Nā nīnau hoʻohālike e kūkākūkā ana i ke kānāwai o ka mālama ʻana i ka ikehu
ʻO ke Kānāwai o ka Mālama ʻana i ka Ikehu he kumumanaʻo nui ia i ka physics, e ʻōlelo ana ʻaʻole hiki ke hana ʻia a luku ʻia paha ka ikehu i loko o kahi ʻōnaehana pani, akā hiki ke hoʻololi ʻia mai kekahi ʻano a i kekahi. He mea koʻikoʻi kēia manaʻo a hoʻohana pinepine ʻia i nā lālā like ʻole o ka ʻepekema a me ka ʻenehana, me ka mechanics, thermodynamics, a me ka electromagnetism. Ma kēia ʻatikala, e kūkākūkā mākou i kekahi mau pilikia hoʻohālike e pili ana i ke Kānāwai o ka Mālama ʻana i ka Ikehu, me nā wehewehe kikoʻī.
Laʻana Nīnau 1: Ikehu Mekanika i loko o kahi Mea Hāʻule Kūʻokoʻa
Nīnau: Ua hāʻule kahi pōpō me ke kaumaha o 0,5 kg mai ke kiʻekiʻe o 20 mika. E hoʻowahāwahā i ke kū'ē ʻana o ka ea. He aha ka wikiwiki o ka pōpō ke hiki i ka honua?
Kūkākūkā:
KaʻAnuʻu Hana 1: E ʻike i ka ikehu mua a me ka ikehu hope.
ʻO ka ikehu mua i ka wā e piʻi ai ka pōpō i ke kiʻekiʻe o 20 mika, ʻo ia ka ikehu hiki ke hoʻopaʻa ʻia e ka umekaumaha (EP), hiki ke helu ʻia me ka hoʻohana ʻana i ke ʻano hana:
\[ EP = mgh \]
Ma hea:
– ʻO \( m \) ke kaumaha o ka pōpō (0,5 kg)
– ʻO \( g \) ka wikiwiki ma muli o ke koʻikoʻi (9,8 m/s²)
– ʻO ke kiʻekiʻe (20 m) ʻo \( h \)
\[ EP_{mua} = 0,5 \times 9,8 \times 20 = 98 \, \kikokikona{J} \]
ʻO ka ikehu hope loa ke hiki ka pōpō i ka honua, ʻo ia ka ikehu kinetic (EK), hiki ke helu ʻia me ka hoʻohana ʻana i ke ʻano hana:
\[ EK = \frac{1}{2} mv^2 \]
Ma hea:
– ʻO \( v \) ka wikiwiki o ka pōpō i kona hiki ʻana i ka honua
KaʻAnuʻu Hana 2: E hoʻohana i ke Kānāwai o ka Mālama ʻana i ka Ikehu e ʻōlelo ai ua like ka ikehu hiki mua me ka ikehu kinetic hope loa.
\[ EP_{mua} = EK_{hope} \]
\[ 98 = \frac{1}{2} \times 0,5 \times v^2 \]
KaʻAnuʻu Hana 3: E hoʻoponopono i ka hoohalike e loaʻa ai \( v \).
\[ 98 = 0,25v^2 \]
\[ v^2 = \frac{98}{0,25} = 392 \]
\[ v = \sqrt{392} \approx 19,8 \, \text{m/s} \]
No laila, ʻo ka wikiwiki o ka pōpō i kona hiki ʻana i ka honua he 19,8 m/s.
Laʻana Nīnau 2: Ikehu i loko o ka Puna
Nīnau: Ua kaomi ʻia kahi pūnāwai me kahi kūpaʻa pūnāwai \( k \) = 200 N/m he 0,1 mika mai kona kūlana kaulike. Ehia ka nui o ka ikehu hiki ke hoʻopili ʻia i mālama ʻia i loko o ka pūnāwai?
Kūkākūkā:
KaʻAnuʻu Hana 1: E hoʻohana i ke ʻano ikehu hiki ke elastic.
\[ EP_{elastic} = \frac{1}{2} kx^2 \]
Ma hea:
– ʻO \( k \) ke kūpaʻa puna (200 N/m)
– ʻO \( x \) ka mamao o ke kaomi ʻana (0,1 m)
KaʻAnuʻu Hana 2: E hoʻokomo i nā waiwai i ʻike ʻia i loko o ke ʻano hana.
\[ EP_{elastic} = \frac{1}{2} \times 200 \times (0,1)^2 \]
\[ EP_{elastic} = \frac{1}{2} \times 200 \times 0,01 \]
\[ EP_{elastic} = 1 \, \text{J} \]
No laila, ʻo ka ikehu hiki ke elastic i mālama ʻia i loko o ka pūnāwai he 1 Joule.
Laʻana Nīnau 3: Ikehu Hiki o ka Gravitasi a me ka Ikehu Kinetic ma ka Neʻe Parabolic
Nīnau: Ua hoʻokuʻu ʻia kahi mea lele me ke kaumaha o 2 kg me ka wikiwiki mua o 30 m/s ma ke kihi o 45° i ka pae. He aha nā ikehu kinetic a me nā ikehu hiki o ka mea lele ma kahi kiʻekiʻe loa o kona ala hele?
Kūkākūkā:
KaʻAnuʻu Hana 1: E wāwahi i ka wikiwiki mua i nā ʻāpana moe a me ke kū.
\[ v_{x} = v_0 \cos \theta \]
\[ v_{y} = v_0 \sin \theta \]
Ma hea:
– ʻO \( v_0 \) ka wikiwiki mua (30 m/s)
– ʻO \( \theta \) ke kihi hoʻokuʻu (45°)
\[ v_{x} = 30 \cos 45° = 30 \times \frac{\sqrt{2}}{2} = 21,21 \, \text{m/s} \]
\[ v_{y} = 30 \sin 45° = 30 \times \frac{\sqrt{2}}{2} = 21,21 \, \text{m/s} \]
KaʻAnuʻu Hana 2: Ma ke kiko kiʻekiʻe loa, ʻo ka wikiwiki kū pololei (v_y) he 0, akā ʻo ka wikiwiki ākea (v_x) e mau ana.
\[ v_{x \, kiko \, kiʻekiʻe loa} = 21,21 \, \text{m/s} \]
KaʻAnuʻu Hana 3: E helu i ka ikehu kinetic o ka projectile ma kona wahi kiʻekiʻe loa.
\[ EK = \frac{1}{2} mv^2 \]
\[ EK_{kiko \, kiʻekiʻe loa} = \frac{1}{2} \times 2 \times (21,21)^2 \]
\[ EK_{kikona \, kiʻekiʻe loa} = 1 \times 449,21 = 449,21 \, \text{J} \]
KaʻAnuʻu Hana 4: E helu i ke kiʻekiʻe loa i hiki i ka projectile.
\[ h = \frac{v_{y}^2}{2g} \]
\[ h = \frac{(21,21)^2}{2 \times 9,8} \]
\[ h \approx 22,9 \, \text{m} \]
KaʻAnuʻu Hana 5: E helu i ka ikehu hiki ke umekaumaha ma kahi kiʻekiʻe loa.
\[ EP_{kiko \, kiʻekiʻe loa} = mgh \]
\[ EP_{kikona \, kiʻekiʻe loa} = 2 \times 9,8 \times 22,9 \]
\[ EP_{kikona \, kiʻekiʻe loa} \approx 449,72 \, \text{J} \]
No laila, ʻo ka ikehu kinetic o ka projectile ma kahi kiʻekiʻe loa he 449,21 Joules, a ʻo ka ikehu hiki ke hoʻokuʻu ʻia ma kahi kiʻekiʻe loa he 449,72 Joules.
Laʻana Nīnau 4: Ikehu Wera i ka Friction
Nīnau: Ua paʻi ʻia kahi pahu me ke kaumaha o 10 kg ma luna o kahi papahele ʻinoʻino no 5 mika me ka ikaika mau o 30 N. ʻO ke koina o ka friction kinetic ma waena o ka pahu a me ka papahele he 0,2. Ehia ka ikehu i hoʻololi ʻia i ikehu wela ma muli o ka friction?
Kūkākūkā:
KaʻAnuʻu Hana 1: E helu i ka ikaika friction.
\[ f_{friction} = \mu N \]
Ma hea:
– ʻO \( \mu \) ke koina o ka friction (0,2)
– ʻO \( N \) ka ikaika maʻamau. No kahi ʻili pālahalaha, \( N = mg \)
\[ f_{friction} = 0,2 \times 10 \times 9,8 = 19,6 \, \text{N} \]
KaʻAnuʻu Hana 2: E helu i ka hana i hana ʻia e ka ikaika friction.
\[ W = f_{friction} \times d \]
Ma hea:
– ʻO \( d \) ka mamao (5 m)
\[ W = 19,6 \times 5 = 98 \, \text{J} \]
ʻO ka ikehu i hoʻololi ʻia i ka ikehu wela ma muli o ka friction he 98 Joules.
Ka hopena
He manaʻo ikaika ke Kānāwai o ka Mālama ʻana i ka Ikehu e pili ana i nā kūlana physics he nui. ʻO ka hoʻomaopopo ʻana iā ia e hiki ai iā mākou ke kālailai i nā ʻano hanana kino like ʻole, mai nā mea hāʻule manuahi a me ka neʻe ʻana o ka projectile a hiki i ka ikehu i hana ʻia e ka friction. Kōkua nā laʻana ma luna iā mākou e hoʻomaopopo pehea e hiki ai i ka ikehu ke hoʻololi i ke ʻano me ka noho mau ʻana i ka nui. He mea nui ka hoʻomaopopo piha ʻana i kēia manaʻo no ka hoʻonaʻauao a me nā noi hana ma ka ʻenekinia a me ka ʻepekema.
