Nā kahua umekaumaha - nā pilikia a me nā hoʻonā

Nā kahua umekaumaha - nā pilikia a me nā hoʻonā

1. He aha ka lakio o ke kahua umekaumaha o ka mea A a me ka mea B?

ʻIke ʻia:

Ka nuipa o ka mea A (m _A ) = 1

Ka nuipa o ka mea B (m _B ) = 2

Ka mamao o ka mea A mai ka honua Honua (r _A ) = 1

ʻO ka mamao o ka mea B mai ka honua Honua (r _B ) = 2

Makemake ʻia: ʻO ka lakio o ke kahua umekaumaha o ka mea A a me ka mea B

Lōlā:

ʻO ke kaulike o ke kahua umekaumaha o ka Honua:

g = ka nui o ke kahua umekaumaha, G = ke kūpaʻa umekaumaha, m _B = ka nuipa o ka Honua, r _B = ka radius o ka Honua

ʻO ka lakio o ke kahua umekaumaha:

g _A : g _B

G: G/2

1: 1/2

2: 1

2. Inā ʻo ke kūlana o ka mea A he 0.5R ma luna o ka ʻili o ka Honua, ʻoiai ʻo ke kūlana o ka mea B he 2R ma luna o ka ʻili o ka Honua, a laila he aha ka lakio o ke kahua umekaumaha i ʻike ʻia e ka mea A a me ka mea B. ʻO R ka radius o ka Honua.

ʻIke ʻia:

ʻO ka mamao o ka mea A mai ke kikowaena o ka Honua = 0.5R + R = 1.5R = 1.5

ʻO ka mamao o ka mea B mai ke kikowaena o ka Honua = 2R + R = 3R = 3

Makemake ʻia: Ka lakio o ke kahua umekaumaha

Lōlā:

ʻO ke kahua umekaumaha i ʻike ʻia e ka mea A (g _A ):

ʻO ke kahua umekaumaha i ʻike ʻia e ka mea B (g _B ):

ʻO ka lakio o ke kahua umekaumaha i ʻike ʻia e ka mea A a me ka mea B:

3. ʻO ke kahua umekaumaha ma ka ʻili o ka Honua he g, a laila he aha ke kahua umekaumaha ma ke kiʻekiʻe o 1.5R ma luna o ka ʻili o ka Honua. ʻO R = ka radius o ka Honua.

pāʻoihana

Ua kūlike pololei ka ikaika o ke koʻikoʻi (F) me ke kahua koʻikoʻi (g). ʻO ka nui o ka ikaika o ke koʻikoʻi, ʻo ka nui o ke kahua koʻikoʻi.

Ua like ka ikaika umekaumaha (F) me 1/r ² , kahi ʻo r = ka mamao o kahi mea mai ke kikowaena o ka honua. Ua like ka ikaika o ka umekaumaha me 1/r ² i like pū ke kahua umekaumaha (g) me 1/r ².

Ke kau ka mea holo mokulele ma luna o ka ʻili o ka Honua ʻo ia hoʻi ʻo R (R = radius o ka honua) mai ke kikowaena o ka honua, ʻo ke kahua umekaumaha he g. Hiki ke hōʻoia ʻia kēia ma o nā helu ʻana aʻe:

Ua like ke kahua umekaumaha (g) me 1 / R ^2. Inā ʻo R = 1 a laila 1 / R ² = 1/1 ² = 1/1 = 1. Inā ʻo ka mamao o ka astronaut mai ke kikowaena o ka honua = 1 a laila ʻike ka astronaut i ke kahua umekaumaha o = (g) (1) = g.

ʻO ka mamao o ka astronaut mai ke kikowaena o ka honua he 1.5R = 1.5 (1) = 1.5 a laila ke hele nei ka astronaut i kahi kahua umekaumaha o: 1 / R2 ⁼ 1 / 1.52 ⁼ 1 / 2.25. No laila, inā ʻo ka mamao o ka astronaut mai ke kikowaena o ka honua = 1.5 a laila he kahua umekaumaha ko ka astronaut = (g) (1 / 2.25) = g / 2.25

4. He aha ka lakio o ke kahua umekaumaha o ka honua no nā mea ʻelua, hoʻokahi ma ka ʻili o ka honua a ʻo kekahi ma ke kiʻekiʻe o ½ R mai ka ʻili o ka honua (R = ka radius o ka honua)?

ʻIke ʻia:

ʻO ka mamao o ka mea A mai ke kikowaena o ka honua (r _A ) = R = 1

ʻO ka mamao o ka mea B mai ke kikowaena o ka honua (r _B ) = 0.5R + R = 1.5R = 1.5

Makemake ʻia: Ka lakio o ke kahua umekaumaha o ka honua

Lōlā:

ʻO ke kahua umekaumaha o ka honua i ʻike ʻia e ka mea A (g _A ):

ʻO ke kahua umekaumaha o ka honua i ʻike ʻia e ka mea A (g _B ):

ʻO ka lakio o ke kahua umekaumaha o ka honua i ʻike ʻia e ka mea A a me ka mea B:

1. He aha ke kahua umekaumaha?
   • pane mai: Hōʻike ke kahua umekaumaha i ka hakahaka a puni kahi nuipa kahi e ʻike ai kekahi nuipa ʻē aʻe i kahi ikaika ma muli o ke umekaumaha. He ala ia e wehewehe ai pehea e hoʻopili ai nā mea kekahi i kekahi ma o ka huki umekaumaha me ka ʻole o ka pili pololei.
2. Pehea e loli ai ka ikaika o ke kahua umekaumaha i kou neʻe ʻana aku mai ka nuipa e hana ana ia mea?
   • pane mai: Hoʻemi ʻia ka ikaika o ke kahua umekaumaha me ka huinahā o ka mamao mai ke kumu nuipa. ʻO ke kikoʻī, hahai ia i ke kānāwai huinahā hoʻohuli: inā ʻoe e pāpālua i ka mamao, lilo ka ikaika o ke kahua i hapahā o kona ikaika mua.
3. Pehea e pili ai ke kahua umekaumaha i ka ikaika umekaumaha?
   • pane mai: ʻO ka ikaika o ke kahua umekaumaha ma kahi kiko ma ka lewa, i hōʻike ʻia e $g$, ua wehewehe ʻia ʻo ia ka ikaika umekaumaha (F) no kēlā me kēia anakahi nuipa (m) i ʻike ʻia e kahi nuipa hoʻāʻo liʻiliʻi i kau ʻia ma ia wahi. Ma ke ʻano makemakika, $g=F/m$.
4. Pehea e loli ai ke kahua umekaumaha o ka Honua me ke kiʻekiʻe?
   • pane mai: I ka piʻi ʻana o ke kiʻekiʻe (i kou neʻe ʻana aku mai ke kikowaena o ka Honua), e emi ana ka ikaika o ke kahua umekaumaha. ʻO ia ke kumu e ʻike ai nā astronauts ma ka orbit i ka microgravity, ʻoiai aia nō lākou i loko o ka mana umekaumaha o ka Honua.
5. He aha ke ʻano o ka ʻōlelo ʻana he "mau kahua conservative" nā kahua umekaumaha?
   • pane mai: ʻO ke kahua mālama ʻole, ʻo ia hoʻi, ʻo ka hana i hana ʻia ma kahi mea e neʻe ana ma waena o ʻelua mau wahi ma ke kahua he kūʻokoʻa ia mai ke ala i lawe ʻia. No nā kahua umekaumaha, ʻo ia hoʻi, ʻo ka hana i hana ʻia e ka ikaika umekaumaha ma kahi mea e neʻe ana ma waena o ʻelua mau wahi he like ia me ka nānā ʻole i ke ala e hele ai.
6. Pehea e hui pū ai nā kahua umekaumaha o nā nuipa he nui?
   • pane mai: Hoʻopili a hui pū paha nā kahua umekaumaha mai nā nuipa he nui ma ke ʻano vector. Ma kekahi wahi i hāʻawi ʻia, ʻo ke kahua umekaumaha hopena ka huina vector o nā kahua umekaumaha i hana ʻia e kēlā me kēia nuipa pākahi.
7. Pehea ka hopena o ke kaumaha o kahi mea i ke kahua umekaumaha e hoʻopuka ai?
   • pane mai: Ua kūlike pololei ke kahua umekaumaha i hana ʻia e kahi mea i kona nuipa. E hoʻopuka kahi mea nui aʻe i kahi kahua umekaumaha ikaika aʻe.
8. Pehea e ana ʻia ai ka ikaika o ke kahua umekaumaha?
   • pane mai: Ana ʻia ka ikaika o ke kahua umekaumaha ma ke ʻano o ka ikaika no kēlā me kēia anakahi nuipa. Ma ka ʻōnaehana anakahi SI, ana ʻia ma $N/kg$ (Nā Newton no ke kilokani).
9. Hiki i nā kahua umekaumaha ke hana? Inā pēlā, pehea?
   • pane mai: ʻAe, hiki i nā kahua umekaumaha ke hana i ka hana. Ke neʻe kahi mea ma ke kuhikuhi o kahi kahua umekaumaha (e like me ka ʻāpala e hāʻule ana i ka Honua), hana ke kahua umekaumaha ma luna o ka mea, a emi iho ka ikehu hiki ke umekaumaha o ka mea.
10. He aha ka pilina ma waena o ke kahua umekaumaha a me ka ikehu hiki ke umekaumaha?

• pane mai: ʻO ka ikehu hiki ke umekaumaha ka ikehu o kahi mea ma muli o kona kūlana i loko o kahi kahua umekaumaha. Pili ka loli o ka ikehu hiki ke umekaumaha o kahi mea i ka hana i hana ʻia e ka ikaika umekaumaha i ka neʻe ʻana o ka mea. Hiki ke loaʻa ke kahua umekaumaha mai ka gradient (a i ʻole ka derivative spatial) o ka hiki ke umekaumaha.