Formula Impulse: Wehewehena, Formula, a me ka Hoʻohana
He manaʻo koʻikoʻi ka Impulse i ka physics e pili ana i ka loli o ka momentum o kahi mea. Hoʻohana pinepine ʻia ia i nā kūlana mai nā ulia kaʻa a i nā haʻuki, kahi e hāʻawi ai ka nānā ʻana i nā loli momentum i ka ʻike i ka dinamika o kahi ʻōnaehana. E wehewehe kēia ʻatikala i ke ʻano o ka impulse, ke ʻano i hoʻohana ʻia e helu ai, a me kāna mau noi i ke ola o kēlā me kēia lā.
Ke Hoʻomaopopo ʻana i ka Impulse
He nui kino ka impulse i loaʻa mai ka ikaika e hana ana ma luna o kahi mea ma luna o kahi manawa kikoʻī. Pili pono ka impulse i ka loli o ka momentum o kēlā mea. Ma kēia ʻano, ʻo ka momentum ka huahana o ka nuipa a me ka wikiwiki o kahi mea.
Ma ka hōʻailona makemakika, hiki ke hōʻike ʻia ka impulse (\(J\)) ma ke ʻano he huahana o ka ikaika (\(F\)) a me ka manawa (\(\Delta t\)):
\[ J = F \cdot \Delta t \]
Eia nō naʻe, ʻoiai ʻaʻole mau ka ikaika, ʻo kahi ʻano hana i hoʻohana pinepine ʻia e pili ana i ka hoʻohui o ka ikaika e pili ana i ka manawa:
\[ J = \int_{t_1}^{t_2} F(t) \, dt \]
Pilina ma waena o ka Impulse a me ka Momentum
Wahi a ke kānāwai ʻelua o Newton, ʻo ka ikaika (\(F\)) e hana ana ma luna o kahi mea ua like ia me ka wikiwiki o ka loli o ka momentum (\(p\)) o ka mea:
\[ F = \frac{dp}{dt} \]
Ma ka hoʻohui ʻana i kēia hoohalike e pili ana i ka manawa, hiki iā mākou ke hōʻike i ka impulse e like me ka loli o ka momentum:
\[ J = \int_{t_1}^{t_2} F(t) \, dt = \Delta p \]
Ma hea:
– ʻO \( \Delta p \) ka loli o ka momentum o ka mea,
– ʻO \( p \) ka momentum i wehewehe ʻia e like me \( p = mv \),
– ʻo \( m \) ke kaumaha o ka mea,
– ʻO \( v \) ka wikiwiki o ka mea.
Formula Impulse
No ke ʻano o ka ikaika mau, hiki ke hoʻomaʻalahi ʻia ke ʻano impulse i:
\[ J = F \cdot \Delta t \]
No nā mana like ʻole, hoʻohana mākou i ka hoʻohui o ka mana e pili ana i ka manawa:
\[ J = \int_{t_1}^{t_2} F(t) \, dt \]
Nā Hoʻohana Impulse i ke Ola o kēlā me kēia lā
He kuleana koʻikoʻi ko nā impulses i nā ʻano he nui o ke ola o kēlā me kēia lā a me ka ʻenehana. Eia kekahi mau laʻana o kā lākou noi:
Kuʻi Kaʻa
I nā ulia kaʻa, kōkua ka loiloi impulse e hoʻomaopopo pehea e hoʻopilikia ai nā ikaika kuʻi i ke kaʻa a me kona poʻe noho. Hoʻohana nā ʻeke ea i loko o nā kaʻa i ke kumumanaʻo impulse e hōʻemi i nā ikaika e hana ana ma luna o ka poʻe noho ma ka hoʻolōʻihi ʻana i ka manawa o ke kuʻi ʻana, a laila e hōʻemi ana i nā ʻeha.
Haʻuki
I nā haʻuki e like me ka mokomoko a i ʻole ka pôpeku, hoʻāʻo nā mea pāʻani e hoʻonui i ko lākou momentum e hāʻawi i kahi punch a i ʻole kiki ikaika. I ka baseball, hoʻāʻo nā mea hahau e hoʻolōʻihi i ka pilina ma waena o ka pōpō a me ka ʻōpeʻapeʻa e hāʻawi i ka momentum kiʻekiʻe loa, e hopena ana i kahi hahau paʻakikī a mamao aku.
Raketa a me ka Pōpō
I ka tennis a i ʻole badminton, hoʻohana nā mea pāʻani i kā lākou mau raketa e hāʻawi i ka momentum i ka pōpō a i ʻole ka shuttlecock, e hoʻololi ana i kona momentum a kuhikuhi iā ia i ko lākou hoa paio. Hoʻoikaika nā mea pāʻani e hoʻolālā i ka manawa a me ka hoʻoikaika i kā lākou mau pana e hoʻonui i ka momentum i hāʻawi ʻia.
Nā Rockets a me ka Propulsion
I ka ʻenehana rocket, hoʻohana ʻia ke kumumanaʻo o ka impulse e hoʻomaopopo ai pehea e hoʻoulu ai nā kinoea i hoʻokuʻu ʻia mai kahi ʻenekini rocket i ka thrust. Ma ka hoʻokuʻu ʻana i nā kinoea i nā wikiwiki kiʻekiʻe i loko o kahi manawa pōkole, loaʻa i ka rocket kahi impulse nui e hoʻoneʻe iā ia i mua.
Laʻana o ka Helu Impulse
Eia kekahi mau laʻana o nā helu e kōkua i ka wehewehe ʻana i ka manaʻo o ka impulse ma nā kūlana like ʻole.
Laʻana 1: Impulse me ka ikaika mau
Ua hahau ʻia kahi pōpō me ke kaumaha o 0.5 kg me ka ikaika mau o 20 N no 0.1 kekona. E helu i ka impulse i hāʻawi ʻia i ka pōpō a me ka loli o kona momentum.
Ua ʻike ʻia:
– Nuipaʻa (\(m\)) = 0.5 kg,
– Ikaika (\(F\)) = 20 N,
– Manawa (\(\Delta t\)) = 0.1 kekona.
Ke helu nei i ka impulse (\(J\)):
\[ J = F \cdot \Delta t \]
\[ J = 20 \, \text{N} \times 0.1 \, \text{kekona} \]
\[ J = 2 \, \text{Ns} \]
ʻOiai ua like ka impulse me ka loli o ka momentum:
\[ J = \Delta p \]
No laila, ʻo ka loli o ka momentum (\(\Delta p\)) he 2 Ns.
Laʻana 2: Impulse me ka ikaika e loli nei
Manaʻo ʻia e loli ka ikaika e hana ana ma luna o kahi mea e like me ke kaulike \( F(t) = 5t \) N, kahi ʻo \( t \) ka manawa ma kekona. E helu i ka impulse i hoʻokau ʻia ma luna o ka mea mai \( t = 0 \) a i \( t = 2 \) kekona.
Ke helu nei i ka impulse (\(J\)):
\[ J = \int_{0}^{2} 5t \, dt \]
Hoʻohui:
\[ J = 5 \int_{0}^{2} t \, dt \]
\[ J = 5 \left[ \frac{t^2}{2} \right]_{0}^{2} \]
\[ J = 5 \left( \frac{2^2}{2} – \frac{0^2}{2} \right) \]
\[ J = 5 \hema( 2 \ʻākau) \]
\[ J = 10 \, \text{Ns} \]
No laila, ʻo ka impulse i hāʻawi ʻia i ka mea he 10 Ns.
Ka hopena
He manaʻo koʻikoʻi ka Impulse i ka physics e pili ana i ka loli o ka momentum o kahi mea ma muli o kahi ikaika e hana ana ma luna o kekahi manawa. Hiki ke helu ʻia ka Impulse me ka hoʻohana ʻana i kahi ʻano maʻalahi no ka ikaika mau a i ʻole ka hoʻohana ʻana i kahi integral no kahi ikaika like ʻole. He mea nui ka hoʻomaopopo ʻana i ka impulse i nā ʻano hana like ʻole, me ka nānā ʻana i nā ulia kaʻa, nā haʻuki, a me ka ʻenehana rocket. Ma ka hoʻomaopopo ʻana a me ka hoʻopili ʻana i ke kumumanaʻo o ka impulse, hiki iā mākou ke kālailai a hoʻolālā i nā ʻōnaehana ʻoi aku ka maikaʻi a me ka palekana i nā ʻano like ʻole o kēlā me kēia lā a me nā ʻenehana.
