1. Te ture a Hooke mō ngā puna
Ki te tōia te puna ki te taha matau, ka totoro te puna, ka roa ake (pikitia 1). Ki te kore e nui te kaha kukume, ka kitea ko te pikinga o te roa o te puna (Δx) he rite ki te rahi o te kaha kukume (F). Ara, ko te nui ake o te kaha kukume, ko te roa ake o te puna. He pumau te whakataurite i te rahi o te kaha kukume (F) me te pikinga o te roa o te puna (Δx).
Ka kumea te puna ki te taha matau kia piki ake te roa o te Δx. He rite tonu te pikinga o te roa o te puna ki te kaha kume.
Tuhia ki te kauwhata te whanaungatanga i waenga i te Kaha (F) me te pikinga o te roa o te puna (Δx), ina he ōrite te F ki te Δx. He pumau te whakatairite i te F ki te Δx.
Ko te ōwehenga o te kaha (F) ki te pikinga o te roa o te puna (Δx) e tohuhia ana e te pari kauwhata kotahi (pikitia 2).
F / Δ x = k
F = k Δ x
Ko k he pūmau puna, arā, te tauwehenga o te ngāwari o te puna. I kitea tuatahitia tēnei whanaungatanga e Robert Hooke (1635 – 1703) i te tau 1678, nō reira i mōhiotia ai ko te ture a Hooke.
Mena ka nui ake te kaha e pā ana ki te puna i te rohe ngāwari o te puna, i muri i te tangohanga o te kaha, kāore te roa o te puna e hoki ki tōna roa taketake. Ka pā anake te ture a Hooke ki te rohe ngāwari. Ko te rohe ngāwari o te puna ko te kaha mōrahi ka taea te hoatu ki te puna i mua i te hurihanga tūturu o te puna, ā, kāore e taea e te roa o te puna te hoki ki tōna roa taketake. Mena ka piki tonu te kaha, ka pakaru te puna.
2. Te ture a Hooke mō te kore-puna
E pā ana hoki te ture a Hooke ki ngā mea totoka katoa. Mēnā ka tukuna te kaha o waho ki runga i tētahi mea totoka, ka rerekē te āhua o te mea. Ka matapakihia e tātou ngā huringa o te āhua o ēnei mea totoka mā te whakamahi i te ariā o te ahotea me te totoro. E kī ana te ahotea i te kaha o ngā kaha e puta ai te huringa o te āhua o te mea. E kī ana te totoro i ngā huringa o te āhua o ngā mea nā te ahotea. I kitea mō te ahotea me te totoro iti rawa, he ōrite te ahotea ki te totoro. He pumau te ōwehenga o te ahotea me te totoro, ā, ka kiia tēnei pūmau whakatairite ko te modulus of elasticity.
Taumahatanga / Taumahatanga = te tauwehenga ngāwari
Ka kiia hoki tēnei whanaungatanga ko te ture a Hooke, me ngā āhuatanga he rite te ahotea ki te taumahatanga, ā, he pumau te ōwehenga i waenga i te ahotea me te taumahatanga. Mena ka nui ake te kaha e pā ana ki tētahi mea i te ngāwari o ngā mea, kāore te ture a Hooke e pā. Ka pā noa te ture a Hooke ki ngā rohe o te ngāwari o te mea.
E toru ngā momo o te modulus rapa, ko te modulus a Young, ko te modulus kutikuti, me te modulus papatipu.
2.1 Te Tauwehenga o Young
Ina tōia ngā pito e rua o te taura, te waea, te taura rānei e te kaha me te kaha ōrite me te ahunga rerekē, ka noho te taura, te waea, te taura rānei i roto i te āhua kume. Ko ētahi tauira o te oranga o ia rā e pā ana ki tēnei ko te taura e pupuri ana i ngā kaipiki toka, te waea e pupuri ana i ngā ararewa, ngā waea, ngā aho tueke, ngā ipu rānei i runga i ngā pūnaha uta me te tango uta i runga i ngā kaipuke, me ētahi atu. Ka pāngia ngā taura kume, ngā waea, ngā taura rānei e te taumahatanga kume nā te pēhanga kume. Ka tautuhia e mātou te pēhanga kume hei ōwehenga o te kaha kume (F) ki te horahanga whakawhiti o tētahi mea (A). Ko te taumahatanga kume e tautuhia ana ko te ōwehenga o te pikinga roa (Δl) ki te roa tīmatanga o te mea (lo). Ko te Modulus a Young te ōwehenga o te pēhanga kume ki te taumahatanga kume.
Pēhanga kume / taumahatanga kume = Te nekehanga a Young
F/A: Δl/lo = Y
Ki te iti te pēhanga kume, ka hoki te roa o te mea ki te āhua noa i muri i te tangohanga o te kaha. Ki te nui ake te pēhanga kume i te ngāwari o te mea, kāore te roa o te mea e hoki ki te āhua noa i muri i te tangohanga o te kaha. Ki te piki tonu te pēhanga kume, ka whati te mea.
2.2 Te rerekētanga kutikuti
Whakatakotoria he pukapuka matotoru ki runga i te mata o te tēpu. Whakatakotoria tō ringa ki runga i te mata o te pukapuka, ka panaia te mata o te pukapuka ki mua. Ka mahi tō pana i te mata o runga o te pukapuka, me tōna ahunga ki mua, kia rite ki te mata o te pukapuka. Ka noho okioki te mata o raro o te pukapuka mā te waku pūmau i te ahunga ke atu i te pana. I te tīmatanga, he tapawhā, he tapawhā rānei te āhua o te pukapuka, ā, i muri i te panaia, ka huri te āhua o te pukapuka hei whakarara. Ko ngā huringa o te āhua o te pukapuka tētahi tauira o te puta mai o te taumahatanga kutikuti nā te noho mai o te pēhanga kutikuti.
Ko te pēhanga kutikuti e tautuhia ana ko te ōwehenga o te kaha (F) ki te horahanga mata (A) e nekehia ana. Ko te taumahatanga kutikuti e tautuhia ana ko te ōwehenga o Δx ki te teitei o te mea (h). Ko te ōwehenga o te pēhanga kutikuti ki te taumahatanga kutikuti e kiia ana ko te modulus kutikuti.
Pēhanga kutikuti/taumahatanga kutikuti = Te tauwehenga kutikuti
F/A: Δx/h = Te nekehanga kutikuti
2.3 Tauwehenga Papatipu
I roto i tētahi kiriata tuhinga mō te Pakanga Tuarua o te Ao, kei reira ngā whakaaturanga pakanga i te moana e whakamahi ana i ngā waka ruku. Nā te mea e hiahia ana rātou ki te huna i ngā waka ruku a te hoariri, ka ruku hohonu te waka ruku moana o tētahi iwi, ā, ka tata tae ki te papa o te moana. He mea whakamiharo, i pakaru te pakitara o te waka ruku kia uru ai te wai moana ki roto i te waka ruku. I pakaru te pakitara o te waka ruku nā te pēhanga o te wai moana ki te mata o te waka ruku. He rite te pēhanga o te wai moana ki te hohonutanga o te wai moana. Ko te hohonutanga o te ruku, ko te nui ake o te pēhanga o te wai moana e pā ana ki a ia. Ki te kore e kaha te hanganga o te pakitara o te waka ruku, ka pakaru te pakitara o te waka ruku.
Ko te kōrero mō tētahi waka ruku i pakaru nā te pēhanga o te wai moana i runga i tōna mata katoa he tauira o tētahi mea e pāngia ana e te taumahatanga rōrahi nā te pēhanga rōrahi. Ko te pēhanga rōrahi e tautuhia ana ko te ōwehenga o te kaha katoa (F) e pā ana ki te mata katoa o te mea ki te horahanga mata (A) o te mea. Ko te taumahatanga rōrahi e tautuhia ana ko te ōwehenga o te whakaiti rōrahi (-ΔV) ki te rōrahi tīmatanga (Vo) o tētahi mea. Ko te ōwehenga pēhanga o te rōrahi ki te taumahatanga rōrahi e kiia ana ko te modulus papatipu.
Pēhanga rōrahi / taumahatanga rōrahi = te tauwehenga papatipu
– ΔF/A : ΔV/V o = te tauwehenga papatipu
Kei ngā mea totoka me ngā mea wai te modulus papatipu, engari ko ngā mea totoka anake kei a rātou te modulus Young me te modulus shear.
