Te tiaki i te pūngao miihini i runga i ngā mata piko – ngā raruraru me ngā otinga
1. Mena ko te tere o te pōro i te pūwāhi A he 6 m/s, ko te tere o te pōro i te pūwāhi B he √92 m/s, ā, ko te whakaterenga nā te kaha ā-papatipu ko g = 10 m/s2 . He aha te teitei o te pūwāhi B (h)?
Mōhiotia:
Tere o te pōro i te pūwāhi A (v)A) = 6 m/s
Tere o te pōro i te pūwāhi B (v B ) = √92 m/s
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s 2
Ko te teitei o A (h A ) = 5.6 mita
Ko te teitei o B (h B ) = h
E hiahiatia ana: Te teitei o te pūwāhi B (h)
Rongoā:
Ko te pūngao ā-pūkaha tīmatanga = te pūngao pūmanawa ā-papa
I te pūwāhi A, ko te tere o te pōro = 0, nō reira ko te pūngao nekeneke o te pōro = 0. KE = 1/2 mv² = 1/2 m (0) = 0.
He pōro kei te teitei o te 5.6 mita, nō reira kei te pōro te pūngao pūmanawa ā-papa. Ko te pūngao pūmanawa ā-papa : PE = mgh = m (10)(5.6) = 56 m
Ko te pūngao miihini tīmatanga = te pūngao pūmanawa ā-papa + te pūngao nekeneke = 56 m + 0 = 56 m
Ko te pūngao miihini whakamutunga = te pūngao pūmanawa ā-papa + te pūngao nekeneke
I te pūwāhi B, ko te teitei o te pōro ko h. Ko te pūngao pūmanawa ā-papa: PE = mgh = m (10) h = 10 mh
Te pūngao nekeneke o te pōro: KE = 1/2 mv 2 = 1/2 m (√92) 2 = 1/2 m (92) = 46 m
Ko te pūngao miihini whakamutunga = te pūngao pūmanawa ā-papa + te pūngao nekeneke = 10 mh + 46 m = m (10 h + 46)
Te mātāpono o te tiaki i te pūngao miihini:
Ko te pūngao miihini tuatahi = te pūngao miihini whakamutunga
56 m = m (10 hāora + 46)
56 = 10 hāora + 46
56 – 46 = 10 hāora
10 = 10 hāora
h = 10/10
h = 1 mita
2.
Mena ko te tere tīmatanga = 0, ko te whakaterenga nā te kaha ā-papatipu = 10 m/s 2 , he aha te tere i te teitei o B?
Mōhiotia:
Ko te tere tīmatanga (v o ) = 0
Ko te teitei tīmatanga (h o ) = 50 m – 10 m = 40 m
Ko te teitei whakamutunga (t ) = 0
Te whakaterenga nā te kaha ā-papa (g) = 10 ms -2
E hiahiatia ana: Te tere whakamutunga (v t )
Rongoā:
Te huringa o te pūngao nekeneke:
ΔKE = 1/2 m (v t 2 – v o 2 ) = 1/2 m (v t 2 – 0) = 1/2 mv t 2
Te huringa o te pūngao pūmanawa:
ΔPE = mg (h t – h o ) = m (10)(0-40) = m (10)(-40) = – 400 m
Tātaihia te tere whakamutunga (vt ) mā te whakamahi i te whārite o te mātāpono o te tiaki i te pūngao ā-pūkaha :
0 = ΔKE + ΔPE
0 = 1/2 mv t 2 – 400 m
1/2 mv t 2 = 400 m
1/2 v t 2 = 400
v t 2 = 2(400)
v t = √(400)(2)
v t = 20√2 m/s
- He aha te tikanga o te "tiakitanga o te pūngao miihini"?
- whakahoki: Ko te tikanga o te tiakitanga o te pūngao miihini ko te pūngao miihini katoa (te tapeke o te pūngao nekeneke me te pūngao pūmanawa) o tētahi pūnaha motuhake ka noho pumau tonu mēnā ko ngā kaha pupuri anake, pērā i te kaha ā-papa, e pā ki runga.
- Me pēhea te tiaki i te pūngao ā-pūkaha o tētahi mea e neke ana i runga i tētahi mata piko (pēnei i te pōro e hurihuri ana i raro i tētahi arawhata piko)?
- whakahoki: I te neke haere o te mea i te mata piko, ka hurihia te pūngao pūmanawa hei pūngao nekeneke, engari ka noho pūmau tonu te pūngao miihini katoa, me te whakaaro kāore he kaha kore-pūmau (pēnei i te waku) e mahi ana.
- Ki te tukuna he pōro mai i te okiokinga i te tihi o te arawhata piko, me pēhea te rerekētanga o tōna pūngao nekeneke i a ia e heke ana i te arawhata?
- whakahoki: Ka piki ake te pūngao nekeneke o te pōro i a ia e heke ana i te arawhata nā te mea ka heke tōna pūngao pūmanawa, ā, ka hurihia hei pūngao nekeneke.
- Ki te kore he waku, ka pēhea te whakataurite i te tere o te pōro i te raro o te reti piko ki te tere o te reti tika he rite tonu te teitei?
- whakahoki: Ka ōrite te tere o te pōro i raro mō ngā paheke piko me ngā paheke tika, nā te mea ko te huringa o te pūngao pūmanawa ki te pūngao nekeneke e whakawhirinaki ana ki te teitei poutū anake, ehara i te ara i tangohia.
- He aha te take e kore ai e eke te pōro ki tōna teitei taketake ina hurihia ake i tētahi arawhata piko i muri i te hekenga iho i tētahi teitei?
- whakahoki: Mena he kaha kore-pūmau e pā ana ki te pōro, pērā i te waku, ka mahi rātou ki te whakahē i te nekehanga, ka huri i ētahi o te kaha ā-pūkaha o te pōro ki ētahi atu āhua, pērā i te wera. Nō reira, kāore pea te pōro e ranea te kaha hei eke ki tōna teitei taketake.
- Ki te mea ka paheke iho ngā mea e rua, he rerekē te āhua (hei tauira, he porowhita me he poraka) i tētahi arawhata piko mai i te teitei kotahi, engari kāore e hurihuri, ka rite tonu te tere o raro? He aha ai?
- whakahoki: Āe, ka rite tonu te tere i raro. Ki te kore e hurihuri, e kore hoki e waku, ko te mea anake e whakatau ana i tō rātou tere ko te tiakitanga o te pūngao i runga i te teitei tīmatanga, ehara i te āhua.
- He pēhea te pānga o te piko o tētahi mata ki te kaha noa i runga i tētahi mea e neke ana i taua mata?
- whakahoki: Mā te piko ka rerekē te ahunga o te kaha noa i te nekehanga o te mea. I runga i te mata piko ki runga (pērā i te taha o roto o te peihana), he nui ake te kaha noa i raro nā te kaha pokapū e hiahiatia ana mō te nekehanga piko. I tetahi atu taha, i runga i te mata piko, ka taea e te kaha noa te heke, te kore rānei (ka wehe te mea i te mata) i te pito rawa o runga.
- He aha te mahi a te pūtoro piko i roto i te tiakitanga o te pūngao miihini i runga i te mata piko?
- whakahoki: Kāore te pūtoro o te piko e pā tika ana ki te tiakitanga o te pūngao ā-ringa. Heoi, ka taea e ia te pā ki te kaha noa, ā, ki te mea he waku, ki te nui o te pūngao e ngaro ana i ngā kaha kore-tiaki.
- Mena he piko kei waenganui o te ara (pērā i te piko āhua-U), ka pēhea te rerekētanga o te pūngao ā-pūkaha o tētahi mea i a ia e neke ana i roto i te piko me te piki ake i tērā taha?
- whakahoki: Ka heke te kaha pūmanawa o te mea i a ia e neke ana ki te tōpana, ā, ka piki ake tōna kaha nekeneke. I a ia e neke ana ki tērā taha, ka heke tōna kaha nekeneke, ā, ka piki ake tōna kaha pūmanawa. Mēnā ko ngā kaha pūmau anake e mahi, ka noho pūmau te kaha miihini katoa puta noa i te nekehanga.
- Ka taea e tētahi mea te whai pūngao nekeneke whakawhiti me te pūngao hurihuri ina neke ana i runga i tētahi mata piko?
- whakahoki: Āe, ki te hurihuri (me te kore e paheke) tētahi mea pērā i te pōro i runga i tētahi mata piko, ka puta he pūngao nekeneke whakawhiti nā te mea e neke ana tōna pokapū papatipu, me te pūngao nekeneke hurihuri nā te mea e huri ana i tōna tuaka.
