Ngā tukinga tino ngāwari
Ka kiia te tukinga o ngā mea e rua he tukinga tino pīwariwari mēnā he ōrite te nekehanga, te pūngao nekeneke rānei o ia mea i mua i te tukinga ki te nekehanga me te pūngao nekeneke o ia mea i muri i te tukinga. Arā, ka tika te ture tiaki nekehanga me te ture tiaki pūngao nekeneke i roto i ngā tukinga tino pīwariwari. Ko te whakamahinga o te kupu pīwariwari e tohu ana i muri i te tukinga, kāore ngā mea e rua e piri tahi, kāore rānei e piri tetahi ki tetahi, engari ka peke atu. Ka tiakina te nekehanga o ia mea.
Ka tiakina te nekehanga o ia mea.
m 1 v 1 + m 2 v 2 = m 1 v 1 ' + m 2 v 2 ' ………………….. Whārite 1.5
Ka tiakina te pūngao nekeneke o ia mea.
1⁄2 mv 1 2 + 1⁄2 mv 2 2 = 1⁄2 mv 1 ' 2 + 1⁄2 mv 2 ' 2 ………………….. Whārite 1.6
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Me noho puku te tukinga tino ngāwari, ā, kaua e whakaputa wera nā te waku i waenga i ngā mea e rua e tukinga ana. Mēnā ka puta he haruru me te wera i te tukinga o ngā mea e rua, kāore te pūngao nekeneke o ngā mea e tiakina. Ka hurihia ētahi pūngao nekeneke hei pūngao oro me te pūngao wera, ā, ka hurihia ētahi hei pūngao ā-roto. Ko tētahi tauira o te tukinga tino ngāwari ko te tukinga o ngā matūriki ngota me ngā matūriki iti-ngota.
I roto i tētahi raruraru o te tukinga tino ngāwari, ki te mōhiotia te tere tīmatanga engari kāore i te mōhiotia te tere whakamutunga, kāore e taea te whakaoti i te raruraru mā te whakamahi noa i ngā whārite 1.5 me 1.6. Nā tēnei take, ka whakarerekētia ngā whārite e rua hei whakaputa i ētahi atu whārite, ka taea te whakamahi hei whakatau i te tere whakamutunga.
Tangohia te tauwehe 1/2, kātahi ka whakarerekē i te 1.6
m 1 v 1 2 + m 2 v 2 2 = m 1 v 1 ' 2 + m 2 v 2 ' 2
m 1 v 1 2 – m 1 v 1 ' 2 = m 2 v 2 ' 2 – m 2 v 2 2
m1 ( v12 – v1'2 ) = m2 ( v2'2 – v22 ) — > (a + b ) ( a – b ) = a2 – b2
m 1 (v 1 + v 1 ') (v 1 – v 1 ') = m 2 (v 2 ' + v 2 ) (v 2 ' – v 2 ) ……………………….. Whārite 1.7
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Whakarerekētia te whārite 1.5
m 1 v 1 – m 1 v 1 ' = m 2 v 2 ' - m 2 v 2
m1 ( v1 – v1 ' ) = m2 ( v2 ' – v2 ) ………………….. Whārite 1.8
Wehea te whārite 1.7 ki te whārite 1.8 hei whiwhi i te hua whakamutunga
(v 1 + v 1 ') = (v 2 ' + v 2 )
v1 – v2 = v2 ' – v1 '
v 1 – v 2 = – (v 1 ' – v 2 ') ………………….. Whārite 1.9
Ka taea te whakamahi i ngā whārite 1.5 me te 1.9 hei whakaoti rapanga o ngā tukinga tino ngāwari. Whakakotahitia ngā whārite 1.5 me te 1.9 kia puta ai ngā whārite e rua hei whakatau i ngā tere whakamutunga o ngā mea e rua mēnā kāore i te mōhiotia ō rātou taumaha me ngā tere tīmatanga.
I te whakaoti pātai mā te whakamahi i ngā whārite i runga ake nei, whakamahia te tohu tika mō v 1 me v 2. Mēnā ka neke te mea 1 ki te taha matau, ka pai a v 1 , ā, ki te neke te mea tuarua ki te taha maui, ka kino a v 2. Mēnā ka neke ngā mea e rua i ngā ahunga rerekē, engari kāore he mōhiohio e pā ana ki ngā ahunga nekehanga, me rerekē te tohu o v 1 me v 2 , hei tauira, he pai a v 1 , ā, he kino a v 2.
4.1.1 Ngā mea e rua o te taumaha kotahi
Mena ko m1 = m2 , ko v1 ' = v2 me v2 ' = v1.
He aha mēnā ka neke ngā mea e rua i ngā ahunga rerekē?
Hei tauira, mēnā i mua i te tukinga ka neke te mea 1 ki te taha matau, ā, ka neke te mea 2 ki te taha maui, ka neke te mea 1 ki te taha maui (v1 ' = –v2 ) ā, ka neke te mea 2 ki te taha matau (v2 ' = v1 ) i muri i te tukinga.
He aha mēnā kei te okioki tetahi o ngā mea i te tīmatanga?
Hei tauira, mēnā i mua i te tukinga kei te okioki te mea 2 (v 2 = 0), ka okioki te mea 1 (v 1 ' = 0) ā, ka neke te mea 2 i te tere ōrite ki te tere tīmatanga o te mea 1 (v 2 ' = v 1 ) i muri i te tukinga. Mēnā i mua i te tukinga ka neke te mea 1 ki te taha matau, ka neke te mea 2 ki te taha matau i muri i te tukinga. Nō reira, ka whakawhitiwhiti tere ngā mea e rua.
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Tauira pātai 4
Ka neke ngā taonga A (2 kg) me B (2 kg) ki ngā ahunga rerekē i te tere o te 4 m/s me te 2 m/s. Mēnā ka tukinga ngā taonga A me B i roto i te tukinga tino pīngore, he aha ngā tere whakamutunga o ngā taonga A me B?
Mōhiotia:
m A = 2 kg, m B = 2 kg, v A = 4 m/s, v B = – 2 m/s
E hiahiatia ana: v A ' me v B '
Rongoā:
v A ' = – 2 m/s me v B ' = 4 m/s
I muri i te tukinga, ka neke te mea A i te tere o te 2 m/s, ā, ka neke te mea B i te tere o te 4 m/s i ngā taha rerekē. Mēnā i mua i te tukinga ka neke te mea A ki te taha matau, ā, ka neke te mea B ki te taha maui, ka neke te mea A ki te taha maui, ā, ka neke te mea B ki te taha matau i muri i te tukinga.
Tauira pātai 5
Ka neke te mea A (2 kg) ki te taha matau i te tere o te 2 m/s, ā, ka tukinga ki te mea B (2 kg) e takoto kau ana. Mēnā ka tukinga ngā mea e rua i roto i te tukinga tino pīngore, he aha ngā tere whakamutunga o ngā mea A me B?
Mōhiotia:
m A = 2 kg, m B = 2 kg, v A = 2 m/s, v B = 0 m/s
E hiahiatia ana: v A ' me v B '
Rongoā:
v A ' = 0 me v B ' = 2 m/s
I muri i te tukinga, kei te okioki te mea A, ka neke te mea B ki te taha matau i te tere o te 2 m/s.
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4.1.2 Ngā mea e rua he rerekē te taumaha
Mena he rerekē ngā tere tīmatanga me ngā taumaha o ngā mea e rua (he rerekētanga iti noa iho), ka mōhiotia ngā tere whakamutunga mā te whakamahi i ngā whārite 1.10 me 1.11.
Mena kei te okioki te mea 2 i te tīmatanga (v 2 = 0), ka huri te whārite 1.10 hei whārite 1.12, ā, ka huri te whārite 1.11 hei whārite 1.13.
Mena ko v 2 = 0, he tino nui a m 1 , ā, he tino iti a m 2 , mā te whakaoti i ngā whārite 1.12 me 1.13 ka whiwhia te v 1 ' = v 1 me te v 2 ' = 2v 1. Mena ko v 2 = 0, he tino iti a m 1 , ā, he tino nui a m 2 , mā te whakaoti i ngā whārite 1.12 me 1.13 ka whiwhia te v 1 ' = -v 1 me te v 2 ' = 0. Ko ngā tohu pai me ngā tohu kino e tohu ana i ngā ahunga nekehanga rerekē.
Tauira pātai 6
Ka neke tētahi mea he 1 kg te taumaha i te tere o te 20 m/s, ā, ka tukinga ki tētahi pakitara i roto i tētahi tukinga tino pīngore. He aha ngā tere whakamutunga o te mea me te pakitara?
Mōhiotia:
m A = 1 kg, v A = 20 m/s, m B = tino pai, v B = 0
E hiahiatia ana : v A ' me v B '
Rongoā:
v A ' = -20 m/s me v B ' = 0
I muri i te tukinga, ka peke atu te mea A i te tere o te 20 m/s, ā, ka noho okioki te mea B. Mēnā i mua i te tukinga ka neke te mea A ki te taha matau, ka neke ki te taha maui i muri i te tukinga.
