Izibonelo ezi-4 zemibuzo yokuxhumana kwesondo nesondo
1. Amasondo amabili u-A no-B axhunywe ngeribhoni (bheka isithombe). Uma irediyasi ka-A iphindwe kabili kunerediyasi ka-B, khona-ke okwenzekayo...
A. vA = 2 vB
B. vA = 1/2 vB
C. vA = vB
D. ωA = ωB
E. ωA = 2 ωB
Ingxoxo
Kuyaziwa ukuthi:
Irediyasi yesondo A (rA) = kabili irediyasi yesondo B (2 rB)
Kubuziwe:
– Ubudlelwano phakathi kwesivinini esiqondile sesondo A (vA) kanye nesivinini esiqondile sesondo B (vB)
– Ubudlelwano phakathi kwejubane le-angular lesondo A (ωA) kanye nejubane le-angular lesondo B (ωA).
Impendulo:
Amasondo A no-B axhunywe ngeteyipu ukuze uma isondo A lijikeleza, isondo B nalo lijikeleze. Uma ngomzuzwana owodwa ubuso besondo A buhamba imitha eli-1, khona-ke ubuso besondo B buhamba imitha eli-1 ngomzuzwana o-1. Ngakho-ke ijubane eliqondile lesondo A lifana nejubane eliqondile lesondo B (vA = vB).
Ngakolunye uhlangothi, uma isondo B seliqedile ukujikeleza kanye, isondo A alikaqedi ukujikeleza kanye ngoba umjikelezo wesondo B mncane kuyilapho umjikelezo wesondo A mkhulu. Ngamanye amazwi, ijubane le-angular lesondo A alifani nejubane le-angular lesondo B. Buyini ubudlelwano phakathi kwejubane le-angular lesondo A kanye nejubane le-angular lesondo B?
Isivinini sesondo A: vA = rA ωA = 2rB ωA
Isivinini sesondo B: vB = rB ωB
Ijubane lesondo A lifana nejubane lesondo B:
vA = vB
2rB ωA = rB ωB
2ωA = ωB
ωA = 1/2 ωB
Impendulo efanele ngu-C.
2. Amasondo amathathu u-A, u-B no-C axhumene njengoba kuboniswe esithombeni. Uma ama-radii amasondo u-A, u-B no-C engama-20 cm, u-8 cm no-4 cm ngokulandelana, futhi isondo u-B lijikeleza ngesivinini esingama-rad.s ayi-10-1, bese isondo C lijikeleza nge ijubane le-angular likhulu njenge…
A. 80 rad.s-1
B. 50 rad.s-1
C. 40 rad.s-1
D. 20 rad.s-1
E. 10 rad.s-1
Ingxoxo
Kuyaziwa ukuthi:
Irediyasi yesondo A (rA) = 20 cm = 0,2 amamitha
Irediyasi yesondo B (rB) = 8 cm = 0,08 amamitha
Irediyasi yesondo C (rC) = 4 cm = 0,04 amamitha
Ijubane le-angular lesondo B (ωB) = 10 rad/s
Umbuzo: Ijubane le-angular lesondo C (ωC)
Impendulo:
Ijubane eliyindilinga kanye nejubane eliqondile lomugqa wesondo A
Isondo A nesondo B zinamathelene, ngakho zijikeleza ndawonye. Uma isondo B lijikeleza ngendilinga ngokujikeleza okukodwa (360o), khona-ke ngesikhathi esifanayo, isondo A nalo lihamba ngendilinga ngokujikeleza okukodwa (360o). Ngenxa yokuthi zijikeleza ndawonye, ijubane le-angular lesondo A (ωA) lifana nejubane le-angular lesondo B (ωB).
Ijubane le-Angular lesondo A:
ωA = ωB = ama-radian ayi-10/isekhondi
Ijubane eliqondile lomugqa wesondo A:
Ubukhulu bejubane eliqondile lomphetho wesondo A libalwa kusetshenziswa ifomula yobudlelwano phakathi kwejubane eliqondile kanye nejubane le-angular, v = r ω.
vA = rA ωA = (0,2 m)(10 rad/s) = 2 m/s
Ijubane eliyindilinga kanye nejubane eliqondile lomngcele wesondo C
Umjikelezo wesondo A mkhulu kakhulu kunomjikelezo wesondo C. Uma isondo C selihambe ngendilinga umjikelezo owodwa (360o), ngesikhathi esifanayo isondo A alikaqedi umjikelezo owodwa (360o).oNgakho-ke, ijubane le-angular lesondo A alifani nejubane le-angular lesondo C.
Kodwa-ke, amasondo u-A no-C axhumene ngentambo noma ngeketanga. Ngenxa yokuthi axhumene, ngesikhathi esifanayo, ibanga elihanjwa ngomphetho wesondo u-A lifana nebanga elihanjwa ngomphetho wesondo u-C. Ngakho-ke ijubane eliqondile lomphetho wesondo u-C (vC) lifana nejubane eliqondile lomphetho wesondo u-A (vA).
Ijubane eliqondile lerimu yesondo C:
vC = vA = 2 m/s
Ijubane le-angular lesondo C:
vC = rC ωC
ωC = vC / rC = 2 / 0,04 = ama-radian angu-50/isekhondi = ama-rad.s angu-50-1.
Impendulo efanele ingu-B.
3. Uhlelo lwamasondo olune-radii RA = 2 cm; i-RB = 4 cm kanye ne-RC = 10 cm luxhunyiwe njengoba kuboniswe esithombeni. Isondo B lijikeleza ngokujikeleza okungu-60 ngomzuzu, ngakho ijubane eliqondile lesondo C…
A. 8π cm.s-1
B. 12 cm.s-1
C. 12π cm.s-1
D. 24 cm.s-1
E. 24π cm.s-1
Ingxoxo
Kuyaziwa ukuthi:
Irediyasi yesondo A (rA) = 2 cm
Irediyasi yesondo B (rB) = 4 cm
Irediyasi yesondo C (rC) = 10 cm
Ijubane le-angular lesondo B (ωB) = imijikelezo engu-60/umzuzu = imijikelezo engu-60/imizuzwana engu-60 = 1 imijikelezo/umzuzwana = 1(2π radian)/umzuzwana = 2π rad/s
Umbuzo: Ijubane eliqondile lesondo C (vC)
Impendulo:
Ijubane eliqondile lomugqa wesondo B
Ijubane eliqondile lomphetho wesondo B:
vB = rB ωB = (4 cm)(2π rad/s) = 8π cm/s
Ijubane eliqondile lomugqa wesondo A
Isondo A kanye nesondo B kuxhunywe ngentambo ngakho ijubane eliqondile lomphetho wesondo A (vA) lifana nejubane eliqondile lomphetho wesondo B (vB).
vA = vB = 8π cm/s
Ijubane eliqondile lerimu yesondo C
Isondo C kanye nesondo A kuxhunywe ngentambo ngakho ijubane eliqondile lomphetho wesondo C (vC) lifana nejubane eliqondile lomphetho wesondo A (vA).
vC = vA = vB = 8π cm/s
Impendulo efanele ngu-A.
4. Cabanga ngobudlelwano bamasondo obulandelayo! I-radii yesondo i-RA = 25 cm, i-RB = 15 cm, i-RC = 40 cm, kanye nesondo u-C lijikeleza ngesivinini sokujikeleza esingu-60 revolutions ngomzuzu. Ijubane le-angular lesondo u-A lingu…
A. 2,5π rad.s-1
B. 3π rad.s-1
C. 3,2π rad.s-1
D. 3,5π rad.s-1
E. 3,8π rad.s-1
Ingxoxo
Kuyaziwa ukuthi:
Irediyasi yesondo A (rA) = 25 cm = 0,25 amamitha
Irediyasi yesondo B (rB) = 15 cm = 0,15 amamitha
Irediyasi yesondo C (rC) = 40 cm = 0,4 amamitha
Ijubane le-angular lesondo C (ωC) = imijikelezo engu-60/umzuzu = imijikelezo engu-60/imizuzwana engu-60 = 1 imijikelezo/umzuzwana = 1(2π radian)/umzuzwana = 2π rad/s
Umbuzo: Ijubane le-Angular lesondo A (ωA)
Impendulo:
Ijubane eliqondile lerimu yesondo C:
vC = rC ωC = (0,4 m)(2π rad/s) = 0,8π m/s
Ijubane eliqondile lomugqa wesondo B
Isondo C kanye nesondo B kuxhunywe ngentambo ngakho ijubane eliqondile lomphetho wesondo C (vC) lifana nejubane eliqondile lomphetho wesondo B (vB).
vB = vC = 0,8π m/s
Ijubane eliyindilinga kanye nejubane eliqondile lomugqa wesondo A
Isondo A kanye nesondo B kuxhumene njengoba kuboniswe esithombeni esingenhla, ngakho-ke ijubane le-angular lesondo A alifani nejubane le-angular lesondo B. Lokhu kungenxa yokuthi umjikelezo wesondo A mkhulu kunowesondo B. Ngesikhathi esifanayo, lapho isondo A selihambe ngendilinga umjikelezo owodwa (360)o), isondo B alikafiki ekujikelezeni okukodwa (360o). Kodwa-ke, phakathi nesikhathi esifanayo, ibanga elihanjwa ngomphetho wesondo A lifana nebanga elihanjwa ngomphetho wesondo B. Ngakho-ke ijubane eliqondile lomphetho wesondo A (vA) lifana nejubane eliqondile lomphetho wesondo B (vB).
Ijubane eliqondile lomugqa wesondo A
vA = vB = vC = 0,8π m/s
Ijubane le-Angular lesondo A
vA = rA ωA
ωA = vA / rA = 0,8π / 0,25 = 3,2π rad/s
Impendulo efanele ngu-C.
