Pakihi ahupūngao

Ki te panaia e koe tētahi pukapuka ki runga i tētahi tēpu kia neke ra ano, kei te mahi koe i te pukapuka. Ina taka tētahi mea ki te mata o te whenua nā te mea e tōia ana e tētahi kaha. kaha ā-papa Ka pā te kaha ā-papa ki te mea. I tetahi atu taha, ki te pana koe i tētahi mea ki tō kaha katoa kia mākū rawa koe i te werawera engari kāore te mea e neke, kāore koe i mahi i tētahi mahi ki runga. I roto i te oranga o ia rā, e kiia ana kua mahi koe, kua mahi kaha rānei koe ki te pana i tētahi mea, engari e ai ki te ahupūngao, kāore koe i mahi i tētahi mahi ki runga i te mea nā te mea kāore te mea i neke (kāore i neke).

Pakihi ka taea te mahi mā te kaha pumau (ka noho tonu te rahi me te ahunga o te kaha) mā te kaha taurangi rānei (ka huri te rahi me te ahunga o te kaha). Ko tētahi tauira o te kaha he nui me te ahunga pumau ko te kaha ā-pūmau e pā ana ki tētahi mea e tata ana ki te mata o te Ao. Ko tētahi tauira o te kaha he nui me te ahunga pumau ko te kaha o te puna. Ki te totoro koe i tētahi puna, ka nui ake tō totoro, ka kaha ake tō kume, nō reira kāore te rahi o te kaha e pumau i te totoro o te puna. Ko tētahi atu tauira ko te neke o tētahi rōkete ki te wāhi, ka tawhiti atu i te mata o te Ao, ka iti ake te kaha ā-pūmau o te Ao e pā ana ki te rōkete.

1.1 Te mahi i mahia e te kaha pumau
I roto i te pāngarau, ko te mahi i mahia e te kaha pumau ki runga i tētahi mea ko te hua o nekehanga he mea kei a ia te kaha, te wāhanga rānei o te kaha e rite ana te ahunga ki te nekehanga o te mea.

Te mahi i mahia e te kaha pana (F):
W = (F)(s)(cos θ) = Fs (cos 0) = Fs (1) = Fs
Ko te mahi i mahia e te wāhanga o te kaha F i te ahunga whakapae (F cos θ):
W = (F cos θ)(s)(cos 0) = (F cos θ)(s)(1) = F s cos θ
Te mahi i mahia e te kaha waku nekeneke (fk):
W = (f_k cos θ)(s)(cos 180) = (f_k )(s)(-1) = – f_k s
Te mahi i mahia e te kaha noa (N):
W = (N)(s)(cos 90^o) = (N)(s)(0) = 0
Te mahi i mahia e te kaha ā-papa (w):
W = (w)(s)(cos 90^o) = (w)(s)(0) = 0
Whakaahuatanga: W = kaha, mahi rānei (Joules), s = nekehanga (mita), θ = koki i hangaia e te kaha me te nekehanga

I te tauira o mua, ko te mahi i mahia e kaha ā-papa Kore te uara o (w) nā te mea he poutū te ahunga o te kaha ā-papa (e hanga ana i te koki 90°)^o) me te ahunga o te nekehanga (te ahunga o te nekehanga) o te mea. Me mōhio ko te mahi i mahia e te taumaha ehara i te kore mena he rite te ahunga o te kaha ā-papa ki te ahunga o te nekehanga, he rerekē rānei.

Ko te mahi i mahia e te kaha o te papatipu (w) ki runga i te mea e hinga noa ana i te ahua a ko:
W = F s (cos θ) = wh (cos 0) = wh (1) = wh = mgh
Ko te mahi i mahia e te kaha o te papatipu (w) i runga i te mea e neke poutū ana ki runga i te ahua b ko:
W = F s (cos θ) = wh (cos 180) = wh (-1) = -wh = -mgh

Whakaahuatanga: w = taumaha (Newton), h = teitei (mita), m = papatipu (kg), g = whakaterenga nā te kaha ā-papatipu (mita ia hekona tapawhā)

I runga i te whakamārama o mua, ka taea te whakatau i ngā kōrero e whai ake nei:
Tuatahi, ki te kore te mea e nekehia, kāore te kaha e pā ana ki te nekehia e mahi. Ki te s = 0, ko W = 0.
TuaruaKi te hanga te kaha i tētahi koki ki te nekehanga o te mea, ko te wāhanga anake o te kaha i te ahunga o te nekehanga o te mea ka mahi ki te mea.
Tuatoru, kāore he mahi a te kaha e poutū ana ki te nekehanga o tētahi mea ki runga i te mea. Mēnā he poutū te kaha ki te nekehanga, ko te koki i hangaia he 90°^o. Kos 90^o = 0.
Tuawhā, Ka taea e te kaha te pai, te kino rānei. Mena kei te ahunga ōrite te kaha ki te nekehanga o te mea, ko te koki i hangaia he 0.^o kātahi ka mahi te kaha i te mahi pai, engari ki te mea kei te taha kē te kaha i te nekehanga, ko te koki i hangaia he 180^o kātahi ka mahi te kaha i te mahi kino ki runga i te mea.
Ko te mahi i mahia e te kaha pumau ki runga i tētahi mea i te wā e nekehia ana te mea he ōrite ki te horahanga kua whakamarumaruhia i roto i te kauwhata o te kaha (F) me te nekenga (s).
Ko te tohu mō te mahi ko W (reta nui) ko te tohu mō te taumaha ko w (reta iti). Ko te waeine pūnaha ā-ao mō te mahi ko te mita Newton (N m). Ko tētahi atu ingoa mō te mita Newton ko te Joule, i whakarāpopototia ko J, i tapaina hei whakahonore i te tohunga ahupūngao Piritana o te rautau 19, a James Prescott Joule.

1.2. Mahi i mahia e te kaha kore-pūmau
Ko tētahi tauira o te kaha taurangi ko te kaha puna. Kei te huri tonu te rahi o te kaha puna, nō reira kāore e taea te tatau i te mahi i mahia e te kaha puna ki runga i tētahi mea mā te whakamahi i te tātai mō te mahi i mahia e te kaha pumau.

Ki te totorohia te puna, ka roa ake te puna, ka nui ake te kaha e hiahiatia ana. Waihoki, ki te nui ake te pēhanga e pēhia ana, ka poto ake te kaha i te wā e totorohia ana te puna, ka nui ake te kaha e hiahiatia ana. I te mea ka pēhia, ka totorohia rānei te puna, ka huri te kaha o te puna mai i te 0 (x = 0) ki te mōrahi (F = kx) nō reira ka tatauhia te kaha o te puna mā te whakamahi i te toharite. Ko te kaha toharite o te puna ko:
F = ½ (0 + kx) = ½ kx
Ko te mahi i mahia e te kaha o te puna ki runga i tētahi mea ko:
W = F x = ½ kx²
Whakaahuatanga: W = mahi (ngā Joule), x = pikinga o te roa o te puna (ngā mita), F = kaha o te puna (ngā Newton).

2. Mahi hua, mahi katoa rānei (mahi i mahia e te kaha katoa)
Mena kotahi anake te kaha e pā ana ki tētahi mea i a ia e neke ana, ko te mahi i mahia e te kaha katoa he ōrite ki te mahi i mahia e taua kaha. Hei tauira, ina hinga noa tētahi mea, ā, kāore e arohia te ātete hau, ko te kaha ā-papa anake e pā ana ki te mea ko te kaha ā-papa.
W = W_{kaha ā-papa}
Mena he maha ngā kaha e pā ana ki tētahi mea i te wā e neke ana te mea, ko te mahi i mahia e te kaha katoa he ōrite ki te tapeke o te mahi i mahia e ngā kaha katoa e pā ana ki te mea.
W = W₁ + W₂ + W₃ + … + W_n
Ka taea hoki te tatau i te mahi i mahia e ētahi kaha e pā ana ki tētahi mea mā te kimi i te rahi o te kaha katoa, kātahi ka whakareatia ki te rahi o te nekehanga.
W = (Te kaha hua)(nekehanga) = (te kaha hua F)(s)

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