2 Ngā tauira o ngā pātai mō ngā karāhe takirua pūkohu pūkohu
1. E rua ngā karāhe arotahi kōpikopiko, he 20 henimita te roa o te arotahi o ia karāhe, he 30 henimita te roa, ā, ko te tawhiti i waenganui i ngā karāhe arotahi e rua he 70 henimita. Kei mua i te karāhe arotahi tuatahi tētahi mea he 30 henimita. Tātaihia te tawhiti o te ahua me te whakanui o te ahua i hangaia e ngā karāhe arotahi e rua. karāhe kōpiko te!
Kōrero
E mōhiotia ana:
Ko te roa o te arotahi o te arotahi kōpiko tuatahi (f1) = +20 henemita
Ko te roa o te arotahi o te arotahi kōpiko tuarua (f2) = +30 henemita
He pai te roa arotahi o te karāhe arotahi pūkohu nā te mea ka haere te hihi mārama mā te pūwāhi arotahi o te karāhe arotahi pūkohu.
Ko te tawhiti i waenganui i ngā karāhe kōpiko e rua (l) = 50 cm
Te tawhiti o te mea mai i te karāhe kōpiko tuatahi (s1) = 30 henemita
He pai te tawhiti o te mea nā te mea ka puta te hihi mārama mā roto i te mea.
Whakautu:
a) Te tawhiti o te atarangi
Te tawhiti o te ahua i hangaia e te karāhe kōpiko tuatahi (te tawhiti o te ahua tuatahi):
1 / s1' = 1/w1 – 1/h1
1 / s1' = 1/20 – 1/30 = 3/60 – 2/60 = 1/60
s1' = 60/1 = 60 henemita
E 60 cm te tawhiti o te ahua tuatahi mai i te karu arotahi 1.
He pai te tawhiti o te ahua tuatahi, arā, he tūturu te ahua tuatahi, arā, kei te noho tonu nā te mea ka whiti te hihi mārama mā roto i te ahua.
Te tawhiti o te ahua i hangaia e te karu arotahi tuarua (te tawhiti o te ahua whakamutunga):
Ko te ahua i hangaia e te karāhe pūkohu tuatahi ka kiia he mea e te karāhe pūkohu tuarua. Ko te tawhiti o te ahua/mea tuatahi mai i te karāhe pūkohu tuarua (s)2) = te tawhiti i waenganui i ngā karāhe kōpikopiko e rua – te tawhiti o te ahua tuatahi mai i te karāhe kōpikopiko tuatahi = 70 cm – 60 cm = 10 cm.
1 / s2' = 1/w2 – 1/h2
1 / s2'= 1/30 – 1/10 = 1/30 – 3/30 = -2/30
s2' = -30/2 = -15 henimita
E 15 cm te tawhiti o te ahua whakamutunga mai i te karu arotahi kōpuku tuarua.
He kino te tawhiti whakamutunga o te ahua, arā, he rūpahu, he teka rānei te ahua whakamutunga nā te mea kāore te hihi mārama e whiti i te ahua (kei te taha maui o te karu arotahi kōpiko tuarua te ahua whakamutunga).
b) Te whakanui i te ahua
Te whakanui i te ahua e te karu arotahi tuatahi:
m1 = -s1'/s1 = -60 henimita/30 henimita = -2 ngā wā
Mā te karāhe arotahi kōpuku ka toru ngā wā e nui ake ai te rahi o te ahua i te rahi o te mea.
Ko te whakanui i te ahua me te tohu kino ko te tikanga kua hurihia te ahua.
Te whakanui i te ahua e te karu arotahi tuarua:
m2 = -s2'/s2 = -(-15 henimita)/10 henimita = 15/10 = 1,5 ngā wā
Ka whakanuia e te karāhe kōpiko tuarua te mea (te ahua o te karāhe kōpiko tuatahi) mā te tauwehenga e 1,5.
Ko te whakanui katoa o te ahua ko:
m = (m1)(m2) = (-2)(1,5) = -3 ngā wā
E toru ngā wā e nui ake ai te rahi o te ahua whakamutunga i te rahi o te mea, e toru rānei ngā wā e teitei ake ai te teitei o te ahua whakamutunga i te teitei o te mea. He kino te whakanui katoa, arā, kua hurihia te ahua. (kua hurihia te ahua whakamutunga, nō reira me noho te ahua whakamutunga ki te taha maui o te karāhe kōpiko tuarua).
2. Ko te tawhiti i waenganui i ngā karāhe kōpiko e rua he 100 cm. Ko te roa arotahi o ia karāhe kōpiko e rua he 20 cm me te 80 cm. Kei mua i te karāhe tuatahi tētahi mea he 30 cm. Tātaihia te tawhiti o te ahua me te whakanui o te ahua i hangaia e ngā karāhe kōpiko e rua!
Kōrero
E mōhiotia ana :
Te tawhiti i waenganui i ngā karāhe e rua (l) = 100 cm
Ko te roa o te arotahi o te arotahi kōpiko tuatahi (f1) = 20 henemita
Ko te roa o te arotahi o te arotahi kōpiko tuarua (f2) = 80 henemita
He pai te roa arotahi o te karāhe arotahi pūkohu nā te mea ka haere te hihi mārama mā te pūwāhi arotahi o te karāhe arotahi pūkohu.
Te tawhiti o te mea mai i te karāhe kōpiko tuatahi (s1) = 30 henemita
He pai te tawhiti o te mea nā te mea ka puta te hihi mārama mā roto i te mea.
Whakautu :
a) Te tawhiti o te atarangi
Te tawhiti o te ahua i hangaia e te karāhe kōpiko tuatahi (te tawhiti o te ahua tuatahi):
1 / s1' = 1/w1 – 1/h1
1 / s1' = 1/20 – 1/30 = 3/60 – 2/60 = 1/60
s1' = 60/1 = 60 henemita
E 60 cm te tawhiti o te ahua tuatahi mai i te karu arotahi 1.
He pai te tawhiti o te ahua tuatahi, arā, he tūturu te ahua tuatahi, arā, kei te noho tonu nā te mea ka whiti te hihi mārama mā roto i te ahua.
Te tawhiti o te ahua i hangaia e te karu arotahi tuarua (te tawhiti o te ahua whakamutunga):
Ko te ahua i hangaia e te karāhe pūkohu tuatahi ka kiia he mea e te karāhe pūkohu tuarua. Ko te tawhiti o te ahua/mea tuatahi mai i te karāhe pūkohu tuarua (s)2) = te tawhiti i waenganui i ngā karāhe kōpikopiko e rua – te tawhiti o te ahua tuatahi mai i te karāhe kōpikopiko tuatahi = 100 cm – 60 cm = 40 cm.
1 / s2' = 1/w2 – 1/h2
1 / s2'= 1/80 – 1/40 = 1/80 – 2/80 = -1/80
s2' = -80/1 = -80 henimita
E 80 cm te tawhiti o te ahua whakamutunga mai i te karu arotahi kōpuku tuarua.
He kino te tawhiti whakamutunga o te ahua, arā, he rūpahu, he teka rānei te ahua whakamutunga nā te mea kāore te hihi mārama e whiti i te ahua (kei te taha maui o te karu arotahi kōpiko tuarua te ahua whakamutunga).
b) Te whakanui i te ahua
Te whakanui i te ahua e te karu arotahi tuatahi:
m1 = -s1'/s1 = -60 henimita/30 henimita = -2 ngā wā
Mā te karāhe arotahi kōpuku ka toru ngā wā e nui ake ai te rahi o te ahua i te rahi o te mea.
Ko te whakanui i te ahua me te tohu kino ko te tikanga kua hurihia te ahua.
Te whakanui i te ahua e te karu arotahi tuarua:
m2 = -s2'/s2 = -(-80 henimita)/40 henimita = 80/40 = 2 ngā wā
Ka whakanuia e te karāhe kōpiko tuarua te mea (te ahua o te karāhe kōpiko tuatahi) mā te tauwehenga e 2.
Ko te whakanui katoa o te ahua ko:
m = (m1)(m2) = (-2)(2) = -4 ngā wā
E whā ngā wā e nui ake ai te rahi o te ahua whakamutunga i te rahi o te mea, e whā rānei ngā wā e teitei ake ai te teitei o te ahua whakamutunga i te teitei o te mea. He kino te whakanui katoa, arā, kua hurihia te ahua (kua hurihia te ahua whakamutunga, nō reira me noho te ahua whakamutunga ki te taha maui o te karāhe kōpiko tuarua).
Ngā pātai mō ngā karāhe takirua kōpiko piko
1. E rua ngā karāhe kōpikopiko, he 40 henimita te roa o te arotahi, he 20 henimita te roa o te arotahi o ia karāhe, ā, ko te tawhiti i waenganui i ngā karāhe kōpikopiko e rua he 100 henimita. Tātaihia te tawhiti o te ahua me te whakanui katoa o te ahua i hangaia e ngā karāhe kōpikopiko e rua i runga i tētahi mea e 120 henimita te tawhiti ki mua i te karāhe kōpikopiko tuatahi!
Kī Whakautu:
(a) te tawhiti whakamutunga o te ahua = s2' = 40
(b) te whakanui katoa o te ahua = m = 0,5
2. Kei te taha mauī o te karāhe kōpikopiko he mea e 10 cm te tawhiti, ā, ko te roa o te arotahi he 20 cm. Kei te taha matau o te karāhe kōpikopiko he karāhe kōpikopiko he 50 cm te roa o te arotahi. Mena he 120 cm te tawhiti i waenganui i ngā karāhe e rua, tātaihia te tawhiti o te ahua me te whakanui o te ahua i hangaia e ngā karāhe kōpikopiko e rua!
Kī Whakautu:
(a) te tawhiti whakamutunga o te ahua = s2' = 133 henemita
(b) te whakanui katoa o te ahua = m = -1,7 ngā wā. Ko te tikanga o te kino kua hurihia te ahua.
