Ngā tukinga - ngā raruraru me ngā otinga
1. E neke ana te mea A (3 kg) i te tere o te 8 m/s, ā, e neke ana te mea B (5 kg) i te tere o te 4 m/s. Mēnā he tino ngāwari te tukinga i waenganui i ngā mea A me B, he aha te tere o ngā mea A me B i muri i te tukinga?
Mōhiotia:
Papatipu o te mea A (m1 ) = 3 kg
Papatipu o te mea B (m² ) = 5 kg
Ko te tere o te mea A (v 1 ) = 8 ms –1
Ko te tere o te mea B (v 2 ) = 4 ms –1
E hiahiatia ana: v 1 ' me v 2 '
Rongoā:
Mena he rerekē te papatipu o ngā mea e rua, ā, kāore anō kia mōhiotia te tere o ngā mea e rua i muri i te tukinga, ka tatauhia te tere i muri i te tukinga mā te whakamahi i tēnei whārite:
He rite tonu te ahunga o ngā mea e rua, ā, he rite tonu te tohu o te tere o ngā mea e rua. Mēnā ka neke ngā mea e rua i ngā ahunga rerekē, ka whai tohu tāpiri tetahi tere, ā, he tohu tango tetahi tere.
Te tere o te mea A (v A ) i muri i te tukinga:
Te tere o te mea B (v B ) i muri i te tukinga:
Ko te tere o te mea A (v 1 ') i muri i te tukinga he 3 m/s, ā, ko te tere o te mea B (v 2 ') i muri i te tukinga he 7 m/s.
2. Ko te nekehanga o te pōro he P, ka tukinga ki te pakitara, ā, ka whakaatahia. He tino ngāwari te tukinga, ā, ko tōna ahunga he poutū ki te pakitara. He aha te panoni o te nekehanga o te pōro?
Mōhiotia:
Papatipu o te pōro = m
Ko te tere o te pōro i mua i te tukinga = v
Te tere o te pōro i muri i te tukinga = -v (ka whakaatahia te pōro ki maui)
Te nekehanga o te pōro i mua i te tukinga (p o ) = mv
Te nekehanga o te pōro i muri i te tukinga (p t ) = m (-v) = – mv
E hiahiatia ana: Te huringa o te nekehanga o te pōro
Rongoā:
Te huringa o te nekehanga:
Δp = pt – p o
Δp = – mv – mv
Δp = – 2 mv
Δp = -2p
Ko te tohu tango e tohu ana i te ahunga o te pōro.
3. E rua ngā mea, a A rāua ko B, he rite te taumaha e neke ana i te taha rerekē, ā, ka tukinga rāua. Ka neke a A ki te rawhiti i te tere o V, ā, ka neke a B ki te hauauru i te tere o 2V. Mena he tino ngāwari te tukinga, he aha te tere o ngā mea e rua i muri i te tukinga?
Mōhiotia:
He ōrite te taumaha o ngā mea e rua.
Ka neke a A ki te rawhiti i te tere o V
Ka neke a B ki te hauauru i te tere o te 2V
E hiahiatia ana: Te tere o ngā mea e rua i muri i te tukinga
Rongoā:
Mena he ōrite te taumaha o ngā mea e rua, ā, he tino pīngore te tukinga, kāti i muri i te tukinga ka rerekē te tere o ngā mea e rua.
I muri i te tukinga, ka neke a A ki te hauauru i te 2V, ka neke a B ki te rawhiti i te V.
4. E rua ngā mea he rite te taumaha e neke ana i te rārangi tika i ngā ahunga rerekē e whakaaturia ana i te pikitia i raro nei. Mena ko te tere o te mea 2 i muri i te tukinga (v 2 ') he 5 m/s ki te taha matau, he aha te rahi o te tere o te mea 1 i muri i te tukinga?
Mōhiotia:
Papatipu o ia mea = m
Te tere o te mea 1 i mua i te tukinga (v 1 ) = 8 m/s
Te tere o te mea 2 i muri i te tukinga (v 2 ) = 10 m/s
Te tere o te mea 2 i muri i te tukinga (v 2 ') = 5 m/s
E hiahiatia ana: Te tere o te mea 1 i muri i te tukinga (v 1 ')
Rongoā:
He āhua pīngorekore te tukinga.
m 1 v 1 + m 2 v 2 = m 1 v 1 ' + m 2 v 2 '
m (v 1 + v 2 ) = m (v 1 ' + v 2 ')
v1 + v2 = v1 ' + v2 '
8 + 10 = v 1 ' + 5
18 = v 1 ' + 5
v1 ' = 18-5
v 1 ' = 13 m/s
Tukinga kore-whakapūmau
5. Ka tukinga tētahi matā 10-karamu i pupuhihia i te 100 ms -1 , ki tētahi poraka rakau e tū ana. Ko te taumaha o te poraka he 490 karamu. He kore-pūmau te tukinga. He aha te tere o te poraka me te matā i muri i te tukinga?
Mōhiotia:
te taumaha o te matā (m1 ) = 10 karamu
Te tere o te matā (v 1 ) = 100 m/s
Taumaha o te poraka (m2 ) = 490 karamu
Tere o te poraka (v 2 ) = 0 m/s (poraka e okioki ana)
E hiahiatia ana: Te tere o te poraka me te matā i muri i te tukinga
Rongoā:
m 1 v 1 + m 2 v 2 = (m 1 + m 2 ) v'
(10)(100) + (490)(0) = (10 + 490) v'
1000 + 0 = 500 v'
1000 = 500 v'
v' = 1000 / 500
v' = 2 m/s
6. Ka tukinga tētahi taraka e neke ana i te 10 m/s ki tētahi motuka e neke ana i te 20 m/s. I muri i te tukinga, ka neke tahi te taraka me te motuka i te tere kotahi. Ko te taumaha o te taraka he 1400 kg, ā, ko te taumaha o te motuka he 600 kg. He aha te tere o te taraka me te motuka i muri i te tukinga?
Mōhiotia:
tere o te taraka (v 1 ) = 10 m/s
tere o te motuka (v 2 ) = 20 m/s
te taumaha o te taraka (m1 ) = 1400 kg
te taumaha o te motuka (m2 ) = 600 kg
E hiahiatia ana: Te tere o te taraka me te motuka i muri i te tukinga
Rongoā:
m 1 v 1 + m 2 v 2 = (m 1 + m 2 ) v
(1400)(10) + (600)(20) = (1400 + 600) v
14000 + 12000 = 2000 v
26000 = 2000 v
v = 13 m/s
7. E neke ana tētahi matā 20-karamu i te 10 m/s i te ahunga whakapae, ka tukinga ki tētahi poraka 60-karamu e takoto ana i runga i te papa. I muri i te tukinga, ka neke tahi te matā me te poraka me te tere ōrite me te ahunga ōrite. He aha te tere o ngā matā me ngā poraka?
Mōhiotia:
Taumaha o te matā (m P ) = 20 karamu = 0.02 kg
Taumaha o te poraka (m B ) = 60 karamu = 0.06 kg
Ko te tere tīmatanga o te matā (v P ) = 10 m/s
Ko te tere tīmatanga o ngā poraka (v B ) = 0
E hiahiatia ana: Te tere o te matā me te poraka i muri i te tukinga (v')
Rongoā:
He kore-whakapūmau te tukinga.
m P v P + m B v B = (m P + m B ) v'
(0.02)(10) + (0.06)(0) = (0.02 + 0.06) v'
0.2 + 0 = 0.08 v'
0.2 = 0.08 v'
v' = 0.2 / 0.08
v' = 2.5 m/s
8. E rua ngā mea, a A rāua ko B, he rite te taumaha = 1.5 kg te tawhiti, ka whakatata atu rāua, ka tukinga. Ko te tere o te mea A (v A ) = 4 m/s, ko te tere o te mea B (v B ) = 5 m/s. Mena he kore-whakapūmau te tukinga, he aha te tere o ngā mea e rua i muri i te tukinga?
Mōhiotia:
Papatipu o te mea A (m A ) = 1.5 kg
Taumaha o te mea B (m B ) = 1.5 kg
Tere o te mea A i mua i te tukinga (v A ) = 4 m/s (pai ki te taha matau)
Tere o te mea B i mua i te tukinga (v B ) = -5 m/s (kino ki maui)
E hiahiatia ana: Te tere o ngā mea e rua i muri i te tukinga
Rongoā:
m A v A + m B v B = (m A + m B ) v'
(1.5)(4) + (1.5)(-5) = (1.5 + 1.5) v'
6 – 7.5 = (3) v'
-1.5 = (3) v'
v' = -1.5 / 3
v' = -0.5 m/s
Ko te tohu tango e tohu ana i muri i te tukinga, ka neke ngā mea e rua ki maui, ko te ahunga kotahi ki te mea B.
- He aha te tukinga i roto i te horopaki o te ahupūngao? WhakautuI roto i te ahupūngao, ko te tukinga e pā ana ki tētahi huihuinga e pā tata mai ai ētahi mea e rua, neke atu rānei, tetahi ki tetahi, ā, i te nuinga o te wā ka whakamahia he kaha ki runga i a rātou anō, ka hua ake he whakawhitiwhiti pūngao me te nekehanga.
- He aha ngā rerekētanga o ngā tukinga pīwariwari me ngā tukinga kore pīwariwari? WhakautuI roto i te tukinga ātete, ka tiakina te kaha me te pūngao nekeneke. I roto i te tukinga kore-ātete, ka tiakina te kaha, engari kāore te pūngao nekeneke. Ko ngā tukinga kore-ātete tino tika he huinga iti e piri tahi ai ngā mea e tukinga ana i muri i te tukinga.
- He aha i puritia tonutia ai te nekehanga i roto i ngā tukinga? WhakautuKa tiakina te nekehanga i roto i ngā tukinga nā te mātāpono tiaki nekehanga, e kī ana ko te nekehanga katoa o tētahi pūnaha kati ka noho pumau tonu ki te kore e pāngia e ngā kaha o waho.
- Ka tiakina tonutia te pūngao nekeneke i ngā tukinga? WhakautuKāo, ka tiakina te pūngao nekeneke i roto i ngā tukinga rapa anake. I roto i ngā tukinga kore-rapa, ka hurihia ētahi o te pūngao nekeneke ki ētahi atu momo pūngao, pērā i te pūngao pūmanawa, te oro, te wera rānei.
- He aha i piri ai ngā waka e rua i muri i te tukinga? WhakautuKi te piri tahi ngā waka e rua i muri i te tukinga, he tauira tēnei o te tukinga kore-whakapūmau. Ka noho tahi ngā waka nā te hononga ā-pūkaha, te whakarerekētanga āhua, ētahi atu kaha rānei e kaha ake ai te kaha ki te hoki whakamuri tetahi i tetahi.
- Ka taea e tētahi mea e tukinga ana te pāngia e te huringa o te pūngao nekeneke ahakoa kāore anō kia rerekē tōna tere? WhakautuĀe, ki te huri te ahunga o tētahi mea i te wā o te tukinga engari kāore i te tere, ka huri tōna tere (he rahinga whārite), engari ka noho tonu tōna tere (he rahinga tauine). Ahakoa kāore pea te rahinga o tōna pūngao nekeneke (i runga i te tere) e huri, kua rerekē te tohatoha pūngao o te mea.
- He aha i pupuhi ai ngā pōro piriata tetahi ki tetahi ina tukinga? WhakautuHe tata rite te tukinga o ngā pōro piriata ki te pūngao tere. Ina tukinga tētahi pōro ki tētahi atu, ka whakawhitia te kaha nekeneke me te nekehanga, ka pekepeke ngā pōro. Nā te hoahoa me te rauemi o ngā pōro piriata ka whai hua rātou ki te tiaki i te kaha nekeneke i roto i ēnei taunekeneke.
- Ki te tukinga ngā mea e rua he rerekē te taumaha, ā, ka piri tetahi ki tetahi, ka rite rānei tō rāua tere whakakotahi ki te toharite o ō rāua tere tīmatanga? WhakautuKāore pea. Ka whakawhirinaki te tere whakakotahi ki te ture tiaki o te nekehanga. Mena he nui ake te taumaha o tētahi mea i tētahi atu, ka tata atu te tere whakakotahi ki te tere tīmatanga o te mea nui ake.
- I te ao tūturu, he pono rānei kei reira ngā tukinga "pūmau"? WhakautuI roto i te mahi, kāore he tukinga e tino ngāwari ana. Ahakoa he tata te tukinga o ētahi tukinga, pērā i ngā tukinga i waenga i ngā pōro piriata, he pūngao tonu kei te ngaro ki ētahi atu momo, pērā i te oro, te wera rānei.
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Me pēhea te whakaiti i te pānga o te tukinga i roto i te aituā motuka e te pēke hau? Whakautu : Ka whakanui ake ngā pēke hau i te wā e huri ai te nekehanga o te tangata i te tukinga. Mā te pera, ka whakaitihia te kaha e pā ana ki te tangata (he rite te ōwehenga ki te wā e huri ai te nekehanga), ka whakaitihia te whara pea.
