Te mātotoru me te rere i te taurite – ngā raruraru me ngā otinga
1. He poraka kua whakanohoia ki roto i ngā wai e rua he rerekē ngā momo. I roto i ngā wai A, 0.6 te wāhanga o tētahi mea kei roto i te wai. I roto i ngā wai B, 0.5 te wāhanga o tētahi mea kei roto i te wai. Whakatauhia te ōwehenga o te mātotoru o te wai A ki te wai B.
Mōhiotia:
Te mātotoru o te poraka = x
Wāhanga o te mea i roto i te wai A = 0.6
Te mātotoru o te wai A = y
Wāhanga o te mea i roto i te wai B = 0.5
Te mātotoru o te wai B = z
E hiahiatia ana: Te ōwehenga o te mātotoru o te wai A ki te wai B (y: z)
Rongoā:
Whakakapia a x i te whārite 2 ki a x i te whārite 1:
2. He mea kei roto i te wai P, 0.5 te wāhanga o te mea kei roto i te wai. Ina whakanohoia te mea ki roto i te wai Q, kei roto i te wai te mea, e whakaaturia ana i te pikitia i raro nei. He aha te ōwehenga o te mātotoru o te wai P ki te wai Q?
Mōhiotia:
Te mātotoru o te mea = x
Wāhanga o te mea i roto i te wai P = 1/2 = 0.5
Te mātotoru o te wai P = y
Wāhanga o te mea i roto i te wai Q = 1
Te mātotoru o te wai Q = z
E hiahiatia ana: Te ōwehenga o te mātotoru o te wai P ki te wai Q (y: z)
Rongoā:
Whakakapia a x i te whārite 2 ki a x i te whārite 1:
3. He rakau e mānu ana i roto i te hinu (ko te mātotoru o te hinu he 800 kg/m3 ) . E 4/5 ngā wāhanga o te rakau kei roto i te hinu . He aha te mātotoru o te rakau?
Mōhiotia:
Te mātotoru o te hinu (ρ) = 800 kg/m -3
Wāhanga rakau i roto i te hinu = 4/5
E hiahiatia ana: Te matotoru o te rakau
Rongoā:
Ko te mātotoru o te rakau he 640 kg/ m3.
4. Ko te taumaha o tētahi poraka he 50 N. I roto i te wai, ko te taumaha o te poraka he 30 N. Mena ko te mātotoru o te wai he 103 kg /m -3, he aha te mātotoru o te poraka?
Mōhiotia:
Taumaha o te poraka i te hau (w) = 50 N
Taumaha o te poraka i roto i te wai (w wai ) = 30 N
Te mātotoru o te wai (ρ wai ) = 103 kg /m3 = 1000 kg/ m3
Te whakaterenga nā te kaha ā-papa (g) = 10 m/s 2
Taumaha o te poraka (m) = w/g = 50/10 = 5 kg
E hiahiatia ana: Te mātotoru o ngā poraka (ρ poraka )
Rongoā:
Te kaha pupuhi:
F A = w – w wai = 50 – 30 = 20 N
Te rōrahi o te poraka i roto i te wai:
F A = ρ g V
20 = (1000)(10) V
20 = (10,000) V
V = 20/10,000
V = 0.002 m3
Te matotoru o te poraka:
ρ = m/V = 5 / 0.002 = 2500 kg/m 3
5. He poraka rakau kua toua ki te wai. E 25% o tōna wāhanga kei runga ake i te mata o te wai , ā, e 75% kei roto i te wai. Ko te mātotoru o te wai he 1 karamu/cm⁻¹ , ā, ko te whakaterenga nā te kaha ā-papa he 10 m/s⁻¹ . Tātaihia te mātotoru o ngā poraka.
A. 0.025 kg/ m3
B. 0.075 karamu/cm 3
C. 0.250 kg/ m3
D. 0.750 karamu/cm 3
Mōhiotia:
Wāhanga o ngā poraka i runga ake i te mata o te wai = 25% = 25/100 = 0.25
Te wāhanga o te poraka i roto i te wai = 75% = 75/100 = 0.75
Ko te mātotoru o te wai (ρ wai ) = 1 karamu/cm3 = 1000 kg/ m3
Te whakaterenga nā te kaha ā-papatipu = 10 m/s 2
E hiahiatia ana: Te mātotoru o ngā poraka (ρ poraka )
Rongoā:
Te rōrahi o ngā poraka i roto i te wai = te ōwehenga o te mātotoru o ngā poraka ki te mātotoru o te wai
Ko te whakautu tika ko D.
- He aha te mātotoru, ā, me pēhea tōna whakamāramatanga pāngarau?
- whakahoki: Ko te mātotoru he ine i te nui o te papatipu kei roto i tētahi rōrahi kua hoatu. I roto i te pāngarau, ka tautuhia ko kiato =.
- Me pēhea te whakatau a te mātotoru o tētahi mea mēnā ka mānu, ka totohu rānei i roto i tētahi wai?
- whakahoki: Ki te iti iho te matotoru o tētahi mea i te matotoru o te wai e whakanohoia ana ki roto, ka mānu te mea. I tetahi atu taha, ki te nui ake te matotoru o te mea i te matotoru o te wai, ka totohu.
- He aha te mātāpono kei muri i te mānu, te totohu rānei o tētahi mea i roto i tētahi wai?
- whakahoki: Ko te mātāpono ko te Mātāpono a Ākirīmete, e kī ana ka rumakina tētahi tinana i roto i tētahi wheako wai o tētahi kaha pōrewarewa ki runga e ōrite ana ki te taumaha o te wai e nekehia ana e ia.
- Mena ka mānu te poraka hukapapa i roto i te wai, me tetahi wāhanga o taua poraka hukapapa kei runga ake i te taumata wai, he aha te tohu o tēnei mō te matotorutanga whanaunga o te hukapapa me te wai?
- whakahoki: E tohu ana tēnei he iti iho te matotoru o te hukapapa i te matotoru o te wai. Koia te take e mānu ai te poraka hukapapa, ā, ko tētahi wāhanga anake o taua poraka hukapapa e toe ana ki roto i te wai hei neke i te nui o te wai e rite ana te taumaha ki te poraka hukapapa.
- He aha ngā kaipuke rino taumaha e mānu ai i runga i te wai, engari ka totohu pea he whao rino iti?
- whakahoki: Ko te matotorutanga whānui o tētahi kaipuke rino, tae atu ki ōna wāhanga tuwhera kua kī tonu i te hau, he iti iho i te matotorutanga o te wai. He rerekē, ko te matotorutanga o tētahi whao rino totoka he nui ake i te matotorutanga o te wai, ka totohu ai.
- He aha te rerekētanga o te ariā o te "pūmau kore" mai i te mānu, te totohu rānei?
- whakahoki: Ka puta te pōrewarewa kūpapa ina taurite tika te taumaha o te mea e te kaha pōrewarewa, ka noho iri te mea i roto i te wai me te kore e piki, e totohu rānei.
- He aha i rere ai te poihau hēriuma i te rangi?
- whakahoki: He iti iho te mātotoru o te hēriuma i te mātotoru o te hau. Nō reira, he iti iho te taumaha o te poihau hēriuma (tae atu ki te rauemi poihau me te hēriuma i roto) i te taumaha o te hau e nekehia ana e ia, ā, ka mānu.
- Ka ahatia te mātotoru o tētahi mea ina pēhia kia iti ake te rōrahi, i te mea e pumau tonu ana tōna papatipu?
- whakahoki: Ka piki ake te mātotoru nā te mea ko te mātotoru te papatipu i wehea ki te rōrahi. Mēnā ka heke te rōrahi, ā, ka noho pūmau te papatipu, ka piki ake te ōwehenga (mātotoru).
- He pēhea te pānga o te tote ki te mātotoru o te wai?
- whakahoki: Mā te whakanui ake i te tote o te wai (arā, te tāpiri atu i te tote) ka nui ake tōna mātotoru. Koia te take e ngāwari ake ai te mānu o ngā mea i roto i te wai tote (pērā i te Moana Mate) i te wai māori.
- Mena kei te mānu tetahi mea i roto i te taurite i roto i te wai, he aha te whakataurite i waenganui i te kaha pōrewarewa me te kaha ā-papa i runga i te mea?
- whakahoki: Ina mānu ana te mea i roto i te taurite, he ōrite te kaha o te pōrewarewa (te kaha piki ake nā te wai) te rahi, ā, he rerekē te ahunga ki te kaha ā-papa (taumaha) e pā ana ki te mea.
