Isibonelo sombuzo wengxoxo mayelana nesimo sezindilinga ezimbili

Imibuzo Eyisibonelo Exoxa Ngesikhundla Semibuthano Emibili

I-Pendahuluan

Indilinga ingenye yezimo eziyisisekelo ku-geometry esivame ukuhlangana nazo ezinkingeni ezahlukene zezibalo. Ukufunda indawo yezindilinga ezimbili kuyisihloko esibalulekile ngenxa yezindlela eziningi zokusebenzisa ekuphileni kwansuku zonke. Kuzibalo, indawo yezindilinga ezimbili ingahlaziywa ngokuhlola izikhundla zazo ezihambisanayo ngokusekelwe ebangeni eliphakathi kwezikhungo zazo kanye ne-radii yazo.

Umqondo Wesikhundla Sezindilinga Ezimbili

Ukuze sinqume indawo yezindilinga ezimbili, sisebenzisa amapharamitha amaningana ayinhloko:
1. Irediyasi yesiyingi sokuqala (r1)
2. Irediyasi yesiyingi sesibili (r2)
3. Ibanga phakathi kwezikhungo zezindilinga ezimbili (d)

Ngokusekelwe kulezi zindinganiso, kunezindawo eziningana ezingaba khona zezindilinga ezimbili:
1. Indilinga inombala oluhlaza okwesibhakabhaka uma usuka ngaphandle
– Kwenzeka uma u-d = r1 + r2.
2. Izindilinga zihlangana ngaphakathi
– Kwenzeka uma u-d = |r1 – r2|.
3. Izindilinga ezihlanganayo
– Kwenzeka uma |r1 – r2| < d < r1 + r2. 4. Izindilinga azihlangene - Kwenzeka uma d > r1 + r2.
5. Indilinga eyodwa ngaphakathi kwenye indilinga ngaphandle kokuthinta
– Kwenzeka uma d < |r1 - r2|. 6. Izindilinga zihlangana ngqo ngaphakathi komunye nomunye - Kwenzeka uma d = 0 kanye no-r1 = r2 (zombili ziyindilinga efanayo).

Imibuzo Nengxoxo Yesibonelo Ake sibukeze eminye imibuzo eyisibonelo ukuze siqonde kangcono indawo yezindilinga ezimbili. Isibonelo Umbuzo 1: Izindilinga Zihlangana Ngaphandle Umbuzo: Uma unikezwe izindilinga ezimbili ezinezikhungo kumaphuzu A no-B, kanti ibanga u-AB lingu-10 cm. Irediyasi yendilinga yokuqala ingu-6 cm, kanti irediyasi yendilinga yesibili ingu-4 cm. Nquma indawo yezindilinga ezimbili. Ingxoxo: - Uma unikezwe: - Irediyasi yendilinga yokuqala, r1 = 6 cm - Irediyasi yendilinga yesibili, r2 = 4 cm - Ibanga eliphakathi kwezikhungo zezindilinga, d = 10 cm Ukuze uthole isimo se-tangency yangaphandle: \[ d = r1 + r2 \] Faka amanani: \[ d = 6 + 4 \] \[ d = 10 \] Njengoba u-d = 10 cm, okulingana nesamba sika-r1 no-r2, lezi zindilinga ezimbili zihlangana ngaphandle. Isibonelo Umbuzo 2: Imibuthano Ihlangana Ngaphakathi Umbuzo: Imibuthano emibili ene-radii engu-8 cm no-3 cm ngokulandelana inebanga phakathi kwezikhungo zayo ezingu-5 cm. Thola indawo yezindilinga ezimbili. Ingxoxo: - Kunikezwe: - Irediyasi yendilinga yokuqala, r1 = 8 cm - Irediyasi yendilinga yesibili, r2 = 3 cm - Ibanga phakathi kwezikhungo zezindilinga, d = 5 cm Ngokwesimo sokuxhumana kwangaphakathi: \[ d = |r1 - r2| \] Bala: \[ d = |8 - 3| \] \[ d = 5 \] Njengoba u-d = 5 cm, okulingana nomehluko ka-r1 no-r2, lezi zindilinga ezimbili zihlangana ngaphakathi. Isibonelo Umbuzo 3: Imibuzo Yezindilinga Ezihlanganayo: Izindilinga ezimbili zine-radii engu-7 cm no-5 cm ngokulandelana kanye nebanga eliphakathi kwezikhungo zazo elingu-9 cm. Thola indawo yezindilinga ezimbili. Ingxoxo: - Njengoba kunikezwe: - I-Radius yesindilinga sokuqala, u-r1 = 7 cm - I-Radius yesindilinga sesibili, u-r2 = 5 cm - Ibanga eliphakathi kwezikhungo zezindilinga, u-d = 9 cm Ngokwesimo sokuhlangana: \[ |r1 - r2| < d < r1 + r2 \] Bala: \[ |7 - 5| < 9 < 7 + 5 \] \[ 2 < 9 < 12 \] Njengoba inani lika-d liwela phakathi kuka-|r1 - r2| no-r1 + r2, khona-ke lezi zindilinga ezimbili ziyahlangana. Isibonelo Umbuzo 4: Izindilinga Ezingahlangene Umbuzo: Izindilinga ezine-radii engu-2 cm no-3 cm zinebanga phakathi kwezikhungo zazo ezingu-7 cm. Thola indawo yezindilinga ezimbili. Ingxoxo: - Kunikezwe: - Irediyasi yendilinga yokuqala, r1 = 2 cm - Irediyasi yendilinga yesibili, r2 = 3 cm - Ibanga phakathi kwezikhungo zezindilinga, d = 7 cm Ezimweni ezingahlangene: \[ d > r1 + r2 \]

Isibalo:
\[ 7 > 2 + 3 \]
\[ 7 > 5 \]

Njengoba u-d emkhulu kunesamba sika-r1 no-r2, lezi zindilinga ezimbili zihlukene.

Isibonelo Umbuzo 5: Indilinga Eyodwa Ngaphakathi Komunye Ngaphandle Kokuthintana

Umbuzo:
Izindilinga ezimbili ezine-radii engu-8 cm kanye no-2 cm ngokulandelana zinebanga phakathi kwezikhungo zazo ezingu-5 cm. Thola indawo yezindilinga ezimbili.

Ingxoxo:
- Kuyaziwa:
– Irediyasi yendilinga yokuqala, r1 = 8 cm
– Irediyasi yesiyingi sesibili, r2 = 2 cm
– Ibanga phakathi kwezikhungo zezindilinga, d = 5 cm

Ngokwesimo senye ngaphakathi kwenye ngaphandle kokuthinta:
\[ d < |r1 - r2| \] Bala: \[ d < |8 - 2| \] \[ 5 < 6 \] Njengoba u-d emncane kunomehluko phakathi kuka-r1 no-r2, indilinga eyodwa ingaphakathi kwenye ngaphandle kokuthinta. Isiphetho Ukuqonda indawo yezindilinga ezimbili kungasisiza ekusetshenzisweni okuhlukahlukene kwe-geometry kanye nokujwayela kwangempela. Ngokuqaphela ubudlelwano phakathi kwerediyasi yesiyingi kanye nebanga eliphakathi kwezikhungo zayo, singanquma ukuthi iziyingi ezimbili zithintana ngaphandle noma ngaphakathi, ziyahlangana, noma azihlangani. Ngezibonelo ezingenhla, kunethemba lokuthi abafundi bangawuqonda kangcono lo mqondo futhi bawusebenzise ezimweni ezahlukene zezibalo. Qhubeka uzijwayeza izinkinga ngezinguquko ezahlukene ukuze uthuthukise amakhono akho okuhlaziya nokuqonda indawo yeziyingi ezimbili. Lapho uzijwayeza kakhulu, kuzoba lula ngathi ukuxazulula izinkinga ezahlukahlukene ezihilela iziyingi ku-geometry.