Mavhiri akabatanidzwa nemabhandi - matambudziko nemhinduro
1. Mavhiri matatu akabatana sezvakaratidzwa mumufananidzo uri pazasi.
Kana R A = 10 cm, R B = 4 cm, uye R C = 40 cm, saka chiyero chekumhanya kwevhiri A nevhiri C ndeche …
Zvinozivikanwa:
Nharaunda yevhiri A (r A ) = 10 cm
Nharaunda yevhiri B (r B ) = 4 cm
Nharaunda yevhiri C (r C ) = 40 cm
Zvinodiwa: chiyero chekumhanya kwevhiri A nevhiri C
Solution:
Kumhanya kwemavhiri A neC kwekona
Kutenderera kwevhiri A kwakakura kupfuura kutenderera kwevhiri C. Kana vhiri C ratenderedzwa denderedzwa rimwe (360 o ), panguva imwe cheteyo vhiri A harisati ratenderedza denderedzwa rimwe (360 o ). Saka, kumhanya kwevhiri A hakuna kuenzana nekumhanya kwevhiri C.
Zvisinei, vhiri A nevhiri C zvakabatana kuburikidza netambo, zvekuti panguva imwe chete, daro rinofambwa nemupendero wevhiri A rakaenzana nedaro rinofambwa nemupendero wevhiri C. Saka kumhanya kwemutsetse wemucheto wevhiri C (v C ) kwakaenzana nekumhanya kwemutsetse wemucheto wevhiri A (v A ).
v A = v C
r A ω A = r C ω C
10 ω A = 40 ω C
ω A / ω C = 40 / 10
ω A / ω C = 4 / 1
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2. Mavhiri B naC ane axis imwechete yekutenderera uye vhiri A rakafanana nevhiri B. Kana radius yevhiri A = radius yevhiri C = 30 cm, radius yevhiri B = 60 cm, saka sarudza chiyero chekumhanya kwakatsetseka pakati pemavhiri A, B, naC.
Zvinozivikanwa:
Nharaunda yevhiri A (r)A) = 30 cm = 0.3 metres
Nharaunda yevhiri B (r B ) = 60 cm = 0.6 mita s
Nharaunda yevhiri C (r C ) = 30 cm = 0.3 mita s
Zvinodiwa: chiyero chekumhanya kwakatwasuka pakati pemavhiri A, B, naC.
Solution:
Kumhanya kwakanangana kwemucheto wevhiri A :
Chitsitsinho cheW A nevhiri B zvakabatana sezvakaratidzwa pamufananidzo uri pazasi, saka kumhanya kwevhiri A hakuna kuenzana nekumhanya kwevhiri B. Izvi zvinodaro nekuti kutenderera kwevhiri B kwakakura kupfuura vhiri A. Munguva imwe chete, kana vhiri A rakatenderedza denderedzwa rimwe (360 o ) , vhiri B harisati ratenderedza denderedzwa rimwe (360 o ). Zvisinei, panguva imwe chete, daro rakafambiswa nemupendero wevhiri A rakaenzana nedaro rakafambiswa nemupendero wevhiri B. Saka kumhanya kwemupendero wevhiri A (v A ) kwakaenzana nekumhanya kwemupendero wevhiri B (v B ).
Kumhanya kwakanangana kwemucheto wevhiri A:
v A = r A ω A = 0.3 ω A
Kumhanya kwakanangana kwemucheto wevhiri B :
Chitsitsinho cheW B nevhiri B zvinonamirana, saka, vhiri B nevhiri C zvinotendererana pamwe chete. Kana vhiri B richitenderera denderedzwa rimwe (360 o ) kupfuura panguva imwe chete, vhiri C rinotendererawo denderedzwa rimwe (360 o ). Sezvo richitenderera pamwe chete, saka kumhanya kwevhiri B (ω B ) kwakaenzana nekumhanya kwevhiri C (ω C ) = ω. Asi kumhanya kwevhiri B (vB) hakuna kuenzana nekumhanya kwevhiri C (v C )
Kumhanya kwakanangana kwemucheto wevhiri B:
v B = r B ω B = 0.6 ω B = 0.6 ω
Kumhanya kwakanangana kwemucheto wevhiri C:
v C = r C ω C = 0.3 ω C = 0.3 ω
Kumhanya kwakanangana kwemucheto wevhiri A (v A ) kwakafanana nekumhanya kwakanangana kwemucheto wevhiri B ( v B )
v A = v B
0.3 ω A = 0.6 ω
ω A = 0.6 ω / 0.3
ω A = 2 ω
Kumhanya kwakanangana kwemucheto wevhiri A (v A ):
v A = 0.3 ω A = 0.3 ( 2 ω) = 0.6 ω
Chiyero chekumhanya kwakanangana pakati pemavhiri A, B, naC.
vA: vB: v C
0.6 ω : 0.6 ω : 0.3 ω
0.6: 0.6: 0.3
6: 6 : 3
2:2:1
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