Inā ʻoe e paʻi i kahi puke ma luna o kahi papaʻaina a hiki i ka neʻe ʻana, ke hana nei ʻoe i ka hana ma luna o ka puke. Ke hāʻule kahi mea i luna o ka honua no ka mea ua huki ʻia e ka ikaika o ke koʻikoʻi , hana ka ikaika o ke koʻikoʻi ma luna o ka mea. I ka ʻaoʻao ʻē aʻe, inā ʻoe e paʻi i kahi mea me kou ikaika a pau a pulu ʻoe i ka hou akā ʻaʻole neʻe ka mea, ʻaʻole ʻoe i hana i ka hana ma luna o ka mea. I ke ola o kēlā me kēia lā, ua ʻōlelo ʻia ua hana ʻoe i ka hana a i ʻole ka hana nui e paʻi ana i kahi mea, akā e like me ke ʻano o ka physics, ʻaʻole ʻoe i hana i ka hana ma luna o ka mea no ka mea ʻaʻole ʻike ka mea i ka neʻe ʻana (ʻaʻole e loli kahi o ka mea).
Hiki ke hana ʻia ka hana e kahi ikaika mau (ʻo ka nui a me ke kuhikuhi o ka ikaika e mau ana ka like) a i ʻole kahi ikaika loli (ʻo ka nui a me ke kuhikuhi o ka ikaika e loli). ʻO kahi laʻana o kahi ikaika me ka nui a me ke kuhikuhi mau, ʻo ia ka ikaika umekaumaha e hana ana ma kahi mea kokoke i ka ʻili o ka Honua. ʻO kahi laʻana o kahi ikaika me ka nui a me ke kuhikuhi loli, ʻo ia ka ikaika o kahi pūnāwai. Inā ʻoe e hoʻolōʻihi i kahi pūnāwai, ʻo ka nui o kou hoʻolōʻihi ʻana, ʻoi aku ka ikaika o kou huki ʻana, no laila, ʻaʻole mau ka nui o ka ikaika i ka wā e hoʻolōʻihi ai ka pūnāwai. ʻO kekahi laʻana, ʻo ia ka wā e neʻe ai kahi rocket i ka lewa, ʻo ka mamao loa mai ka ʻili o ka Honua, ʻoi aku ka liʻiliʻi o ka ikaika umekaumaha o ka Honua e hana ana ma ka rocket.
1.1 Hana i hana ʻia e ka ikaika mau
Ma ke ʻano makemakika, ʻo ka hana i hana ʻia e ka ikaika mau ma luna o kahi mea, ʻo ia ka huahana o ka neʻe ʻana he mea me kahi ikaika a ʻāpana paha o ka ikaika e like ana me ka neʻe ʻana o ka mea.
Hana i hana ʻia e ka ikaika e hoʻokuke ana (F):
W = (F)(s)(cos θ) = Fs (cos 0) = Fs (1) = Fs
ʻO ka hana i hana ʻia e ka ʻāpana o ka ikaika F ma ke kuhikuhi pae (F cos θ):
W = (F cos θ)(s)(cos 0) = (F cos θ)(s)(1) = F s cos θ
Hana i hana ʻia e ka ikaika friction kinetic (fk):
W = (fk cos θ)(s)(cos 180) = (fk )(s)(-1) = – fk s
Hana i hana ʻia e ka ikaika maʻamau (N):
W = (N)(s)(cos 90o) = (N)(s)(0) = 0
Hana i hana ʻia e ke koʻikoʻi (w):
W = (w)(s)(cos 90o) = (w)(s)(0) = 0
Wehewehe: W = ka hoʻoikaika a i ʻole ka hana (Joules), s = ka neʻe ʻana (mika), θ = ke kihi i hoʻokumu ʻia e ka ikaika me ka neʻe ʻana
Ma ka laʻana ma mua, ʻo ka hana i hana ʻia e umekaumaha ʻO (w) he waiwai o ka ʻole no ka mea he kū pololei ke kuhikuhi o ka ikaika umekaumaha (e hana ana i kahi kihi 90°)o) me ke kuhikuhi o ka neʻe ʻana (kuhikuhi o ka neʻe ʻana) o ka mea. Pono e hoʻomaopopo ʻia ʻaʻole ʻo ka hana i hana ʻia e ke kaumaha he zero inā like ke kuhikuhi o ka ikaika umekaumaha me ke kuhikuhi o ka neʻe ʻana a i ʻole ke kūʻē i ke kuhikuhi.
ʻO ka hana i hana ʻia e ka ikaika o ke koʻikoʻi (w) ma luna o ka mea e hāʻule manuahi ana ma ke kiʻi a penei:
W = Fs (cos θ) = wh (cos 0) = wh (1) = wh = mgh
ʻO ka hana i hana ʻia e ka ikaika o ke koʻikoʻi (w) ma luna o ka mea e neʻe ana i luna ma ke kiʻi b penei:
W = Fs (cos θ) = wh (cos 180) = wh (-1) = -wh = -mgh
Wehewehe: w = kaumaha (Newton), h = kiʻekiʻe (mika), m = nuipa (kg), g = wikiwiki ma muli o ke koʻikoʻi (mika i kekona kuea)
Ma muli o ka wehewehe ʻana ma mua, hiki ke hoʻoholo ʻia nā manaʻo aʻe:
Ka mua, inā ʻaʻole ʻike ka mea i ka neʻe ʻana, a laila ʻaʻole hana ka ikaika e hana ana ma ka neʻe ʻana. Inā s = 0 a laila W = 0.
Ka luaInā hoʻokumu ka ikaika i kahi kihi i ka neʻe ʻana o ka mea, a laila ʻo ka ʻāpana o ka ikaika ma ke kuhikuhi o ka neʻe ʻana o ka mea wale nō ka hana ma ka mea.
Ke kolu, ʻaʻole hana ka ikaika e kū pono ana i ka neʻe ʻana o kahi mea i kekahi hana ma luna o ka mea. Inā kū pono ka ikaika i ka neʻe ʻana, ʻo ke kihi i hana ʻia he 90°o.Cos 90o = 0.
Ka ʻehā, Hiki i ka hoʻoikaika ke maikaʻi a maikaʻi ʻole paha. Inā like ka ikaika me ka neʻe ʻana o ka mea, ʻo ke kihi i hoʻokumu ʻia he 0o a laila hana ka ikaika i ka hana maikaʻi, ma ke ʻano ʻē aʻe inā aia ka ikaika ma ke kuhikuhi ʻē aʻe i ka neʻe ʻana no laila ʻo ke kihi i hoʻokumu ʻia he 180o a laila hana ka ikaika i ka hana maikaʻi ʻole ma ka mea.
ʻO ka hana i hana ʻia e ka ikaika mau ma luna o kahi mea i ka wā e neʻe ai ka mea ua like ia me ka ʻāpana i aka ʻia ma ka pakuhi o ka ikaika (F) a me ka neʻe ʻana (s).
ʻO W (huapalapala nui) ka hōʻailona no ka hana ʻoiai ʻo w (huapalapala liʻiliʻi) ka hōʻailona no ke kaumaha. ʻO ke anakahi ʻōnaehana honua no ka hana ʻo ia ka mika Newton (N m). ʻO kekahi inoa no ka mika Newton ʻo Joule, i hoʻopōkole ʻia ʻo J, i kapa ʻia no ka hoʻohanohano ʻana i ka mea loea kino Pelekane o ke kenekulia 19 ʻo James Prescott Joule.
1.2. Hana i hana ʻia e ka ikaika mau ʻole
ʻO kahi laʻana o ka ikaika loli ka ikaika puna. Ke loli mau nei ka nui o ka ikaika puna, no laila ʻaʻole hiki ke helu ʻia ka hana i hana ʻia e ka ikaika puna ma kahi mea me ka hoʻohana ʻana i ke ʻano hana no ka hana i hana ʻia e kahi ikaika mau.
Inā e kīkoʻo ʻia ka pūnāwai, ʻo ka lōʻihi o ka pūnāwai, ʻo ka nui o ka ikaika e pono ai. Pēlā nō, ʻo ka ʻaoʻao ʻē aʻe, ʻo ka nui o ke kaomi ʻia, ʻo ka pōkole o ka ikaika i ka wā e kīkoʻo ai ka pūnāwai, ʻo ka nui o ka ikaika e pono ai. I ka lōʻihi o ke kaomi ʻia ʻana a i ʻole ke kīkoʻo ʻia ʻana o ka pūnāwai, e loli ka ikaika o ka pūnāwai mai 0 (x = 0) a i ka palena kiʻekiʻe (F = kx) no laila ua helu ʻia ka ikaika o ka pūnāwai me ka hoʻohana ʻana i ka awelika. ʻO ka ikaika o ka pūnāwai awelika:
F = ½ (0 + kx) = ½ kx
ʻO ka hana i hana ʻia e ka ikaika puna ma luna o kahi mea:
W = F x = ½ kx2
Wehewehe: W = hana (nā anakahi Joules), x = piʻi ʻana o ka lōʻihi o ka pūnāwai (nā anakahi mika), F = ikaika pūnāwai (nā anakahi Newton).
2. Hana hopena a i ʻole hana holoʻokoʻa (hana i hana ʻia e ka ikaika holoʻokoʻa)
Inā hoʻokahi wale nō ikaika e hana ana ma luna o kahi mea i kona neʻe ʻana, a laila ua like ka hana i hana ʻia e ka ikaika holoʻokoʻa me ka hana i hana ʻia e kēlā ikaika. No ka laʻana, i ka wā e hāʻule manuahi ai kahi mea a hoʻowahāwahā ʻia ke kū'ē ʻana o ka ea, ʻo ka ikaika wale nō e hana ana ma luna o ka mea ʻo ia ka umekaumaha.
W = Wumekaumaha
Inā he nui nā mana e hana ana ma luna o kahi mea i ka wā e neʻe ana ka mea, a laila ua like ka hana i hana ʻia e ka mana holoʻokoʻa me ka huina o ka hana i hana ʻia e nā mana a pau e hana ana ma luna o ka mea.
W = W1 + W2 + W3 + … + Wn
Hiki ke helu ʻia ka hana i hana ʻia e kekahi mau mana e hana ana ma kahi mea ma ka ʻike mua ʻana i ka nui o ka ikaika holoʻokoʻa a laila e hoʻonui iā ia me ka nui o ka neʻe ʻana.
W = (Ka ikaika hopena)(neʻe ʻana) = (ka hopena F)(s)
