Mana hoʻomalu a me ka mana hoʻomalu ʻole
1. Pūʻali Koa Hoʻomalu
1.1 Kaumaha (w)
E nānā i kahi mea e neʻe kū pololei ana i luna a hiki i ka hiki ʻana i kahi kiʻekiʻe loa ma mua o ka neʻe ʻana i lalo i kona kūlana mua. Ke neʻe kū pololei ana i luna ma o h, ua kūʻē ke kaumaha i ke kuhikuhi mai ka neʻe ʻana. No laila, hana ke kaumaha i ka hana maikaʻi ʻole ma luna o ka mea.
W = wh (cos 180o) = – wh = – mgh
Ma hope o ka hiki ʻana i ke kiʻekiʻe loa, neʻe ka mea i lalo i kona kūlana mua ma o h. Ke neʻe i lalo, aia ke kaumaha ma ke kuhikuhi like me ka neʻe ʻana. No ka mea aia ia ma ke kuhikuhi like me ka neʻe ʻana, hana ke kaumaha i ka hana maikaʻi.
W = wh (cos 0o) = wh = mgh
Ua like ke kaumaha o ka mea (m), ka wikiwiki o ka umekaumaha (g), a me ke kiʻekiʻe (h), no laila ua hana ʻia ka hana e ke kaumaha ʻoiai ua hoʻomaka ka mea e neʻe pololei i luna a hiki i ka hoʻi ʻana i kona kūlana mua he ʻole.
W = mgh – mgh = 0
1.2 Mana Puna
E nānā i kahi pūnāwai i kau ʻia ma ke kūlana moe. Inā paʻi ʻia a kaomi ʻia paha ka ʻaoʻao ʻākau o ka pūnāwai i ka hema, hoʻopuka ka pūnāwai i kahi ikaika hoʻokuke i ka ʻākau. Hiki iā ʻoe ke hōʻoia i kēia ma ke kaomi ʻana i kahi pūnāwai. No ka laʻana, e kau i kahi mea ma ka ʻaoʻao ʻākau, a laila e kaomi i ka mea i ka hema. Ma hope o ka haʻalele ʻana o ka pūnāwai e Δx, e wehe i kou lima mai ka mea a me ka pūnāwai. Ke pau ka pili ʻana o ka lima me ka pūnāwai, e hoʻihoʻi ka pūnāwai i ka mea i ka ʻākau.
Ke neʻe ka mea i ka hema, ʻo ke kuhikuhi o kona neʻe ʻana a me kona neʻe ʻana ua kūʻē i ke kuhikuhi o ka ikaika o ka pūnāwai. Ma muli o ke kūʻē ʻana o nā kuhikuhi kekahi i kekahi, hana ka ikaika o ka pūnāwai i ka hana maikaʻi ʻole.
W = – ½ k (Δx)2
Ke neʻe ka mea i ka ʻākau, ua like ke kuhikuhi o kona neʻe ʻana a me kona neʻe ʻana me ka ikaika o ka pūnāwai. No ka mea ua like nā kuhikuhi, hana ka ikaika o ka pūnāwai i ka hana maikaʻi.
W = ½ k (Δx)2
Ua like ka pūnāwai i hoʻohana ʻia, no laila ua like ke kūpaʻa o ka pūnāwai (k). Ua like nō hoʻi ka ʻokoʻa o ka pūnāwai (Δx).
No laila, hana ʻia ka hana ma ke kaumaha ke hoʻomaka ka mea e neʻe i ka hema ma o Δx a laila neʻe hou i ka ʻākau ma o Δx he ʻole.
W = ½ k (Δx)2 – ½ k (Δx)2 = 0
Hana ʻia ka hana e ke kaumaha a me ka ikaika puna mai ka hoʻomaka ʻana o ka mea e neʻe mai kona kūlana mua a hiki i kona hoʻi ʻana mai ua like ia me ka ʻole. Inā ua hana ʻia ka hana e kahi ikaika mai ka neʻe ʻana mai kona kūlana mua a hiki i kona hoʻi ʻana mai ua like ia me ka ʻole, ua kapa ʻia ka ikaika he ikaika conservative. No laila, ʻo ka ikaika puna a me ke kaumaha he mau laʻana o nā ikaika conservative.
2. Mana Hoʻomalu ʻole
E nānā i kahi mea i paʻi ʻia i ka ʻākau a laila hoʻihoʻi ʻia i ka hema. Ke neʻe nei ka mea a i ʻole e neʻe ʻia i ka ʻākau, ʻo ke kuhikuhi o ka neʻe ʻana o ka mea ua like ia me ke kuhikuhi o ka ikaika hoʻokuʻi (F) a kūʻē i ke kuhikuhi o ka ikaika frictional kinetic (fk). Ma muli o ke kuhikuhi like me ka neʻe ʻana, hana ka ikaika hoʻokuke i ka hana maikaʻi ma luna o ka mea.
W = Fs
I ka ʻaoʻao ʻē aʻe, hana ka ikaika frictional kinetic i kahi hana maikaʻi ʻole ma ka mea.
W = – fk s
Ua hana ʻia ka hana e ka ikaika hoʻokuʻi a me ka ikaika frictional ma luna o ka mea i ka wā e hoʻomaka ai ka mea e neʻe mai kona kūlana mua a hiki i kona hoʻi ʻana mai, aia kēia mau mea:
W = 2 Fs
W = -2 fk s
Hana ʻia ka hana e ka ikaika hoʻokuʻi a me ka ikaika frictional kinetic ʻoiai ke hoʻomaka nei ka mea e neʻe mai kona kūlana mua a hiki i kona hoʻi ʻana mai ʻaʻole like me ka ʻole. Inā ʻaʻole like ka hana i hana ʻia e kahi ikaika mai ka hoʻomaka ʻana o ka mea e neʻe mai kona kūlana mua a hiki i kona hoʻi ʻana mai ʻaʻole like me ka ʻole, ua kapa ʻia ka ikaika he ikaika non-conservative. No laila, ʻo ka ikaika hoʻokuʻi a me ka ikaika frictional kinetic he mau laʻana o nā ikaika non-conservative.
1. He aha ka mana conservative? ʻO ka ikaika conservative kekahi mea nona ka hana i hana ʻia i ka hoʻoneʻe ʻana i kahi mea ma waena o ʻelua mau wahi he kūʻokoʻa ia o ke ala i hele ʻia. ʻO nā ikaika umekaumaha a me nā ikaika electrostatic nā hiʻohiʻona o nā ikaika conservative.
2. Pehea e pili ai ka hana a kahi ikaika conservative i ka ikehu hiki? ʻO ka hana i hana ʻia e kahi ikaika conservative ma kahi mea e neʻe ana mai kahi A a i kahi B ua like ia me ka loli maikaʻi ʻole o ka ikehu hiki (∆U) ma waena o kēlā mau wahi ʻelua: ʻO ke ʻano kēia inā loaʻa i kahi mea ka ikehu hiki, he maikaʻi ʻole ka hana i hana ʻia e ka ikaika conservative, a ʻo ka ʻaoʻao ʻē aʻe.
3. He aha ka mana hoʻomalu ʻole? ʻO ka ikaika nonconservative kekahi mea nona ka hana i hana ʻia i ka neʻe ʻana i kahi mea ma waena o ʻelua mau wahi e hilinaʻi ʻia ma ke ala i hele ʻia. ʻO ka friction a me ke kū'ē ʻana o ka ea nā hiʻohiʻona maʻamau o nā ikaika nonconservative.
4. Pehea ka hopena o ka ikaika nonconservative i ka ikehu mechanical o kahi ʻōnaehana? Hiki i kahi ikaika nonconservative ke hoʻololi i ka ikehu mechanical holoʻokoʻa (ka huina o nā ikehu kinetic a me nā ikehu hiki) o kahi ʻōnaehana. ʻO kēia no ka mea ʻaʻole mālama ʻia ka hana i hana ʻia e kahi ikaika nonconservative ma ke ʻano he ikehu hiki akā ua hoʻololi pinepine ʻia i nā ʻano ikehu ʻē aʻe, e like me ka wela.
5. Pehea e hiki ai i kekahi ke hoʻoholo inā he conservative a nonconservative paha kahi ikaika me ka hoʻohana ʻana i kahi ala loop pani? No ka ikaika conservative, ʻo ka hana upena i hana ʻia ma luna o kahi mea ma hope o kona hele ʻana i kahi ala loop pani piha he zero. Inā ʻaʻole zero ka hana upena i hana ʻia ma luna o kahi loop pani, ʻaʻole conservative ka ikaika.
6. He aha ke kuleana o ka wili ʻana o kahi kahua ikaika i ka hoʻoholo ʻana inā he ikaika conservative? Inā ʻo ka wili ʻana o kahi kahua ikaika he ʻole ma nā wahi āpau o ka lewa, he conservative ka ikaika. Inā ʻaʻole he zero ka wili ʻana, a laila ʻaʻole conservative ka ikaika.
7. Pehea e pili ai ka ikehu hiki ke hoʻohana ʻia e ka umekaumaha me nā mana kūpaʻa? Hoʻāla ʻia ka ikehu hiki ke umekaumaha ma muli o ke ʻano mālama o ka ikaika umekaumaha. ʻO ka piʻi ʻana o ke kiʻekiʻe i loko o kahi kahua umekaumaha e alakaʻi ai i ka piʻi ʻana o ka ikehu hiki ke umekaumaha, ʻoiai ʻo ka hana i hana ʻia e ka ikaika umekaumaha he maikaʻi ʻole, e hōʻike ana i ka emi ʻana o ka ikehu hiki ke neʻe aku kahi mea i ka Honua.
8. No ke aha ʻaʻohe ikehu hiki ke pili o ka friction e like me nā mana conservative ʻē aʻe? He ikaika mālama ʻole ka haʻihaʻi; no laila, ʻaʻole mālama ʻia ka hana i hana ʻia e ka haʻihaʻi ma ke ʻano he ikehu hiki. Akā, hoʻololi pinepine ʻia ia i nā ʻano ʻē aʻe, e like me ka wela, a ʻaʻole hiki ke hoʻihoʻi piha ʻia ma ke ʻano he ikehu mechanical.
9. I loko o kahi hiʻohiʻona kahi e paheʻe ai kahi mea i lalo o kahi mokulele hilig, pehea lā e pāʻani ai nā mana conservative a me nā mana nonconservative? Ke paheʻe kahi mea i lalo i kahi mokulele hilig, hana ka ikaika umekaumaha, kahi ikaika conservative, ma luna o ka mea, e hoʻololi ana i kona ikehu hiki i ka ikehu kinetic. Inā he friction ma waena o ka mea a me ka mokulele hilig (kahi ikaika nonconservative), e kūʻē ia i ka neʻe ʻana a hoʻemi i ka ikehu kinetic o ka mea, e hoʻololi ana i kekahi o ia mea i wela.
10. Hiki ke mālama ʻia ka ikehu holoʻokoʻa o kahi ʻōnaehana ʻoiai inā e pāʻani ana nā mana nonconservative? ʻAe, ʻo ka ikehu holoʻokoʻa o kahi ʻōnaehana (me nā ʻano ikehu āpau e like me ka mechanical, thermal, a me nā mea ʻē aʻe) e mālama mau ʻia e like me ke kānāwai o ka mālama ʻana i ka ikehu. Eia nō naʻe, ke hana nā mana nonconservative, ʻaʻole paha e mālama ʻia ka ikehu mechanical (ka huina o nā ikehu kinetic a me nā ikehu hiki) no ka mea ua hoʻololi ʻia kekahi o ia mau mea i nā ʻano ikehu ʻē aʻe, e like me ka wela a i ʻole ke kani.
