7 Ngā tauira o ngā pātai whakaterenga ā-pokapū
1. Ka herea he kōhatu ki te taura, kātahi ka hurihia whakapaetia kia huri rā anō te kōhatu ki te koki 360°.o ia hēkona 1. Mena he 20 cm te roa o te taura, tautuhia te rahi o te whakaterenga porotītaha o te mea!
Kōrero
E mōhiotia ana :
Te tere koki (ω) = 360o/hēkona = 1 hurihanga / hēkona = 6,28 rātiana/hēkona
Te roa o te taura = te pūtoro (r) o te ara porowhita = 20 cm = 0,2 mita
I pātaihia : te whakaterenga ā-pokapū (as)
Whakautu :
2. E 30 cm te whānui o tētahi wira e hurihuri ana i te tere koki o te 180 rpm. Tātaihia te whakaterenga ā-pokapū o tētahi pūwāhi i te taha o te wira!
Kōrero
E mōhiotia ana :
Te whānui (r) o te wira = 30 cm = 0,3 mita
Tere koki (ω) = 180 hurihanga / 60 hēkona = 3 hurihanga / hēkona = (3)(6,28 rātiana) / hēkona = 18,84 rātiana/hēkona
I pātaihia : te whakaterenga ā-pokapū (as) i te r = 0,3 mita
Whakautu :
3. E taraiwa ana tētahi kaiwhakataetae i tētahi motuka i tētahi piko haurua-porowhita me te radius piko o te 50 mita. Mena ko te tere o te motuka he 72 km/haora, he aha te whakaterenga pokapū o te motuka?
Kōrero
E mōhiotia ana :
Te whānui (r) = 50 mita
Tere (v) = 72 km/h = (72)(1000 mita) / 3600 hēkona = 20 mita/h
I pātaihia : te rahi o te whakaterenga ā-pokapū (a)s)
Whakautu :
Te rahi o te whakaterenga ā-pokapū o te motuka:
as = v2 / r = 202 / 50 = 400 / 50 = 8 m/s2
4. Kei te haere tētahi motuka i te piko me te whakaterenga porowhita o te 10 m/s2, koinei te whakaterenga pūrua mōrahi rawa atu ka taea e te motuka te whakatutuki me te kore e paheke i te ara. Mena ko te tere o te motuka he 108 km/h, he aha te radius o te piko o te pihi kia kore ai te motuka e paheke?
Kōrero
E mōhiotia ana :
Te whakaterenga ā-pokapū (a)s) = 10 m/s2
Te tere o te motuka (v) = 108 km/haora = (108)(1000) / 3600 = 30 mita/hekona
I pātaihia : te pūtoro (r)
Whakautu :
Te pūtoro o te piko o te piko:
r=v2 / hes
r = 302 / 10 = 900 / 10 = 90 mita
5. Ngā Pātai Whakamātautau ā-Motu 2003/2004
He kauwhata e whakaatu ana i te whanaungatanga i waenga i te whakaterenga ā-pokapū (a s ) me te tere rārangi (v) i roto i te nekehanga porowhita ōrite...
Kōrero
Te tātai whakaterenga pūrua:
Whakaahuatanga: a s = whakaterenga ā-pokapū, v = tere rārangi, r = tawhiti mai i te tuaka hurihuri.
Ka rangahauhia e mātou te whanaungatanga i waenga i te whakaterenga ā-pokapū (a s ) me te tere rārangi (v) kia pumau ai te tawhiti mai i te tuaka hurihuri (r). Me kī ko r = 1.
Ka piki rārangi te uara o v, ka piki pūngao te uara o as.
Ko te whakautu tika ko A.
6. Ngā Pātai Whakamātautau ā-Motu mō te SMA/MA Ahupūngao U-ZC-2013/2014 Nama 4
Ka mirohia he māpere i roto i tētahi peihana porowhita, ko te whānui he 1 m. Mēnā ka huri te māpere i te taha o te peihana i te tere koki pumau o te 50 rpm, ko te tere rārangi me te whakaterenga pokapū o te māpere ko….
A. 50 ms -1 me te 2500 ms -2
B. 5π ms -1 me te 25π 2 ms -2
C. 5π/3 ms -1 me 25π 2 /18 ms -2
D. 5π/6 ms -1 me te 25π 2 /18 ms -2
E. 5π/12 ms -1 me 25π 2 /36 ms -2
Kōrero
E mōhiotia ana:
Te whānui o te porowhita (D) = 1 mita
Te whānui o te porowhita (r) = 0,5 mita
Te tere koki (ω) = 50 rpm = 50 hurihanga / 1 meneti
1 hurihanga = 2π ngā rātiana
50 hurihanga = 50 (2π rātiana) = 100π rātiana
1 meneti = 60 hēkona
Tere koki (ω) = 100π rātiana / 60 hēkona = (10π/6) rātiana/hēkona
Pātai: Te tere rārangi (v) me te whakaterenga ā-pokapū (a s )
Whakautu:
Tere raina (v):
v = r ω = (0,5)(10π/6) = 5π/6 m/s
Te whakaterenga ā-pokapū (a)s):
a s = v 2 /r = (5π/6) 2 : 0,5 = 25π 2 /36 : 0,5 = (25π 2 /36)(1/0,5)
a s = (25π 2 /18) m/s 2
Ko te whakautu tika ko D.
7. Ngā Pātai Whakamātautau ā-Motu 2007/2008 P4 Nama 6
Ka neke tētahi mea i te tere pumau v i runga i tētahi ara porowhita me te pūtoro R me te whakaterenga pokapū (a s ). Kia rua te tere o te whakaterenga pokapū i te mea taketake, kāti...
E whā ngā wā i hangaia ai a A. v, ā, e rua anō ngā wā i hangaia ai a R.
B. ka hangaia a v kia rua ngā wā, ā, ka hangaia anō a R kia whā ngā wā
E rua ngā wā i hangaia ai a C. v, ā, e rua anō ngā wā i hangaia ai a R.
Ka noho tonu a D. v, ā, ka takiruatia anō a R
E. ka tāruatia anō a v, ā, ka noho tonu a R
Kōrero
