Formula Impulse Momentum Collision
Pengantar
ʻO ka impulse a me ka momentum he mau manaʻo koʻikoʻi i ka physics e koʻikoʻi no ka hoʻomaopopo ʻana i nā hanana like ʻole, ʻoiai nā mea e pili ana i nā collisions. Ma kēia ʻatikala, e kūkākūkā mākou i nā wehewehena, nā haʻilula, a me nā loina e pili ana i ka impulse, momentum, a me nā collisions. E nānā pū mākou i nā laʻana helu a me nā hoʻohana pono o kēia mau manaʻo.
Ka Wehewehena o ka Impulse a me ka Momentum
Ka manawa
ʻO ka Momentum (\(p\)) ke ana o ka nui o ka neʻe ʻana o kahi mea. ʻO ka Momentum kahi nui vector e hilinaʻi ana i ka nuipa a me ka wikiwiki o kahi mea. Ma ke ʻano makemakika, ua wehewehe ʻia ka momentum penei:
\[ p = mv \]
Ma hea:
– ʻo \( p \) ka momentum (kg m/s),
– ʻO \( m \) ke kaumaha o ka mea (kg),
– ʻO \( v \) ka wikiwiki o ka mea (m/s).
Hōʻike ka momentum i ka paʻakikī o ka hoʻōki ʻana i kahi mea e neʻe ana. ʻO ka nui o ka nuipa a i ʻole ka wikiwiki o kahi mea, ʻo ka nui o kona momentum.
Nā Impuls
ʻO ka Impulse (\(I\)) ka loli o ka momentum i hana ʻia e kahi ikaika e hana ana ma luna o kahi mea ma luna o kekahi manawa. He nui vector nō hoʻi ka Impulse a ua wehewehe ʻia penei:
\[ I = F \Delta t \]
Ma hea:
– ʻO \( I \) ka impulse (N s a i ʻole kg m/s),
– ʻO \( F \) ka ikaika e hana ana ma luna o ka mea (N),
– ʻO \( \Delta t \) ka manawa ma luna o ia mea e hana ai ka ikaika (s).
Ua like ka Impulse me ka loli o ka momentum o ka mea:
\[ I = \Delta p = p_f – p_i \]
Ma hea:
– ʻO \( \Delta p \) ka loli o ka momentum (kg m/s),
– ʻO \( p_f \) ka momentum hope loa (kg m/s),
– ʻO \( p_i \) ka momentum mua (kg m/s).
Kuʻi ʻana
He pilina ka hoʻokuʻi ʻana kahi e hoʻololi ai ʻelua a ʻoi aku paha mau mea i ka momentum. Hiki ke hoʻokaʻawale ʻia nā hoʻokuʻi ʻana i ʻelua ʻano nui: nā hoʻokuʻi elastic a me nā hoʻokuʻi inelastic.
Hoʻokuʻi ʻana o ka elastic
I loko o kahi kuʻi elastic, ʻo ka ikehu kinetic holoʻokoʻa o ka ʻōnaehana ma mua a ma hope o ke kuʻi ʻana e mau ana ka like. ʻO ke ʻano kēia, ʻaʻohe ikehu kinetic i nalowale ma ke ʻano he wela, kani, a i ʻole ka deformation mau loa. Pili nā kānāwai o ka mālama ʻana i ka momentum a me ka mālama ʻana i ka ikehu kinetic i nā kuʻi elastic.
Kuʻi ʻole ʻia
I loko o kahi kuʻi ʻana inelastic, nalowale kekahi o ka ikehu kinetic o ka ʻōnaehana ma ke ʻano he ikehu ʻē aʻe (e.g., ka wela, ke kani, a i ʻole ke ʻano o nā mea). ʻOiai ke pili nei ke kānāwai o ka mālama ʻana i ka momentum, ʻaʻole i mālama ʻia ka ikehu kinetic holoʻokoʻa.
Nā Haʻilula Koʻikoʻi
Ka Mālama ʻana i ka Momentum
ʻŌlelo ke kānāwai o ka mālama ʻana i ka momentum ua like ka momentum holoʻokoʻa o ka ʻōnaehana ma mua o ke kuʻi ʻana me ka momentum holoʻokoʻa o ka ʻōnaehana ma hope o ke kuʻi ʻana, inā ʻaʻohe mana o waho e hana ma ka ʻōnaehana:
\[ m_1 v__{1i} + m_2 v_{2i} = m_1 v_{1f} + m_2 v__{2f} \]
Ma hea:
– ʻO \( m_1 \) a me \( m_2 \) nā kaumaha o ka mea 1 a me ka mea 2 (kg),
– ʻO \( v_{1i} \) a me \( v_{2i} \) nā wikiwiki mua o ka mea 1 a me ka mea 2 (m/s),
– ʻO \( v_{1f} \) a me \( v_{2f} \) nā wikiwiki hope loa o ka mea 1 a me ka mea 2 (m/s).
Ka Mālama ʻana i ka Ikehu Kinetic (no nā Kuʻi Elastic)
No kahi kuʻi elastic, ʻo ka ikehu kinetic holoʻokoʻa o ka ʻōnaehana ma mua a ma hope o ke kuʻi ʻana e mau ana:
\[ \frac{1}{2} m_1 v_{1i}^2 + \frac{1}{2} m_2 v_{2i}^2 = \frac{1}{2} m_1 v_{1f}^2 + \frac{1}{2} m_2 v_{2f}^2 \]
Laʻana Heluhelu
E nānā kākou i kekahi mau laʻana helu e hoʻomaopopo ai pehea e pili ai kēia mau haʻilula i nā kūlana maoli.
Laʻana 1: Kuʻi ʻana inelastic
Manaʻo ʻia e neʻe ana ʻelua mau kaʻa, me ke kaumaha o 1000 kg kēlā me kēia, kekahi i kekahi ma 10 m/s a me 15 m/s, kēlā me kēia. Ma hope o ke kuʻi ʻana, neʻe pū nā kaʻa ʻelua me ka wikiwiki hope like. Makemake mākou e hoʻoholo i kēlā wikiwiki hope loa.
1. Ka nui o ka momentum mua o ka ʻōnaehana:
\[ p_{total\_initial} = m_1 v_{1i} + m_2 v_{2i} \]
\[ p_{total\_initial} = 1000 \times 10 + 1000 \times (-15) \]
\[ p_{total\_initial} = 10000 – 15000 \]
\[ p_{total\_initial} = -5000 \, \text{kg m/s} \]
2. Ma hope o ke kuʻi ʻana, neʻe pū nā kaʻa ʻelua i hiki ai i ka nuipa holoʻokoʻa ke \(m_1 + m_2\), a ʻo ka wikiwiki hope loa ke \(v_f\):
\[ p_{huina\_hopena} = (m_1 + m_2) v_f \]
\[ -5000 = (1000 + 1000) v_f \]
\[ -5000 = 2000 v_f \]
\[ v_f = \frac{-5000}{2000} \]
\[ v_f = -2.5 \, \text{m/s} \]
ʻO ka wikiwiki hope loa o nā kaʻa ʻelua ma hope o ke kuʻi ʻana he -2.5 m/s, ʻo ia hoʻi ke neʻe pū nei lāua ma ke kuhikuhi like ma ka wikiwiki o 2.5 m/s ma ke kuhikuhi mua o ke kaʻa ʻelua.
Laʻana 2: Kuʻi ʻana o ka elastic
Ke manaʻo nei he pōpō me ke kaumaha o 2 kg e neʻe ana i ka ʻākau ma ka wikiwiki o 4 m/s e kuʻi elasticly me kekahi pōpō me ke kaumaha o 3 kg e neʻe ana i ka hema ma ka wikiwiki o 2 m/s. Makemake mākou e hoʻoholo i nā wikiwiki hope loa o nā pōpō ʻelua ma hope o ke kuʻi ʻana.
1. Ka nui o ka momentum mua o ka ʻōnaehana:
\[ p_{total\_initial} = m_1 v_{1i} + m_2 v_{2i} \]
\[ p_{total\_initial} = 2 \times 4 + 3 \times (-2) \]
\[ p_{total\_initial} = 8 – 6 \]
\[ p_{ka huina\_initial} = 2 \, \text{kg m/s} \]
2. Ka ikehu kinetic holoʻokoʻa o ka ʻōnaehana ma mua o ke kuʻi ʻana:
\[ KE_{total\_initial} = \frac{1}{2} m_1 v_{1i}^2 + \frac{1}{2} m_2 v_{2i}^2 \]
\[ KE_{total\_initial} = \frac{1}{2} \times 2 \times 4^2 + \frac{1}{2} \times 3 \times 2^2 \]
\[ KE_{total\_initial} = 16 + 6 \]
\[ KE_{total\_initial} = 22 \, \text{J} \]
3. Ma hope o ke kuʻi ʻana, pono mākou e hoʻoponopono i nā kaulike mālama o ka momentum a me ka ikehu kinetic i ka manawa like e ʻike ai i nā wikiwiki hope loa \(v_{1f}\) a me \(v_{2f}\).
\[
nā hihia
m_1 v__{1i} + m_2 v_{2i} = m_1 v__{1f} + m_2 v_{2f} \\
\frac{1}{2} m_1 v_{1i}^2 + \frac{1}{2} m_2 v_{2i}^2 = \frac{1}{2} m_1 v_{1f}^2 + \frac{1}{2} m_2 v_{2f}^2
nā hihia
\]
Ma o ka hoʻololi ʻana a me ka helu ʻana, hiki iā mākou ke loaʻa nā wikiwiki hope loa o nā pōpō ʻelua. ʻO ka hopena hope loa:
\[ v_{1f} \approx -2.2 \, \text{m/s} \]
\[ v_{2f} \approx 3.2 \, \text{m/s} \]
No laila, ma hope o ke kuʻi ʻana o ka elastic, neʻe ka pōpō mua i ka hema ma kahi o 2.2 m/s, a neʻe ka lua o ka pōpō i ka ʻākau ma kahi o 3.2 m/s.
Nā Hoʻohana Kūpono
1. Kaʻa a me ka Palekana
He mea koʻikoʻi nā manaʻo o ka impulse a me ka momentum i ka hoʻolālā ʻana i ka ʻōnaehana palekana kaʻa. Ua hoʻolālā ʻia nā ʻeke ea a me nā crumple zones e hoʻolōʻihi i ka manawa hopena, e hōʻemi i nā ikaika e hana ana ma luna o ka poʻe noho, a e hōʻemi i nā ʻeha.
2. Nā Haʻuki
I nā haʻuki e like me ka pôpeku, ka mokomoko, a me ka hockey, ʻo ka hoʻomaopopo ʻana i ka impulse a me ka momentum e kōkua i nā mea pāʻani e hoʻomaikaʻi i kā lākou hana. No ka laʻana, i ka mokomoko, ʻo ka punch maikaʻi e pili ana i ka hoʻonui ʻana i ka hoʻoili momentum i ka manawa pōkole loa.
3. ʻEnekinia Kūkulu a me ka Hoʻolālā
Hoʻohana nā ʻenekinia i nā kumumanaʻo o ka impulse a me ka momentum e hoʻolālā i nā hale e hiki ke kū i nā ukana ikaika, e like me nā alahaka a me nā hale kiaʻi kiʻekiʻe, a hōʻoia i ke kūpaʻa a me ka palekana o nā hale i ka wā o nā hopena a i ʻole nā haʻalulu.
