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. Imibuthano ihlangana ngqo phakathi komunye – Kwenzeka uma d = 0 kanye no-r1 = r2 (zombili ziyindilinga efanayo). Imibuzo Yesibonelo Nengxoxo Ake sibukeze eminye imibuzo eyisibonelo ukuze siqonde kangcono indawo yezindilinga ezimbili. Isibonelo Umbuzo 1: Imibuthano Ihlangana Ngaphandle Umbuzo: Uma unikezwe imibuthano emibili enezindawo ezimaphakathi 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: - Okunikeziwe: - Irediyasi yendilinga yokuqala, r1 = 6 cm - Irediyasi yendilinga yesibili, r2 = 4 cm - Ibanga eliphakathi kwezikhungo zendilinga, d = 10 cm Ngezimo ze-tangent zangaphandle: \[ d = r1 + r2 \] Faka amanani: \[ d = 6 + 4 \] \[ d = 10 \] Njengoba d = 10 cm, okulingana nesamba sika-r1 no-r2, le mibuthano emibili i-tangent yangaphandle. Isibonelo Umbuzo 2: Imibuthano Ye-Tangent Yangaphakathi Umbuzo: Imibuthano emibili ene-radii engu-8 cm no-3 cm ngokulandelana inebanga eliphakathi kwezikhungo ezingu-5 cm. Nquma indawo yemibuthano emibili. Ingxoxo: - Okunikeziwe: - Irediyasi yendilinga yokuqala, r1 = 8 cm - Irediyasi yendilinga yesibili, r2 = 3 cm - Ibanga eliphakathi kwezikhungo zemibuthano, d = 5 cm Ngezimo ze-tangent zangaphakathi: \[ d = |r1 - r2| \] 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.
