Te ope tiaki me te ope kore tiaki
1. Te Rōpū Tiaki
1.1 Taumaha (w)
Mātakihia tētahi mea e neke poutū ana ki runga kia tae rā anō ki tōna teitei mōrahi i mua i te neke ki raro ki tōna tūranga tīmatanga. Ina neke poutū ana ki runga mā te h, he rerekē te ahunga o te taumaha i tōna nekehanga. Nō reira, ka mahi kino te taumaha ki runga i te mea.
W = wh (cos 180 o ) = – wh = – mgh
Kia eke ki te teitei mōrahi, ka neke te mea ki raro ki tōna tūranga tīmatanga mā te h. Ina neke ki raro, ka rite te ahunga o te taumaha ki te nekehanga. Nā te mea kei te rite te ahunga ki te nekehanga, ka mahi pai te taumaha.
W = wh (cos 0 o ) = wh = mgh
He rite tonu te papatipu (m), te whakaterenga ā-papa (g), me te teitei (h) o te mea, nō reira ka mahia te mahi e te taumaha nā te mea ka tīmata te neke poutū ki runga i te mea tae noa ki te hokinga ki tōna tūranga tīmatanga ko te kore.
W = mgh – mgh = 0
1.2 Te Kaha o te Puna
Mātakihia tētahi puna kua whakatakotoria ki te tūnga whakapae. Mēnā ka panaia, ka pēhia rānei te pito matau o te puna ki te taha maui, ka puta he kaha pana ki te taha matau. Ka taea e koe te whakaatu i tēnei mā te pēhi i tētahi puna. Hei tauira, whakatakotoria tētahi mea ki te pito matau, kātahi ka pēhia te mea ki te taha maui. Kia rerekē te puna mā te Δx, tangohia tō ringa i te mea me te puna. Ina kore te ringa e pā ki te puna, ka panaia te mea e te puna ki te taha matau.
Ina neke te mea ki te taha mauī, ko te ahunga o tōna nekehanga me tōna nekehanga he rerekē ki te ahunga o te kaha o te puna. Nā te mea he rerekē ngā ahunga tetahi ki tetahi, ka mahi kino te kaha o te puna.
W = – ½ k (Δx) 2
Ina neke te mea ki te taha matau, ka rite te ahunga o tōna nekehanga me tōna nekehanga ki te kaha o te puna. Nā te mea he rite ngā ahunga, ka mahi pai te kaha o te puna.
W = ½ k (Δx) 2
He rite tonu te puna i whakamahia, nō reira he rite tonu te pūmau o te puna (k). He rite anō hoki te pekapeka o te puna (Δx).
Nō reira, ka oti te mahi mā te taumaha ina tīmata te mea ki te neke ki maui mā te Δx, kātahi ka hoki ki matau mā te kore o Δx.
W = ½ k (Δx) 2 – ½ k (Δx) 2 = 0
Ka mahia te mahi e te taumaha me te kaha puna, mai i te mea ka tīmata te neke o te mea mai i tōna tūranga tīmatanga tae noa ki tōna hokinga mai, he ōrite ki te kore. Mena i mahia te mahi e te kaha, mai i te mea ka neke mai i tōna tūranga tīmatanga tae noa ki tōna hokinga mai, he ōrite ki te kore, ka kiia te kaha he kaha pūmau. Nō reira, ko te kaha puna me te taumaha he tauira o ngā kaha pūmau.
2. Te Mana Kore-Kaitiaki
Mātakihia tētahi mea e panaia ana ki te taha matau, kātahi ka panaia whakamuri ki te taha maui. Ina neke te mea, ina nekehia rānei ki te taha matau, ko te ahunga o te nekehanga o te mea he rite ki te ahunga o te kaha pana (F) engari he rerekē ki te ahunga o te kaha waku nekeneke (f k ). I te mea kei te ahunga rite ki te nekehanga, ka mahi pai te kaha pana ki te mea.
W = Fs
Heoi anō, ka mahi kino te kaha waku nekeneke ki runga i te mea.
W = – f k s
I mahia te mahi e te kaha pana me te kaha waku i runga i te mea i te tīmatanga o te nekehanga o te mea mai i tōna tūranga tīmatanga tae noa ki tōna hokinga mai, koinei ngā mea e whai ake nei:
W = 2 Fs
W = -2 f k s
Ka mahia te mahi e te kaha pana me te kaha waku nekeneke mai i te mea ka tīmata te neke o te mea mai i tōna tūranga tīmatanga tae noa ki tōna hokinga mai kāore i te ōrite ki te kore. Mena kāore te mahi i mahia e te kaha mai i te mea ka tīmata te neke mai i tōna tūranga tīmatanga tae noa ki tōna hokinga mai kāore i te ōrite ki te kore, ka kiia te kaha he kaha kore-pūmau. Nō reira, ko te kaha pana me te kaha waku nekeneke he tauira o ngā kaha kore-pūmau.
1. He aha te kaha pūmau? Ko te kaha pūmau he kaha e kore e pā te mahi i mahia i te neke i tētahi mea i waenga i ngā pūwāhi e rua ki te ara i tangohia. Ko ngā kaha ā-papa me ngā kaha hiko-pūmau he tauira o ngā kaha pūmau.
2. He aha te hononga o te mahi a te kaha pūmau ki te pūngao pūmanawa? Ko te mahi a te kaha pūmau ki runga i tētahi mea e neke ana mai i te pūwāhi A ki te pūwāhi B he rite ki te huringa kino o te pūngao pūmanawa (∆U) i waenganui i aua pūwāhi e rua: Ko te tikanga tēnei, ki te whiwhi pūngao pūmanawa tētahi mea, ka kino te mahi a te kaha pūmau, ā, ka pērā anō hoki.
3. He aha te kaha kore-pūmau? Ko te kaha kore-pūmau he kaha e whakawhirinaki ana te mahi i mahia i te neke i tētahi mea i waenga i ngā pūwāhi e rua ki te ara i tangohia. Ko te waku me te ātete hau he tauira noa o ngā kaha kore-pūmau.
4. He aha te pānga o te kaha kore-pūmau ki te pūngao miihini o tētahi pūnaha? Ka taea e te kaha kore-pūmau te whakarerekē i te pūngao miihini katoa (te tapeke o ngā pūngao nekeneke me ngā pūngao pūmanawa) o tētahi pūnaha. Nā te mea kāore te mahi a te kaha kore-pūmau e rongoatia hei pūngao pūmanawa engari ka hurihia ki ētahi atu momo pūngao, pērā i te wera.
5. Me pēhea te whakatau mēnā he kaha pūmau, he kaha kore pūmau rānei te kaha mā te whakamahi i tētahi ara porowhita kati? Mō tētahi kaha pūmau, ko te mahi kupenga i mahia ki tētahi mea i muri i tana haerenga i tētahi ara porowhita kati katoa he kore. Ki te kore te mahi kupenga i mahia ki runga i tētahi porowhita kati he kore, he kaha kore pūmau te kaha.
6. He aha te mahi a te piko o te āpure kaha ki te whakatau mena he pūmau te kaha? Mena he kore te piko o te āpure kaha i ngā wāhi katoa o te wāhi, he pūmau te kaha. Mena ehara te piko i te kore, kāti he kore pūmau te kaha.
7. He aha te hononga o te pūngao pūmanawa ā-papatipu ki ngā kaha pūmau? Ka puta te pūngao pūmanawa ā-papatipu nā te āhua pūmau o te kaha ā-papatipu. Mā te pikinga o te teitei i roto i te papa ā-papatipu ka piki ake te pūngao pūmanawa ā-papatipu, engari he kino te mahi a te kaha ā-papatipu, e tohu ana i te hekenga o te pūngao pūmanawa ina neke tata atu tētahi mea ki te Ao.
8. He aha te korenga o te pūngao pūmanawa e pā ana ki te waku pērā i ētahi atu kaha pūmau? He kaha kore-pūmau te waku; nō reira, kāore te mahi i mahia e te waku e rongoatia hei pūngao pūmanawa. Engari, he maha ngā wā ka hurihia ki ētahi atu āhua, pērā i te wera, ā, kāore e taea te whakahoki katoa hei pūngao miihini.
9. I roto i tētahi horopaki e paheke ana tētahi mea i raro i tētahi papa piko, he aha te mahi a ngā kaha pūmau me ngā kaha kore-pūmau? Ina paheke tētahi mea i raro i tētahi papa piko, ka pā te kaha tōpana, he kaha pūmau, ki te mea, ka huri i tōna kaha pūmanawa ki te kaha nekeneke. Mena he waku i waenganui i te mea me te papa piko (he kaha kore-pūmau), ka ātete i te nekehanga ka whakaiti i te kaha nekeneke o te mea, ka huri i ētahi o aua kaha hei wera.
10. Ka taea te tiaki i te pūngao katoa o te pūnaha ahakoa kei te whakamahia ngā kaha kore-pūmau? Ae, ka noho tonu te pūngao katoa o te pūnaha (tae atu ki ngā momo pūngao katoa pēnei i te pūngao miihini, te pūngao wera, me ētahi atu) kia rite ki te ture tiaki pūngao. Heoi, ina mahi ngā kaha kore-pūmau, kāore pea e tiakina te pūngao miihini (te tapeke o ngā pūngao nekeneke me ngā pūngao pūmanawa) nā te mea ka hurihia ētahi o aua pūngao ki ētahi atu momo pūngao, pēnei i te wera, te oro rānei.
