5 Ngā tauira o ngā pātai mō te arotahi pūkohu
1. Ko te roa o te arotahi o tētahi karāhe kōpikopiko (karāhe whakapūmau) he 15 cm. Kei te taha maui o te karāhe tētahi mea he 5 cm te teitei. Tātaihia te tawhiti o te ahua, te whakanui o te ahua, te teitei o te ahua me ngā āhuatanga o te ahua mēnā he 5 cm te tawhiti o te mea mai i te karāhe kōpikopiko.
Kōrero
E mōhiotia ana:
Roanga arotahi (f) = 15 cm
He pai te roa arotahi o te arotahi o te arotahi pūkohu nā te mea ka tukuna te pūwāhi arotahi o te arotahi e te hihi mārama, he tūturu rānei.
Teitei o te mea (h) = 5 cm
Te tawhiti o te mea (s) = 5 cm
I pātaihia : te tawhiti o te atarangi, te whakanui o te atarangi, te teitei o te atarangi me ngā āhuatanga o te atarangi
Whakautu:
Te ahua o te hanganga ahua o tētahi mea e te karu arotahi kōpikopiko:
Te tawhiti o te whakaahua (s'):
1/s' = 1/f – 1/s = 1/15 – 1/5 = 1/15 – 3/15 = -2/15
s' = -15/2 = -7,5 henemita
Ko te tawhiti atarangi kino he tikanga mariko te atarangi, kāore rānei te hihi mārama e tika ana mā roto i te atarangi.
He nui ake te tawhiti o te ahua he 7,5 cm i te tawhiti o te mea he 5 cm.
Whakanuia o te ahua (M):
M = -s'/s = -(-7,5)/5 = 7,5/5 = 1,5 ngā wā
Ko te whakanui pai o te ahua ko te tikanga he poutū te ahua, kāore rānei i hurihia.
Ko te rahi o te ahua he 1,5 ngā wā nui ake i te rahi o te mea.
Teitei o te atarangi (h'):
M = h'/h
h' = M h = (1,5)5 = 10/3 = 7,5 cm
He pai te teitei o te atarangi, arā, he poutū te atarangi, kāore rānei i te huripokitia.
He nui ake te teitei o te ahua he 7,5 cm i te teitei o te mea he 5 cm.
Ngā āhuatanga o ngā atarangi
I runga i ngā tātaitanga i runga ake nei, ka taea te whakatau ko ngā āhuatanga o te ahua o tētahi mea i hangaia e tētahi karu whāiti ko:
– kāore ngā hihi mariko, ngā hihi mārama rānei e whiti ana i te atarangi
– Tū tika, kāore rānei i te huripokitia
– Kua whakanuia, kua iti iho rānei te rahi o te ahua i te rahi o te mea
– He nui ake te tawhiti o te ahua i te tawhiti o te mea
2. Kei mua i te arotahi kōpikopiko he mea 10 cm te teitei, e 30 cm te tawhiti o te ahua, ā, ko te roa arotahi he 15 cm. Tātaihia te tawhiti o te ahua, te whakanui o te ahua, te teitei o te ahua me ngā āhuatanga o te ahua!
Kōrero
E mōhiotia ana:
Roanga arotahi (f) = 15 cm
He pai te roa arotahi o te arotahi o te arotahi pūkohu nā te mea ka tukuna te pūwāhi arotahi o te arotahi e te hihi mārama, he tūturu rānei.
Teitei o te mea (h) = 10 cm
Te tawhiti o te mea (s) = 30 cm
I pātaihia: te tawhiti o te atarangi, te whakanui o te atarangi, te teitei o te atarangi me ngā āhuatanga o te atarangi
Whakautu:
Te ahua o te hanganga ahua o tētahi mea e te karu arotahi kōpikopiko:
Te tawhiti o te whakaahua (s'):
1/s' = 1/f – 1/s = 1/15 – 1/30 = 2/30 – 1/30 = 1/30
s' = 30/1 = 30 henimita
Ko te tawhiti atarangi pai he tikanga kei te tūturu te atarangi, kei te whiti rānei te hihi mārama mā roto.
He rite te tawhiti o te atarangi he 30 cm ki te tawhiti o te mea he 30 cm.
Whakanuia o te ahua (M):
M = -s'/s = -(30)/30 = -30/30 = -1 ngā wā
Ko te whakanui i te ahua me te tohu kino ko te tikanga kua hurihia te ahua.
Ko te whakanui o te 1 te tikanga he rite te rahi o te atarangi ki te rahi o te mea.
Teitei o te atarangi (h'):
M = h'/h
h' = M h = (-1)10 = -10 henemita
He tōraro te teitei o te atarangi, arā, kua hurihia te atarangi.
Ko te teitei o te atarangi he 10 cm, he rite tonu ki te teitei o te mea, arā, he 10 cm.
Ngā āhuatanga o ngā atarangi
I runga i ngā tātaitanga i runga ake nei, ka taea te whakatau ko ngā āhuatanga o te ahua o tētahi mea i hangaia e tētahi karu whāiti ko:
– ka whiti te hihi tūturu, te hihi mārama rānei i roto i te atarangi
- whakamuri
– he rite te rahi o te atarangi ki te rahi o te mea
– he rite te tawhiti o te atarangi ki te tawhiti o te mea
Ngā pātai mō ngā karāhe kōpuku
1. Kei mua i tētahi karu arotahi kōpikopiko he 5 cm te teitei o tētahi mea, 10 cm te tawhiti. Whakatauhia: (a) te tawhiti o te ahua, (b) te whakanui o te ahua, (c) te teitei o te ahua me (d) ngā āhuatanga o te ahua!
Kī Whakautu:
(a) s' = -15 henemita
(b) m = 1,5
(c) h' = 7,5 henemita
(d) ngā āhuatanga o te ahua: mariko, poutū, whakanuia
2. Ko te roa o te arotahi o te karu arotahi he 10 cm, ko te tawhiti o te mea mai i te karu arotahi he 15 cm, ā, ko te teitei o te mea he 2 cm. Tātaihia te tawhiti o te ahua, te whakanui o te ahua, te teitei o te ahua me ngā āhuatanga o te ahua!
Kī Whakautu:
(a) s' = 30 henemita
(b) m = -2
(c) h' = -15 henimita
(d) ngā āhuatanga o te ahua: tūturu, hurihia, whakanuia
3. Whakamātautau ā-Motu mō te Pūtaiao mō te Kura Tuarua C4-P12 Nama 13
Tirohia te ahua e whai ake nei! E ai ki ngā raraunga e whakaaturia ana i te ahua, ko te roa o te arotahi o te karu arotahi ko...
A. 4,5 henemita
B. 7,5 henemita
C. 10 henimita
D. 12 henimita
Kōrero
I runga i te ahua o te ara o te mārama, ka whakatauhia ko te momo karāhe he karāhe pūkohu, he karāhe pai rānei.
E mōhiotia ana:
Te tawhiti o te mea (s) = 20 cm
Te tawhiti atarangi (s') = 30 cm
I pātaihia: Roa arotahi o te karu (f)
Whakautu:
Te tauira o te karāhe kōpiko:
1/s + 1/s' = 1/f
He whakamārama mō ngā tātai me ngā ture tohu:
s = te tawhiti o te mea (he pai nā te mea ka whiti te hihi mārama i te mea)
s' = tawhiti atarangi (he pai nā te mea ka tukuna te atarangi mā roto i te hihi mārama, he tūturu rānei te atarangi)
f = te roa o te arotahi (he pai te arotahi o te karu arotahi pūkohu nā te mea ka whiti mā roto i te hihi mārama)
Nā reira, ko te roa o te arotahi o te karu arotahi (f):
1/w = 1/20 + 1/30 = 3/60 + 2/60 = 5/60
f = 60/5 = 12 henemita
Ko te whakautu tika ko D.
4. Te Whakamātautau Pūtaiao ā-Motu o te Kura Tuarua 2011 Pātai Nama 12 – Ngā karāhe kōpikopiko
Kei mua i te arotahi pūkohu tētahi mea e whakaaturia ana i te pikitia. Mēnā he 20 henemita te roa o te arotahi o te arotahi, ka...
ka hangaia he ahua o tētahi mea mā te whakanui...
A. 3 ngā wā
B. 2 ngā wā
C. 1,5 wā
D. 0,5 ngā wā
Kōrero
E mōhiotia ana:
Te roa o te arotahi o te karu arotahi (f) = 20 cm
Ka tukuna te pūwāhi arotahi o te karāhe kōpuku e te hihi mārama kia tūturu ai te roa arotahi o te karāhe kōpuku, ā, he tohu pai tōna.
Te tawhiti o te mea (s) = 30 cm
I pātaihia: Whakanuia o te ahua (M)
Whakautu:
I mua i te tatau i te whakanui o te ahua, me tatau tuatahi te tawhiti (s') o te ahua.
1/s' = 1/f – 1/s = 1/20 – 1/30 = 3/60 – 2/60 = 1/60
s' = 60/1 = 60 henimita
Whakanuia o te ahua:
M = s'/s = 60 henimita / 30 henimita = 60/30 = 2 ngā wā
Ko te whakautu tika ko B.
5. EBTANAS-SMP-01-14
Ko te ahua e whakaatu ana i te ara tika o ngā hihi motuhake i roto i te karu arotahi ko...
Kōrero
Ka kiia hoki te karāhe pūkohu he karāhe whakapūmau nā te mea ka kohia e ia te mārama. Ka kiia hoki he karāhe pai nā te mea ka haere te mārama mā te pūwāhi arotahi o te karāhe pūkohu, ka tūturu ai.
I tētahi atu ringa, ka kiia hoki he karāhe kōpiko he karāhe wehewehe nā te mea ka horahia e ia te mārama. Ka kiia he karāhe kino nā te mea kāore te mārama e whiti i te pūwāhi arotahi o te karāhe kōpiko nā te mea
he mariko.
Kei te taha o tēnei he tauira o te hanganga o tētahi ahua ki runga i tētahi karāhe arotahi pūkohu mā te whakamahi i ngā hihi motuhake e toru.
Ko te whakautu tika ko A.
