4 Ngā tauira o ngā rahinga i ahu mai, ngā tātai ine ā-ao me ngā tātai waeine
| Ngā rahinga i ahu mai | Tātai | He aha te moni matua kei roto? | Ngā rahinga o ngā rahinga i ahu mai | Pūnaha Ao o ngā Wāhanga Ngā rahinga i ahu mai |
| Rorarau | Te roa x te whānui | Roa (2) | [L2] | m2 |
| Te rōrahi o te porowhita | Te roa x te whānui x te teitei | Roa (3) | [L3] | m3 |
| Kiato | Taumaha / Rōrahi | Taumaha (1), roa (3) | [M] / [L]3] = [M][R-3] | Kg / m3 |
| Te tere | Tawhiti / wā | Roa (1), wā (1) | [R] / [T] = [R] [T]-1] | m / s |
| Whakaterenga | Tere / wā | Roa (1), wā (2) | [L] [T]-1] / [T] = [L] [T-2] | m / s2 |
| Gaya | Papatipu x whakaterenga | Papatipu (1), roa (1), wā (2) | [M][L][T-2] | Kg m/s2 |
| Pakihi | Te kaha x te nekehanga | Papatipu (1), roa (2), wā (2) | [M][L][T-2[R] = [M][R2[T-2] | kg m2/s2 |
Hei kimi i te maha o ngā rahinga taketake, tuatahi titoa te tātai rahinga kua ahu mai.
Rahinga i ahu mai: Mana
Tātai Mana
P = W / t
Whakaahuatanga: P = mana, W = mahi, t = wā
He rahinga taketake te wā, he rahinga ahu mai ia a W, nō reira whakaitihia te mahi kia toe rā anō ko te rahinga taketake anake.
Tātai Pakihi
W = Fs
Whakaahuatanga: W = kaha, F = kaha, s = nekehanga
He rahinga taketake te nekehanga o te roa, ko te kaha ia he rahinga i ahu mai, nō reira whakaitihia te kaha kia toe rā anō ko te rahinga taketake anake.
Tātai kaha
F = ma
Whakaahuatanga: F = kaha, m = papatipu, a = whakaterenga
Ko te papatipu te rahinga taketake o te roa, ko te whakaterenga ia he rahinga i ahu mai, nō reira whakaitihia te whakaterenga kia toe ra ano ko te rahinga taketake anake.
Tātai whakaterenga
a = v / t
Whakaahuatanga: a = whakaterenga, v = tere, t = wā
He rahinga taketake te wā, he rahinga ahu mai ia te tere, nō reira whakaitihia te tere kia toe rā anō ko te rahinga taketake anake.
Tātai tere
v = s / t
Whakaahuatanga: v = tere, s = nekehanga, t = wā
Ko te nekehanga he rahinga taketake o te roa, ko te wā he rahinga taketake.
Tātai Mana
Hurihia te tātai mana:
Whakaahuatanga: m = papatipu, s = roa, t = wā
Te moni matua
Ko te mana kei roto i tēnei ko te rahinga papatipu kotahi, ngā rahinga roa e rua, me ngā rahinga wā e toru.
Ahu Mana
I runga i te tātai mana e titoa ana i ngā rahinga taketake o runga ake nei, ko ngā inenga o te mana ko:
[M][L]2] / [T3] = [M][R2[T3]
Te Wāhanga Mana o te Ao
I runga i te tātai mana me ngā inenga i runga ake nei, ko te waeine mana ā-ao ko:
Kirokaramu mita tapawhā ia hekona tapawhā (kg m2/s3)
Ngā pātai rahinga i ahu mai
| Ngā rahinga i ahu mai | Tātai rahinga i ahu mai | E hia ngā rahinga taketake o ngā rahinga i ahu mai? | Ngā rahinga o ngā rahinga i ahu mai | Pūnaha ā-ao o ngā waeine i ahu mai |
| Maikura | Ngā mahi / wā (W / t) | |||
| Pūngao nekeneke | ½ x papatipu x tapawhā o te tere (½ mv2) | |||
| Pūngao pūmanawa | Papatipu x whakaterenga nā te kaha ā-papatipu x teitei (mgh) | |||
| torohaki | Papatipu x tere (mv) | |||
| Peke | Te kaha x te wā (F t) | |||
| Taipana | Te kaha x te nekehanga (F s) | |||
| Te kaha hiko | Pūmau ā-papatipu x utu 1 x utu 2 / tapawhā o te tawhiti (kqq / r2) | |||
| Utu hiko | Iahiko hiko x wā (I t) | |||
| Te wā o te korekore | Papatipu x pūtoro tapawhā (mr2) | |||
| Tekana | Te kaha / te horahanga (F / A) | |||
| Ngā Kaora | Papatipu x wera motuhake x huringa pāmahana (mc T) | |||
| Te kaha o te mara hiko | Te kaha hiko / te utu hiko (F / q) |
1. Kia tūpato ki ngā rahinga e whai ake nei!
E ai ki te ripanga i runga ake nei, ko te rahinga i ahu mai me tōna waeine tika i roto i te Pūnaha Ao ko…
A. (1), (2), me (3)
B. (2), (3) me (4)
C. (2), (4) me te (5)
D. (3), (4) me (5)
Kōrero
Ngā rahinga ā-tinana e rua ngā rahinga, arā, ngā rahinga taketake me ngā rahinga ahu mai.
Te moni matua
Ko ngā rahinga taketake he rahinga ā-tinana kua whakatauhia ngā waeine i mua. Kei te ripanga i raro nei ngā rahinga taketake e 7 me ō rātou waeine ā-ao.
Ngā rahinga i ahu mai
Ko ngā rahinga i ahu mai ko ngā rahinga ā-tinana e ahu mai ana i ngā rahinga taketake. Haunga ngā rahinga taketake e whitu kua whakahuatia i runga ake nei, ka ahu mai anō hoki ētahi atu rahinga ā-tinana. Ko ngā rahinga i ahu mai i te pātai i runga ake nei ko te rōrahi, te tere, me te mātotoru.
rōrahi
Te tātai rōrahi (hei tauira, te rōrahi o te porowhita) = te roa x te whānui x te teitei
Ko te roa he waeine taketake mō te roa, ko te whānui he waeine taketake mō te roa, ā, ko te teitei he waeine taketake mō te roa. Ahakoa he rerekē ngā kupu e whakamahia ana, ka inehia te roa, te whānui, me te teitei mā te whakamahi i te taputapu ine kotahi, arā, te roa. He kotahi anō te waeine ā-ao o te roa, te whānui, me te teitei, arā, te mita. Nō reira, ko te waeine ā-ao mō te rōrahi ko te mita x mita x mita = mita pūtoru, e whakarapopototia ana ko m.3
Te tere
Te tātai tere = te nekehanga / te wā
Ko te nekehanga he rahinga taketake o te roa, ā, ko te wā he rahinga taketake o te wā. Ko te waeine nekehanga ā-ao ko te mita, ā, ko te waeine wā ā-ao ko te hēkona. Nō reira, ko te waeine nekehanga ā-ao ko te mita/hēkona, he whakarāpopototanga m/s.
Kiato
Tātai kiato = papatipu / rōrahi
He rahinga taketake te papatipu, ā, he rahinga ahu mai te rōrahi. Ko te waeine papatipu ā-ao ko te kirokaramu, ā, ko te waeine rōrahi ā-ao ko te mita pūtoru. Nō reira, ko te waeine mātotoru ā-ao ko te kirokaramu/mita pūtoru, he whakarapopototanga kg/m3.
Ko te whakautu tika ko C.
2. Tirohia te ripanga e whai ake nei!
I runga i te ripanga, ko te tau kei roto i te rōpū rahinga i ahu mai me ngā waeine i roto i te Pūnaha Ao (SI) ko...
A. (1), (2), me (3)
B. (1), (3), me (5)
C. (2), (4), me te (5)
D. (3), (4), me te (5)
Kōrero
Ko ngā rahinga taketake ko (1) te papatipu me (3) te roa. Ko ngā rahinga i ahu mai ko (2) te kiato, (4) te horahanga, (5) te ngaohiko hiko.
Kiato
Ko te waeine mō te mātotoru ko te kirokaramu/mita pūtoru, he whakarāpopototanga ko te kg/m3Tirohia te whakamārama i roto i te matapakinga o te pātai nama 1.
Rorarau
Tātai horahanga (hei tauira, horahanga o te tapawhā) = roa x whānui.
Ko te roa he waeine taketake mō te roa, ā, ko te whānui he waeine taketake mō te roa. Ko te waeine ā-ao mō te roa ko te mita, ā, ko te waeine ā-ao mō te whānui ko te mita. Nō reira, ko te waeine ā-ao mō te horahanga ko te mita x mita = mita tapawhā, arā, m.2.
Ngaohiko hiko
Ko te waeine ā-ao mō te ngaohiko hiko, te rerekētanga pūmanawa hiko rānei, ko te Joule/Coulomb. Ko tētahi atu ingoa mō te waeine ā-ao mō te ngaohiko hiko ko te Volt.
Ko te whakautu tika ko C.
3. Kei roto i te ripanga e whai ake nei ētahi rahinga me ō rātou waeine.
Ko te rōpū o ngā rahinga i ahu mai me ā rātou waeine i roto i te Pūnaha Ao tika e tohuhia ana e ngā tau...
A. (1), (2), me (3)
B. (1), (3), me (4)
C. (2), (3), me te (5)
D. (3), (4), me te (5)
Kōrero
Ko ngā rahinga taketake o te ripanga ko (5) te kaha o te mārama. Ko ngā rahinga i ahu mai i te ripanga ko (1) te rōrahi, (2) te mātotoru, (3) te kaha, me (4) te tere.
rōrahi
Ko te waeine ā-ao mō te rōrahi ko te mita pūtoru, he whakarāpopototanga m3Tirohia te whakamārama i roto i te matapakinga o te pātai nama 1.
Kiato
Ko te waeine ā-ao mō te mātotoru ko te kirokaramu/mita pūtoru, he whakarapopototanga ko te kg/m3. Karamu/henimita3 ehara i te waeine ā-ao. Tirohia te whakamārama i roto i te matapakinga o te pātai nama 1.
Gaya
Ko te tātai mō te kaha = papatipu x whakaterenga. He rahinga taketake te papatipu, ā, he rahinga ahu mai te whakaterenga. Ko te waeine papatipu ā-ao ko te kirokaramu, he whakarāpopototanga kg, ā, ko te waeine whakaterenga ā-ao ko te mita/hēkona tapawhā, he whakarāpopototanga m/s.2Nō reira, ko te waeine ā-ao mō te kaha ko te kirokaramu mita / hekona tapawhā, he whakarāpopototanga kg m/s2. Ka tapaina tēnei waeine ki te ingoa motuhake ko Newton, hei whakanui i te tohunga ahupūngao a Isaac Newton.
Te tere
Ko te ine ā-ao mō te tere ko te mita/hēkona, he whakarāpopototanga m/h. Tirohia te whakamārama i roto i te matapakinga o te pātai nama 1.
Ko te whakautu tika ko B.
4. I runga i te tātaritanga ā-ahu, ko ngā rahinga ā-tinana i raro nei he rite ngā ā-ahu ko…
- te kaha me te kaha
- te mana me te pēhanga
- te kaha me te nekehanga
- mahi me te wera
Kōrero
E mōhiotia ana:
Ahu Roa Ahu = Whānui Ahu = Nekehanga Ahu = L
Ahu Wā = T
Ahu Papatipu = M
Whakautu:
Ahu Horahanga = Roa Ahu x Whānui Ahu = [R][R] = [R]2
Ahu o te Tere = Ahu o te Nekehanga / Ahu o te Wā = [L] / [T] = [L][T]-1
Ahu o te Whakaterenga = Ahu o te Tere / Ahu o te Wā = [L][T]-1 / [T] = [L][T]-1[T]-1 = [L][T]-2
Ahu o te Kaha = Ahu o te Papatipu x Ahu o te Whakaterenga = [M][L][T]-2
Ahu o te Mahi = Ahu o te Kaha x Ahu o te Nekehanga = [M][L][T]-2 [R] = [M][R]2[T]-2
Ahu Mana = Ahu Mahi / Ahu Wā = [M][L]2[T]-2 / [T] = [M][L]2[T]-2[T]-1 = [M][R]2[T]-3
Ahu o te Pēhanga = Ahu o te Kaha / Ahu o te Horahanga = [M][L][T]-2 / [R]2 = [M][L][T]-2 [L]-2 = [M] [L]-1[T]-2
Ahu o te Momentum = Ahu o te Papatipu x Ahu o te Tere = [M][L][T]-1
Ahu o te Wera = Ahu o te Pūngao = Ahu o te Mahi = [M][L]2[T]-2
Ko te whakautu tika ko D.
Tuhipoka:
Ko te wera he pūngao e whakawhitihia ana nā ngā rerekētanga pāmahana.
Ko te mahi te tukanga whakawhiti pūngao mā te nekehanga o ngā mea.
Nō reira, ko te taha o te wera = te taha o te pūngao = te taha o te mahi.
