Te tiaki i te pūngao miihini – ngā raruraru me ngā otinga
1. Ka tukuna he poraka m-kg mai i te tihi o te papa whakarara maeneene , e whakaaturia ana i te pikitia i raro nei. Ko te whakataurite i waenga i te pūngao pūmanawa ā-papa me te pūngao nekeneke o te poraka i te pūwāhi M ko…
otinga
Pūngao pūmanawa ā-papa i te pūwāhi M:
PE M = mg (1/3h) = 1/3 mgh
Pūngao nekeneke i te pūwāhi M:
KE M = EP = mg (2/3 h) = 2/3 mgh
EP M : EK M
1/3 mg/h : 2/3 mg/h
3/1 : 3/2
1: 2
2. He kaitākiri hukapapa e reti ana mai i te teitei o A, e whakaaturia ana i te pikitia i raro nei. Mena ko te tere tīmatanga = 0, ā, ko te whakaterenga nā te kaha ā-papa he 10 ms -2 , he aha te tere o te kaitākiri i te pūwāhi B?
Mōhiotia:
Te tere tīmatanga (v o ) = 0
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s 2
Te panonitanga o te teitei = 50 mita – 10 mita = 40 mita
E hiahiatia ana: Te tere o te kaitākiri i te pūwāhi B
Rongoā:
Ko te mātāpono o te tiaki i te pūngao ā-pūngao e kī ana ko te pūngao ā-pūngao tuatahi = te pūngao ā-pūngao whakamutunga.
Ko te pūngao ā-ringa tuatahi = te pūngao pūmanawa i te pūwāhi B (teitei = 40 mita)
Ko te pūngao miihini whakamutunga = te pūngao nekeneke i te pūwāhi B
Te pūngao mīhini whakamutunga = Te pūngao mīhini tuatahi
½ mv t 2 = mgh
½ v t 2 = gh
½ v t 2 = (10)(50-10)
½ v t 2 = (10)(40)
½ v t 2 = 400
v t 2 = (2)(400) = 800
v t = √800 = √(2)(400) = 20√2 m/s
3. Ka tīmata te paheke o tētahi mea mai i tētahi pūwāhi o A, kāore he tere tīmatanga. Mēnā kāore he kaha waku, he aha te tere o te mea i te pūwāhi iti rawa?
Mōhiotia:
Papatipu o te mea = m
Te tere tīmatanga (v o ) = 0
Teitei (h) = 20 mita
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s 2
E hiahiatia ana: Te tere whakamutunga ( vt )
Rongoā:
Pūngao miihini tīmatanga (ME 1 ) = Pūngao pūmanawa ā-papa i te pūwāhi A (PE A ) = mgh = (m)(10)(20) = 200 m
Pūngao miihini whakamutunga (ME 2 ) = pūngao nekeneke (KE) = ½ mv t 2
Ko te tere o te mea i te pūwāhi iti rawa (vt )?
Whakamahia te mātāpono o te tiakitanga o te pūngao ā-pūngao i runga i te kīanga ko te pūngao ā-pūngao tīmatanga = te pūngao ā-pūngao whakamutunga.
EM1 = EM2
200 m = ½ mv t 2
200 = ½ v t 2
400 = v t 2
v t = 20 m/s
4. Ka taka noa tētahi pōro 2-kg te taumaha mai i te pūwāhi A, e whakaaturia ana i te pikitia i raro nei (g = 10 ms -2 ). I muri i te taenga ki te pūwāhi B, ko te pūngao nekeneke = 2 ngā wā o te pūngao pūmanawa. He aha te teitei o te pūwāhi B i runga ake i te mata o te whenua?
Mōhiotia:
Taumaha o te pōro (m) = 2 kg
Te whakaterenga nā te kaha ā-papa (g) = 10 ms -2
Teitei o te pūwāhi A (h A ) = 90 mita
E hiahiatia ana: Teitei o te pūwāhi B (h B )
Rongoā:
Ina tae ki te pūwāhi B, ko te pūngao nekeneke o te pōro i te pūwāhi B = 2 whakarea o te pūngao pūmanawa ā-papa i te pūwāhi B.
EK = 2 EP
½ mv 2 = 2 mgh B
½ v 2 = 2 gh B
v 2 = 2(2)(10) h B
v 2 = 40 h B
Te tere (v) o te pōro ina tae ki te pūwāhi B i muri i te hinganga noa mai i te pūwāhi A:
v 2 = 2 gh = 2(10)(90–h B ) = 20(90–h B )
Whakakapia te v 2 i te whārite i runga ake nei ki te v 2 i tēnei whārite.
v 2 = 40 h B
20(90–h B ) = 40 h B
1800–20 hāora B = 40 hāora B
1800 = 40 hāora B + 20 hāora B
1800 = 60 hāora B
h B = 1800 / 60
h B = 30 mita
5. Ka tukuna he pōro 1-kg te taumaha, ka paheke iho i te pūwāhi A ki te pūwāhi C, e whakaaturia ana i te pikitia i raro nei. Mēnā ko te whakaterenga nā te kaha ā-papatipu = 10 ms -2 , he aha te kaha nekeneke o te pōro ina tae ki te pūwāhi C.
Mōhiotia:
Taumaha o te pōro (m) = 1 kg
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s 2
Ko te panonitanga o te teitei (h) = 0.75 m
Ko te pūngao pūmanawa tuatahi (PE o ) = mgh = (1)(10)(0.75) = 7.5 Joules
Pūngao nekeneke tīmatanga (KE o ) = ½ mv o 2 = ½ m (0) 2 = 0
Ko te pūngao pūmanawa ā-papa whakamutunga (PE t ) = mgh = mg (0) = 0
E hiahiatia ana: Pūngao nekeneke o te pōro i te pūwāhi C
Rongoā:
Ko te pūngao miihini tīmatanga (ME₂o ) = Ko te pūngao miihini whakamutunga ( ME₂t )
Ko te pūngao pūmanawa ā-papa tuatahi (PE o ) + te pūngao nekeneke tuatahi (KE o ) = Ko te pūngao pūmanawa ā-papa whakamutunga (PE t ) + te pūngao nekeneke whakamutunga (KE t )
7.5 Joule + 0 = 0 + KE t
7.5 Joules = KE t
Pūngao nekeneke o te pōro i te pūwāhi C = 7.5 Joule.
6. Ka tukuna he pōro 2-kg te taumaha mai i te pūwāhi A, e whakaaturia ana i te pikitia i raro nei. He maeneene te papa kōpiko. Mena ko te whakaterenga nā te kaha ā-papa he 10 ms -2 , he aha te kaha nekeneke o te pōro i te pūwāhi B.
Mōhiotia:
Taumaha o te pōro (m) = 2 kg
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s 2
Ko te panonitanga o te teitei (h) = 120 cm = 1.2 mita
Ko te pūngao pūmanawa tōpana tuatahi (PE o ) = mgh = (2)(10)(1.2) = 24 Joules
Ko te pūngao nekeneke tīmatanga (KE o ) = ½ mv o 2 = ½ m (0) 2 = 0
Ko te pūngao pūmanawa ā-papa whakamutunga (PE t ) = mgh = mg (0) = 0
E hiahiatia ana: Pūngao nekeneke o te pōro i te pūwāhi B
Rongoā:
Ko te pūngao miihini i te pūwāhi A (pūngao miihini tīmatanga) = te pūngao miihini i te pūwāhi B (te pūngao miihini whakamutunga)
Ko te pūngao miihini tīmatanga (ME₂o ) = te pūngao miihini whakamutunga ( ME₂t )
Ko te pūngao pūmanawa ā-papa tuatahi (PE o ) + te pūngao nekeneke tuatahi (KE o ) = te pūngao pūmanawa ā-papa whakamutunga (PE t ) + te pūngao nekeneke whakamutunga (KE t )
24 Joule + 0 = 0 + KE t
24 Joules = KE t
Pūngao nekeneke (KE) o te pōro i te pūwāhi C = 24 Joules.
7. He pūngao ā-pūkaha pumau tō te mea, he nui ake te pūngao nekeneke, ā, he iti ake te pūngao pūmanawa ā-papa. Ko te mea…
A. I te okiokinga
B. neke ake
C. neke ki raro
D. Whakatereterehia ki runga
Rongoā:
Kei te nui haere te pūngao nekeneke, arā, kei te nui haere te tere o te mea, ā, kei te iti haere te pūngao pūmanawa ā-papa, arā, kei te iti haere te teitei o te mea mai i te mata o te oneone. Ka puta tēnei ina neke te mea mai i tētahi teitei ki raro ki te whenua.
Ko te whanaungatanga i waenga i te tere me te pūngao nekeneke e whakaaturia ana e te tātai pūngao nekeneke:
KE = ½ mv 2
Whakaahuatanga o te tātai: KE = pūngao nekeneke, m = papatipu, v = tere
Ko te whanaungatanga i waenga i te teitei me te pūngao pūmanawa ā-papa e tohuhia ana e te tātai pūngao pūmanawa ā-papa:
PE = mgh
Whakaahuatanga o te tātai: PE = pūngao pūmanawa ā-papa, m = papatipu, g = whakaterenga o te ā-papa, h = teitei
Ko te whakautu tika ko C.
- He aha te pūngao ā-pūkaha?
- whakahoki: Ko te pūngao miihini te tapeke o te pūngao nekeneke me te pūngao pūmanawa o tētahi mea. E pā ana te pūngao nekeneke ki te nekehanga o tētahi mea, ko te pūngao pūmanawa ia e pā ana ki tōna tūranga, ki tōna hanganga rānei.
- He aha te tikanga o te mātāpono o te tiaki i te pūngao ā-pūkaha?
- whakahoki: E mea ana te mātāpono, i roto i tētahi pūnaha motuhake me ngā kaha pūmau anake e mahi ana, ka noho pūmau tonu te pūngao miihini katoa. Ko te tikanga, kāore te tapeke o te pūngao nekeneke me te pūngao pūmanawa e rerekē i roto i te wā.
- He aha te pānga o ngā kaha pūmau me ngā kaha kore-pūmau ki te tiakitanga o te pūngao miihini?
- whakahoki: Kāore ngā kaha pūmau, pērā i te kaha ā-papa, e whakarerekē i te pūngao miihini katoa o tētahi pūnaha. Tērā pea ka hurihia e rātou te pūngao pūmanawa ki te pūngao nekeneke, ki te pūngao hurihuri rānei, engari ka noho pūmau tonu te tapeke. Ka taea e ngā kaha kore-pūmau, pērā i te waku, te whakamarara i te pūngao miihini, ā, ka hurihia hei pūngao wera.
- He aha te take kāore i tiakina ai te pūngao miihini i roto i ngā horopaki o te ao tūturu e pā ana ki te waku?
- whakahoki: He kaha kore-pūmau te waku. I te neke haere o ngā mea tetahi ki tetahi, ka hurihia e te waku tetahi wāhanga o te pūngao miihini o te pūnaha hei pūngao wera, ka heke te pūngao miihini katoa o te pūnaha.
- Me pēhea te whakaatu i te tiakitanga o te pūngao miihini i roto i tētahi pendulum e piu ana?
- whakahoki: I te korenga o te ātete hau (he kaha kore-pūmau), i te piu ake o te pendulum, ka hurihia tōna pūngao nekeneke hei pūngao pūmanawa ā-papa. I te wāhi teitei rawa o tōna piu, he pūngao pūmanawa mōrahi tōna, he pūngao nekeneke iti hoki. I a ia e piu ake ana ki raro, ka hurihia tēnei pūngao pūmanawa hei pūngao nekeneke. Ka noho pūmau tonu te pūngao miihini katoa, ahakoa kei te whakawhitiwhiti ngā āhua o te pūngao.
- He aha i tū ai te pōro e pekepeke ana ahakoa te korenga o ngā kaha o waho?
- whakahoki: Ina pekepeke te pōro, kāore e hurihia katoatia tōna pūngao nekeneke hei pūngao pūmanawa. Ka ngaro ētahi pūngao, he maha ngā wā he oro, he rerekētanga rānei o te pōro, ā, nā te waku o roto i te rauemi o te pōro. He momo kaha kore-pūmau ēnei e whakamahia ana, e whakaiti ana i te pūngao ā-pūkaha o te pōro i ia pekepeketanga tae noa ki te wā e okioki ai.
- I roto i te waka rerehua, kei hea te pūngao ā-ringa teitei rawa me te iti rawa?
- whakahoki: Ka noho pūmau tonu te pūngao ā-pūkaha katoa o te waka hurihuri mēnā ka warewarehia te ātete hau me te waku. Heoi, i te wāhi teitei rawa, kei te teitei rawa te pūngao pūmanawa, ko te pūngao nekeneke kei te iti rawa. I a ia e heke ana, ka huri te pūngao pūmanawa ki te pūngao nekeneke, nō reira i te wāhi iti rawa, kei te teitei rawa te pūngao nekeneke, ā, kei te iti rawa te pūngao pūmanawa.
- He pēhea te āwhina a te tiaki i te pūngao miihini ki te mārama ki ngā porowhita o ngā aorangi?
- whakahoki: Ko ngā aorangi e porowhita ana i tētahi whetū pērā i te Rā, he pūngao nekeneke (nā tō rātou nekehanga) me te pūngao pūmanawa ā-papa (nā tō rātou tūranga e pā ana ki te Rā). I te neke tata atu o te aorangi ki te Rā, ka tere ake, ka piki ake tōna pūngao nekeneke, ka heke iho tōna pūngao pūmanawa ā-papa, ā, pērā anō hoki. Ka noho pūmau tonu te pūngao miihini katoa o te aorangi i roto i te wā, me te whakaaro he iti noa iho ngā kaha kē atu (pērā i ngā aorangi kē atu).
- He aha te take kāore ai he amiorangi e taka ana ki te Ao i roto i tētahi porowhita pumau?
- whakahoki: Ahakoa e tōia ana te amiorangi ki te Ao nā te kaha ā-papa, ko tōna kaha nekeneke whakamua ka pupuri i a ia kia neke i roto i tōna porowhita. Mā te taurite o tēnei kaha nekeneke me te kaha pūmanawa ā-papa ka pupuri i te amiorangi kia noho i roto i tētahi porowhita pumau me te kaha ā-pūkaha pumau.
- Ki te tīmata te kaireti reti mai i te okiokinga i te tihi o te puke kore-waku, kātahi ka reti iho, ka pēhea te tere o tōna tere i raro i tōna tere mēnā i tīmata ia i waenganui o te hekenga o te puke?
- whakahoki: I runga i te puke kore-waku, ka tiakina te pūngao ā-pūkaha katoa o te kaireti reti. Ki te tīmata ia mai i te tihi rawa, ka nui ake tōna pūngao pūmanawa hei tīmatanga i te tīmatanga i te tīmatanga i waenganui o te heke. Ka huri katoa tēnei pūngao pūmanawa hei pūngao nekeneke i a ia e heke ana. Nō reira, ka tere ake ia i raro mēnā ka tīmata ia i te tihi i te tīmatanga i waenganui o te heke.
