Pehea e helu ai i ka hana a me ka ikehu
ʻO ka hoʻomaopopo ʻana i nā manaʻo o ka hana a me ka ikehu a me ka ʻike pehea e helu ai iā lākou he mea nui ia ma ke kahua o ka physics. ʻAʻole wale kēia mau manaʻo he kumu no ka physics theoretical akā he mau noi kūpono hoʻi ma nā ʻano like ʻole e like me ka ʻenekinia, kemika, a me ka biology. Ma kēia ʻatikala, e ʻeli mākou i nā wehewehe ʻana o ka hana a me ka ikehu, nā mea hana makemakika e pono ai e helu iā lākou, a me nā laʻana e wehewehe maikaʻi i kēia mau manaʻo.
He aha ka Hana?
Ma ke ao o ke kino, he manaʻo ʻokoʻa ko "hana" i hoʻohālikelike ʻia me kona hoʻohana ʻana i kēlā me kēia lā. Hana ʻia ka hana ke hoʻoneʻe ʻia kahi mea e kahi ikaika. Ma ke ʻano makemakika, ua wehewehe ʻia ka hana (W) ʻo ia ka huahana kiko o ka ikaika a me nā vectors neʻe:
\[ W = \mathbf{F} \cdot \mathbf{d} \]
Where:
– ʻO ka hana i hana ʻia ʻo \(W\),
– ʻo \(\mathbf{F}\) ka ikaika i hoʻopili ʻia,
– ʻO \(\mathbf{d}\) ka neʻe ʻana.
No ka ikaika i hoʻopili ʻia ma kahi kihi \(\theta\) i ka neʻe ʻana, lilo ke ʻano hana:
\[ W = F d \cos(\theta) \]
Maanei, ʻo \(F\) a me \(d\) nā nui o ka ikaika a me ka neʻe ʻana, kēlā me kēia, a ʻo \(\theta\) ke kihi ma waena o nā vectors ikaika a me ka neʻe ʻana.
Nā ʻĀpana Hana
ʻO ke anakahi SI no ka hana ʻo Joule (J), kahi e like ai ʻo 1 Joule me 1 Newton-mika (N·m). Ma nā anakahi ʻole SI, hiki ke ana ʻia ka hana ma nā calorie a i ʻole nā kapuaʻi-paona, a me nā mea ʻē aʻe.
Nā Laʻana o ka Helu Hana
1. Neʻe ʻAoʻao: Manaʻo ʻoe e paʻi i kahi pahu me ka ikaika o 50 N ma luna o ka papahele no 10 mika.
\[ W = F \times d \cos(\theta) \]
Ke manaʻo nei ua hoʻopili ʻia ka ikaika ma ke kuhikuhi o ka neʻe ʻana (\(\theta = 0^\circ\), \(\cos(0) = 1\)):
\[ W = 50 \, \text{N} \times 10 \, \text{m} \times 1 = 500 \, \text{J} \]
2. Papahele Hiligila: Inā paheʻe ka pahu like i luna i kahi alapiʻi i hiligila ʻia ma 30° me ka ikaika like o 50 N, a uhi ia i 10 mika ma ke alapiʻi.
\[ W = F \times d \times \cos(\theta) \]
Eia, \(\theta = 30^\circ\), (\(\cos(30^\circ) = \sqrt{3}/2\)):
\[ W = 50 \, \text{N} \times 10 \, \text{m} \times \frac{\sqrt{3}}{2} \approx 433 \, \text{J} \]
He aha ka Energy?
ʻO ka ikehu ka hiki ke hana i ka hana. Loaʻa ia ma nā ʻano like ʻole, e like me ka ikehu kinetic, ka ikehu hiki, ka ikehu wela, a pēlā aku. ʻO nā ʻano ʻelua i kūkākūkā pinepine ʻia i ka mechanics classical, ʻo ia ka ikehu kinetic a me ka ikehu hiki.
Ikehu Kinetic
ʻO ka ikehu kinetic (\(K\)) ka ikehu o ka neʻe ʻana a ua hāʻawi ʻia e:
\[ K = \frac{1}{2}mv^2 \]
Where:
– ʻO \(m\) ka nuipa o ka mea,
– ʻo \(v\) kona wikiwiki.
Ka ikehu kūpono
ʻO ka ikehu hiki ke hana ʻia (\(U\)) ka ikehu i mālama ʻia i loko o kahi mea ma muli o kona kūlana a i ʻole ke ʻano. ʻO ke ʻano maʻamau ka ikehu hiki ke hana ʻia me ka umekaumaha, i hāʻawi ʻia e:
\[ U = mgh \]
Where:
– ʻo \(m\) ka nuipa,
– ʻO \(g\) ka wikiwiki ma muli o ke koʻikoʻi (9.8 m/s² ma ka Honua),
– ʻO \(h\) ke kiʻekiʻe.
Ka mālama ʻana i ka ikehu
ʻO ke kumumanaʻo o ka mālama ʻana i ka ikehu e ʻōlelo nei ʻaʻole hiki ke hana ʻia a luku ʻia paha ka ikehu, hoʻoili wale ʻia a hoʻololi ʻia paha mai kekahi ʻano i kekahi. Ma ke ʻano makemakika:
\[ E_{\text{total}} = K + U \]
No kahi ʻōnaehana i hoʻokaʻawale ʻia, e mau ana ka ikehu holoʻokoʻa:
\[ \Delta E_{\text{ka huina}} = 0 \]
Nā ʻĀpana o ka Ikehu
E like me ka hana, ʻo Joule (J) ka anakahi SI no ka ikehu.
Nā Laʻana o nā Helu Ikehu
1. Ikehu Kinetic: Ke neʻe nei kahi kaʻa he 1000 kg ke kaumaha ma ka wikiwiki o 20 m/s.
\[ K = \frac{1}{2}mv^2 \]
\[ K = \frac{1}{2} \times 1000 \, \text{kg} \times (20 \, \text{m/s})^2 \]
\[ K = \frac{1}{2} \times 1000 \times 400 \]
\[ K = 200,000 \, \kikokikona{J} \]
2. Ikehu Hiki: Aia kahi pōhaku he 10 kg ke kaumaha ma ka piko o kahi puʻu he 5 mika ke kiʻekiʻe.
\[ U = mgh \]
\[ U = 10 \, \text{kg} \times 9.8 \, \text{m/s}^2 \times 5 \, \text{m} \]
\[ U = 490 \, \kikokikona{J} \]
Kumumanaʻo Hana-Ikehu
Ua like ka hana i hana ʻia ma luna o kahi mea me ka loli o kona ikehu kinetic. Ua ʻike ʻia kēia ʻo ke kumumanaʻo hana-ikehu:
\[ W = \Delta K \]
Where:
\[ \Delta K = K_f – K_i \]
– ʻO \(K_f\) ka ikehu kinetic hope loa,
– ʻO \(K_i\) ka ikehu kinetic mua.
Laʻana o ke Kumumanaʻo Hana-Ikehu
Manaʻo ʻia e holo wikiwiki ana kahi kaʻa 1000-kg mai 10 m/s a i 20 m/s. E helu i ka hana i hana ʻia ma ke kaʻa.
\[ K_i = \frac{1}{2} m v_i^2 \]
\[ K_i = \frac{1}{2} \times 1000 \, \text{kg} \times (10 \, \text{m/s})^2 = 50,000 \, \text{J} \]
\[ K_f = \frac{1}{2} m v_f^2 \]
\[ K_f = \frac{1}{2} \times 1000 \, \text{kg} \times (20 \, \text{m/s})^2 = 200,000 \, \text{J} \]
\[ \Delta K = K_f – K_i \]
\[ \Delta K = 200,000 \, \text{J} – 50,000 \, \text{J} = 150,000 \, \text{J} \]
No laila, ʻo ka hana i hana ʻia ma ke kaʻa he 150,000 J.
Panina
ʻO ka hoʻomaopopo ʻana i ke ʻano o ka helu ʻana i ka hana a me ka ikehu e hāʻawi i kahi kahua paʻa i ka physics hiki ke hoʻopili ʻia i nā hiʻohiʻona a me nā kahua he nui. Mai nā neʻe maʻalahi e like me ke kaomi ʻana i kahi pahu a i nā ʻōnaehana paʻakikī e like me nā kaʻa e neʻe ana, kōkua nā kumumanaʻo o ka hana a me ka ikehu e wehewehe pehea e unuhi ai nā ikaika a me nā neʻe i nā hiki mechanical. ʻO ka mālama ʻana
