaha o tētahi mea te kaha e meinga ai te mea kia tere te hinganga kore utu (te tere ā-papa):

w = mg

Whakakotahitia ngā whārite e rua, arā, w = F g me w = mg:

E whakamārama ana tēnei whārite i te whakaterenga ā-papa e pāngia ana e tētahi mea i tētahi teitei i runga ake i te mata o te whenua. Mā tēnei whārite, e mōhiotia ana ka heke te whakaterenga ā-papa i te pikinga ake o te teitei, ā, kāore e whakawhirinaki ki te papatipu o ngā mea e taka noa ana.

Te whakaterenga o te kaha ā-papa o ngā mea kei runga ake i te mata o te whenua, kei runga ake rānei i te taumata whenua:

Ka taea te tatau i te papatipu o te whenua mā te whakarerekē i te whārite i runga ake nei ki:

Tātaihia te papatipu o te whenua mā te whakamahi i tēnei whārite!

Ngā Raru me ngā Otinga

1. E rua ngā mea m₁ me te m₂ he 6 kg te taumaha o ia mea, ā, he 9 kg te taumaha, he 5 cm te tawhiti e wehea ana. He ahanoa m₃ = 1 kg te rahi kei waenganui i ngā mea e rua. Mēnā ko te kaha ā-papa e pāngia ana e m₃ = 0 kātahi ka tawhiti m₃ mai i te m1 ko …

Te kaha ā-papatipu = 0 mēnā ko F₁₃ =F₂₃.

a = -1, b = -20, c = 50

Whakamahia te tātai tapawhā:

Kāore e taea te kī he kino ngā hua. Nō reira, x = r₁₃ = tawhiti m₃ me te m₁ = 2.25cm.

2. E 60 cm te tawhiti o ngā mea e rua, a A rāua ko B. Ko te taumaha o A he 24 kg, ā, ko te taumaha o B he 10 kg. Kei hea te tūnga o tētahi pūwāhi he kaha te papa tōpana ōrite ki te kore?

Papa tōpana = 0 mēnā he karamu_A = karamu_B.

ki = 7

b = -1440

c = 43200

Whakamahia te tātai tapawhā:

x = r_A = 169.25 henimita rānei

x = r_A = 36.46cm