Nā Formula Modulus Density a me Elastic no kekahi mau Solids, Liquids, a me Gases
ʻO ke kinoea ke aʻo kumu o nā waiwai a me nā hanana o ke ʻano. ʻElua mau manaʻo koʻikoʻi i ka kinoea e pāʻani ana i kahi kuleana nui i ka hoʻomaopopo ʻana i nā waiwai o nā mea, ʻo ia ka nui o ka density a me ka modulus o ka elasticity. E kūkākūkā kēia ʻatikala i nā wehewehena, nā haʻilula, a me nā laʻana noi o kēia mau manaʻo ʻelua no nā mea like ʻole i ʻekolu mau pae: paʻa, wai, a me ke kinoea.
Ka nui o ka paʻa
ʻO ka density kahi nui e hōʻike ana i ka nuipa o kahi mea ma kēlā me kēia anakahi leo. Hiki i ka density ke hāʻawi i ka ʻike e pili ana i ka density o kahi mea a hoʻohana pinepine ʻia ma nā ʻano ʻepekema like ʻole a me nā ʻoihana.
1. Ka Wehewehena a me ke ʻAno o ka Density
Hiki ke wehewehe ʻia ka density (\( \rho \)) ʻo ia ka lakio ma waena o ka nuipa (\( m \)) a me ka nui (\( V \)) o ka mea. ʻO ke ʻano makemakika:
\[
\rho = \frac{m}{V}
\]
Ma hea:
– ʻo \( \rho \) ka nui o ka mānoanoa,
– ʻo \( m \) ka nuipa,
– ʻO \( V \) ka leo.
2. Ka nui o nā mea paʻa
ʻOi aku ka nui o ka nui o nā mea paʻa ma mua o nā wai a me nā kinoea no ka mea ua ʻoi aku ka paʻa o ko lākou mau ʻāpana. ʻO nā hiʻohiʻona o ka nui o kekahi mau mea paʻa:
– Alumini: \( 2.7 \, \text{g/cm}^3 \)
– Hao: \( 7.87 \, \text{g/cm}^3 \)
– Gula: \( 19.32 \, \text{g/cm}^3 \)
3. Ka nui o ka wai
ʻOi aku ka haʻahaʻa o ka nui o nā wai ma mua o nā mea paʻa, akā ʻoi aku ke kiʻekiʻe ma mua o nā kinoea. Eia nā hiʻohiʻona o ka nui o kekahi mau wai:
– Wai: \( 1 \, \text{g/cm}^3 \)
– ʻAila: \( 0.789 \, \text{g/cm}^3 \)
– Mereki: \( 13.6 \, \text{g/cm}^3 \)
4. Ka nui o ke kinoea
ʻOi aku ka haʻahaʻa o ka nui o ke kinoea ma mua o ke kaomi a me ka mahana. ʻOi aku ka haʻahaʻa o ka nui o nā kinoea ma mua o nā mea paʻa a me nā wai. Eia nā hiʻohiʻona o ka nui o kekahi mau kinoea:
– Ea: \( 0.001225 \, \text{g/cm}^3 \)
– ʻAilakona: \( 0.00008988 \, \text{g/cm}^3 \)
– Kalapona ʻokikene: \( 0.001977 \, \text{g/cm}^3 \)
Modulus o ka Elasticity
ʻO ke modulus o ka elasticity ke ana o ka paʻakikī o kahi mea a i ʻole ke kūʻē ʻana i ka deformation elastic ke kau ʻia i kahi ikaika. Aia kekahi mau ʻano o ka modulus o ka elasticity, akā ʻo ka mea maʻamau ka modulus a Young, ka modulus shear, a me ka modulus bulk.
1. Modulus o Young
ʻO ka modulus a Young (\( E \)) ke ana o ka paʻakikī o kahi mea i ka wā e kīkoʻo ʻia ai a i ʻole i kaomi ʻia. Hiki ke wehewehe ʻia ka modulus a Young ma ke ʻano he lakio o ke koʻikoʻi (\( \sigma \)) i ke kaumaha (\( \varepsilon \)) ma ka palena elastic o ka mea:
\[
E = \frac{\sigma}{\varepsilon}
\]
Ma hea:
– ʻO ka modulus o Young ka \( E \),
– ʻO \( \sigma \) ke koʻikoʻi (ikaika no kēlā me kēia ʻāpana),
– ʻO \( \varepsilon \) ke ʻano (ka loli o ka lōʻihi e pili ana i ka lōʻihi mua).
ʻO nā hiʻohiʻona o ka modulus Young o kekahi mau mea:
– Kila: \( 200 \, \text{GPa} \)
– Alumini: \( 69 \, \text{GPa} \)
– Laho: \( 0.01 \, \text{GPa} \)
2. Modulus ʻokiʻoki
ʻO ke modulus shear (\( G \)) kahi ana o ke koʻikoʻi o kahi mea i ka wā e kau ʻia ai ka ikaika shear. Hiki ke wehewehe ʻia ke modulus shear ma ke ʻano he lakio o ke koʻikoʻi shear (\( \tau \)) i ke koʻikoʻi shear (\( \gamma \)):
\[
G = \frac{\tau}{\gamma}
\]
Ma hea:
– ʻO \( G \) ka modulus shear,
– ʻo \( \tau \) ke koʻikoʻi shear,
– ʻO \( \gamma \) ke kaumaha o ka ʻokiʻoki.
ʻO nā hiʻohiʻona o nā moduli shear o kekahi mau mea:
– Kila: \( 80 \, \text{GPa} \)
– Alumini: \( 25 \, \text{GPa} \)
– Laho: \( 0.0006 \, \text{GPa} \)
3. Modulus Nui
ʻO ke modulus nui (\( K \)) kahi ana o ke kūpaʻa o kahi mea i ka wā e kau ʻia ai kahi ikaika compressive like mai nā ʻaoʻao āpau (isotropic compression). Hiki ke wehewehe ʻia ke modulus nui ma ke ʻano he lakio o ke kaomi (\( P \)) i ka loli pili o ka leo (\( \Delta V / V \)):
\[
K = – \frac{P}{\Delta V / V}
\]
Ma hea:
– ʻO \( K \) ka modulus nui,
– ʻo ke kaomi ʻo \( P \),
– ʻo \( \Delta V \) ka loli o ka leo,
– ʻO \( V \) ka leo mua.
ʻO nā hiʻohiʻona o ka modulus bulk o kekahi mau mea:
– Kila: \( 160 \, \text{GPa} \)
– Wai: \( 2.2 \, \text{GPa} \)
– Aniani: \( 35 \, \text{GPa} \)
Nā Hoʻohana i ke Ola o kēlā me kēia Lā
1. Ka nui o ka paʻa
Hoʻohana ʻia ka density i nā ʻano hana like ʻole, e like me ka hoʻoholo ʻana inā e piholo a lana paha kahi mea i ka wai. No ka laʻana, hana ʻia nā waʻa mai nā mea me ka density haʻahaʻa ma mua o ka wai e ʻae iā lākou e lana. He mea nui nō hoʻi ka density i ka ʻoihana mea kūkulu hale no ka hoʻoholo ʻana i ka maikaʻi a me ka ikaika o nā mea.
2. Modulus o ka Elasticity
Hoʻohana ʻia ka modulus o ka elasticity i ka ʻenekinia a me ka hoʻolālā e hoʻoholo i nā mea kūpono no nā noi like ʻole. No ka laʻana, hoʻohana pinepine ʻia ke kila i ke kūkulu ʻana a me ke kūkulu ʻana i ke alahaka no ka mea he kiʻekiʻe kona modulus Young, ʻo ia hoʻi hiki iā ia ke kū i nā ukana nui me ka ʻole o ka deformation koʻikoʻi. Hoʻohana ʻia ka laholio i ka hana ʻana i nā kaila no ka mea he haʻahaʻa kona modulus Young, kahi e hiki ai iā ia ke omo i nā haʻalulu a hāʻawi i kahi holo ʻoluʻolu.
Ka hopena
He mea nui ka hoʻomaopopo ʻana i nā manaʻo o ka nui a me ka modulus o ka elasticity i nā ʻano ʻepekema like ʻole a me nā ʻoihana. Kōkua ka nui iā mākou e hoʻomaopopo i ka nui a me ka hoʻolaha nui o kahi mea, ʻoiai ʻo ka modulus o ka elasticity e hāʻawi i ka ʻike e pili ana i ka paʻakikī o kahi mea a me ka hiki ke kūʻē i ka deformation. Ma ka hoʻomaopopo ʻana i nā ʻano hana a me nā noi o kēia mau manaʻo ʻelua, hiki iā mākou ke hoʻomaopopo maikaʻi i nā waiwai o ka mea a hoʻopili iā lākou i ke ola o kēlā me kēia lā.
