Physics

1. A capacitor yofanana ndi mbale ali koyamba mphamvu C, chilolezo cha malo omasuka is ε_o, malo osungira mbale is A, mtunda pakati pa mbale is d. Ngatie Malo a mbale awonjezeka ndi nthawi 4, mtunda pakati pa mbale imakhala 2d ndipo chilolezo cha malo omasuka ndi 5ε_o, kodi mphamvu yomaliza ya capacitor ya parallel-plate ndi yotani?

Zodziwika:

Mphamvu ya capacitor = C

T chilolezo cha malo omasuka = ​​ε _o

Malo ochedwa a P = A

Mtunda pakati pa mbale = d

Kufunika: Kutha kwa capacitor (C)

Yankho:

[irp]

2. Kachipangizo kamene kali ndi mphamvu yaikulu kwambiri kutengera chithunzi chomwe chili pansipa ndi …

Yankho:

Fomula ya capacitor yofanana ndi mbale:

Mphamvu ya ma capacitor:

Capacitor yomwe ili ndi mphamvu yayikulu kwambiri ya y ndi capacitor C3_.

[irp]

3.

Taganizirani zinthu zotsatirazi!
(1) Chokhazikika cha Dielectric
(2) The kusiyana komwe kungatheke pakati pa mbale
(3) Mbale tchikwapu
(4) Malo ozungulira mbale
(5) Mtunda pakati pa mbale
(6) Kuchuluka kwa mtengo wamagetsi
Zinthu zomwe zimakhudza mphamvu za mbale zofanana ma capacitor ndi…

Yankho:

(1), (4) ndi (5)

4. Kuyerekeza mphamvu ya capacitor 1 ndi 2 ndi…

Zodziwika:

Capacitor 1:

Malo ozungulira = 2A

Mtunda pakati pa mbale = d ₁

Capacitor 2:

Malo ozungulira = A

Mtunda pakati pa mbale = 2 d ₁

Kufunidwa: Kuyerekeza mphamvu ya ma capacitor 1 ndi 2

Yankho:

[irp]

5.

Dziwani kufananiza kwa mphamvu ya capacitor ya Parallel-plate I ndi II.

Yankho:

Kuyerekeza mphamvu ya ma capacitor a Parallel-plate I ndi II:

[irp]

6. Ma capacitor awiri ofanana omwe akuwonetsedwa pachithunzi chili pansipa.

Ngati A ₁ = ½ A ₂ ndi d ₂ = 3 d ₁ ndiye dziwani chiŵerengero cha mphamvu za capacitor ya parallel -plate pakati pa chithunzi 2 ndi chithunzi 1.

Zodziwika:

Kaputeni wa mbale yofanana I:

A ₁ = 1

d ₁ = 1

Kapitoli wa mbale yofanana II:

A ₂ = 2

d ₂ = 3

Chifuniro: chiŵerengero cha mphamvu za capacitor ya parallel-plate pakati pa chithunzi 2 ndi chithunzi 1

Yankho:

Kaputeni wa mbale yofanana I:

Kapitoli wa mbale yofanana II:

Chiŵerengero cha mphamvu za ma capacitor a parallel- plate II ndi I:

Werengani zambiri

1. Dziwani mphamvu yamagetsi pamalo omwe ali pa 1 cm kuchokera pa chaji 5.0 μ C. Coulomb constant (k) = 9 x 10 ⁹ Nm ² C ⁻² , 1 μC = 10 ⁻⁶ C.

Zodziwika:

Mtunda wochokera ku chaji (r) = 1 cm = 1/100 m = 0.01 m = 10 ^-2 m

Kuchaja (q) = 5.0 μ C = 5.0 x 10 ^-6 C

Coulomb yosasintha (k) = 9 x 10 ⁹ Nm ² C ⁻²

Kufunidwa: Mphamvu yamagetsi (V)

Yankho:

Mphamvu yamagetsi:

Mphamvu yamagetsi ndi 4.5 x 10 ⁶ Volts

[irp]

2. kulipiritsa Q₁ = 5.0 μC ndi kulipira Q₂ = 6.0 μC. Chokhazikika cha Coulomb (k) = 9 x 10⁹ Nm²C^-2, 1 μC = 10^-6 C. Mfundo A ili pakati pa milandu. Dziwani mphamvu yamagetsi pamalo A.

Zodziwika:

Cholipiritsa Q ₁ = -5.0 μ C = -5.0 x 10 ^-6 C

Mtunda wa mfundo A kuchokera ku Q ₁ = 10 cm = 0.1 m = 10 ^-1 m

Cholipiritsa Q ₂ = 6.0 μ C = 6.0 x 10 ^-6 C

Mtunda wa mfundo a kuchokera ku Q ₂ = 10 cm = 0.1 m = 10 ^-1 m

Chosasintha cha Coulomb (k) = 9 x 10 ⁹ Nm ² C ⁻²

Kufunidwa: Mphamvu yamagetsi pamalo A

Yankho:

Mphamvu yamagetsi 1 :

Mphamvu yamagetsi 2 :

Mphamvu yamagetsi pa mfundo A :

V = V ₂ – V ₁

V = (54 – 45) x 10 ⁴

V = 9 x 10 ⁴

[irp]

3. kulipiritsa q₁ = 5.0 μC ndi kulipira q₂ = 6.0 μC. Chokhazikika cha Coulomb (k) = 9 x 10⁹ Nm²C^-2, 1 μC = 10^-6 C. Dziwani mphamvu yamagetsi pa mfundo A.

Zodziwika:

Cholipiritsa Q ₁ = -5.0 μ C = -5.0 x 10 ^-6 C

Mtunda wa mfundo A kuchokera ku Q ₁ = 40 cm = 0.4 m = 4 x 10 ^-1 m

Cholipiritsa Q ₂ = 6.0 μ C = 6.0 x 10 ^-6 C

Mtunda wa mfundo A kuchokera ku Q ₂ = 50 cm = 0.5 m = 5 x 10 ^-1 m

Chosasintha cha Coulomb (k) = 9 x 10 ⁹ Nm ² C ⁻²

Kufunidwa: Mphamvu yamagetsi pamalo A

Yankho:

Mphamvu yamagetsi 1 :

Mphamvu yamagetsi 2 :

Mphamvu yamagetsi pa mfundo A :

V = V ₁ + V ₂

V = (-11.25 + 10.8) x 10 ⁴

V = -0.45 x 10 ⁴

V = -4.5 x 10 ³

Mphamvu yamagetsi pamalo A ndi -4.5 x 10 ³ Volts

Werengani zambiri

1. Electron imathamanga kuchokera ku mpumulo kudzera mu kusiyana kwa mphamvu ya 12 V. Kodi kusintha kwa mphamvu yamagetsi ya electron ndi kotani?

Zodziwika:

Kulipiritsa pa elekitironi (e) = -1.60 x 10 ^-19 Coulomb

Mphamvu yamagetsi = mphamvu yamagetsi (V) = 12 Volts

Kufunidwa: Kusintha kwa mphamvu yamagetsi ya elekitironi (ΔPE)

Yankho:

ΔPE = q V = (-1.60 x 10 ^-19 C)(12 V) = -19.2 x 10 ^-19 Joules

Chizindikiro cha minus chimasonyeza kuti mphamvu zomwe zingatheke zimachepa.

[irp]

2. Ma plate awiri ofanana amapatsidwa mphamvu. Kulekana pakati pa ma plate ndi 2 cm ndipo kukula kwa mphamvu yamagetsi pakati pa ma plate ndi 500 Volt/mita. Kodi kusintha kwa mphamvu ya proton kumachitika bwanji ikathamangitsidwa kuchokera ku plate yomwe yapatsidwa mphamvu yabwino kupita ku plate yomwe yapatsidwa mphamvu zoipa?

Zodziwika:

Kukula kwa mphamvu yamagetsi pakati pa mbale (E) = 500 Volt/mita

Mtunda pakati pa mbale (s) = 2 cm = 0,02 m

Kulipiritsa pa protoni = +1.60 x 10 ^-19 Coulombs

Kufunidwa: Kusintha kwa mphamvu yamagetsi (ΔPE)

Yankho:

Mphamvu yamagetsi:

V = E s

V = (500 Volt/m)(0.02 m)

V = 10 Volt

Kusintha kwa mphamvu zamagetsi:

ΔPE = q V

ΔPE = (1,60 x 10 ^-19 C)(10 V)

ΔPE = 16 x 10 ^-19 Joule

ΔPE = 1.6 x 10 ^{-1 8} Joule

[irp]

3. Ma point charge awiri amalekanitsidwa ndi mtunda wa 10 cm. Ma charge pa point A = +9 μC ndipo ma charge pa point B = -4 μC. k = 9 x 10 ⁹ Nm ² C ⁻² , 1 μC = 10 ⁻⁶ C. Kodi kusintha kwa mphamvu yamagetsi ya charge pa point B ndi kotani ngati ikulitsidwa kufika pa point A?

Zodziwika:

Chaji A (q ₁ ) = +9 μC = +9 x 10 ⁻⁶ C

Chaji B (q ₁ ) = -4 μC = -4 x 10 ⁻⁶ C

k = 9 x 10 ⁹ Nm ² C ⁻²

Mtunda pakati pa zolipiritsa A ndi B (r) = 10 cm = 0.1 m = 10 ^-1 m

Kufunidwa: Kusintha kwa mphamvu yamagetsi (ΔEP)

Yankho:

Werengani zambiri

1. Mphamvu yamagetsi yofanana E = 8000 N/C imadutsa m'dera lathyathyathya lalikulu A = 10 m2 ^. Dziwani kuchuluka kwa mphamvu yamagetsi.

Zodziwika:

Kukula kwa mphamvu yamagetsi (E) = 8000 N/C

Malo (A) = 10 m ²

θ = 0 ^o (ngodya pakati pa njira yamagetsi ndi mzere wokokedwa molunjika kuderali)

Kufunidwa: Kutuluka kwa magetsi ( Φ)

Yankho:

Fomula ya flux yamagetsi:

Φ = EA cos q

Φ = flux yamagetsi ( Nm ² /C) , E = munda wamagetsi (N/C), A = dera (m ² ), q = ngodya pakati pa mzere wamagetsi ndi mzere wamba.

Kutuluka kwa magetsi:

Φ = EA cos q = (8000) (10) ( cos 0) = (8000) (10) (1 ) = 80,000 = 8 x 10 ⁴ Nm ² /C

[irp]

2. Mphamvu yamagetsi yofanana E = 5000 N/C imadutsa m'dera lathyathyathya lalikulu A = 2 m 2. ^Dziwani mphamvu yamagetsi.

Zodziwika:

Malo amagetsi (E) = 5000 N/C

Malo (A) = 2 m ²

θ = 60 ^o (ngodya pakati pa njira yamagetsi ndi mzere wokokedwa molunjika kuderali)

Kufunidwa: Kutuluka kwa magetsi ( Φ)

Yankho:

Kutuluka kwa magetsi:

Φ = EA cos q = (5000) (2) ( cos 60) = (5000) (2) (0.5 ) = 5000 = 5 x 10 ³ Nm ² /C

[irp]

3. Mpira wolimba wokhala ndi utali wa mamita 0.5 uli ndi mphamvu yamagetsi ya 10 μC pakati pake. Dziwani mphamvu yamagetsi yomwe ikudutsa mu mpira wolimba.

Zodziwika:

Ulalo wa mpira (r) = 0.5 m

Mphamvu yamagetsi (Q) = 10 μC = 10 x 10 ^-6 C

Kufunidwa: Kutuluka kwa magetsi ( Φ)

Yankho:

Malo amagetsi:

E = kq/r ²

E = (9 x 10 ⁹ Nm ² /C ² ) ( 10 x 10 ^-6 C) / 0.5 ²

E = (90 x 10 ³ ) / 0,25

E = 360 x 10 ³

E = 3.60 x 10 ⁵ N/C

Malo ozungulira:

A = 4 π r ² = 4 (3.14) (0.5) ² = (12.56) (0.25) = 3.14 m ²

Kutuluka kwa magetsi:

Mizere yamagetsi imakhala yolunjika kudera, kotero kuti ngodya pakati pa njira yamagetsi ndi mzere wokokedwa wolunjika kudera, ndi 0 ^o.

Φ = EA cos q

Φ = ( 3.60 x 10 ⁵ )( 3.14 )( cos 0)

Φ = (11.304 x 10 ⁵ )(1)

Φ = 11.304 x 10 ⁵

Φ = 1.13 x 10 ⁶ Nm ² /C

Werengani zambiri

1. Werengani kukula ndi komwe magetsi akupita pa mfundo A yomwe ili pa 5 cm kuchokera pa mfundo imodzi Q = +10 μC. k = 9 x 10 ⁹ Nm ² C ⁻² , 1 μC = 10 ⁻⁶ C)

Zodziwika:

Mphamvu yamagetsi (Q) = +10 μC = +10 x 10 ^-6 C

Mtunda pakati pa mfundo A ndi point charge Q (r A ₎ = 5 cm = 0.05 m = 5 x 10 ^-2 m

k = 9 x 10 ⁹ Nm ² C ⁻²

Kufunidwa: Kukula ndi komwe magetsi akuyendera pamalo A

Yankho:

Kuwongolera kwa munda wamagetsi pamalo A:

Mphamvu yamagetsi ndi yabwino kotero kuti njira ya magetsi ili kutali ndi mphamvu yamagetsi ndi mfundo A.

[irp]

2. Werengerani kukula ndi njira ya magetsi pamalo P omwe ali pamtunda wa 10 cm kuchokera pa malo ochapira Q = -2 0 μC. k = 9 x 10 ⁹ Nm ² C ⁻² , 1 μC = 10 ⁻⁶ C.

Zodziwika:

Mphamvu yamagetsi (q) = -20 μC = -20 x 10 ^-6 C

Mtunda pakati pa mfundo P ndi mphamvu yamagetsi (r _P ) = 10 cm = 0.1 m = 1 x 10 ^-1 m

k = 9 x 10 ⁹ Nm ² C ⁻²

Kufunidwa: Kukula ndi komwe magetsi akuyendera pamalo P

Yankho:

Kuwongolera kwa magetsi pamalo A:

Mphamvu yamagetsi ndi yoipa motero mphamvu yamagetsi imapita ku mphamvu yamagetsi.

[irp]

3. Ma charge awiri a nsonga amalekanitsidwa ndi mtunda wa masentimita 40. Kodi kukula ndi komwe magetsi amachokera pa nsonga P pakati pa ma charge awiriwa ndi kotani, komwe kuli masentimita 20 kuchokera pa nsonga A?

Zodziwika:

Chaji A (q _A ) = -2 μC = -2 x 10 ^-6 C

Chaji B (q _B ) = + 4 μC = +4 x 10 ^-6 C

Mtunda pakati pa chaji A ndi mfundo P (r _AP ) = 20 cm = 0.2 m = 2 x 10 ^-1 m

Mtunda pakati pa chaji B ndi mfundo P (r _BP ) = 20 cm = 0.2 m = 2 x 10 ^-1 m

Kufunidwa: Kukula ndi komwe magetsi ali pamalo a P.

Yankho:

Chaji A ndi yoipa kotero kuti njira ya malo olumikizira magetsi ikupita ku Q _A (kumanzere).

Chaji B ndi yabwino kotero kuti njira ya malo olumikizira magetsi ili kutali ndi Q _B (kumanzere).

Mphamvu yonse yamagetsi pa mfundo A:

E = E _A + E _B

E = (4.5 x 10 ⁵ ) + (9 x 10 ⁵ )

E = 13.5 x 10 ⁵ N/C

Kulunjika kwa mphamvu yamagetsi kumayang'ana ku Q _A (kumanzere).

[irp]

4. Kukula kwa mphamvu yamagetsi ndi zero pa…

Chaji A ndi yabwino ndipo chaji B ndi yabwino kotero kuti kukula kwa mphamvu yamagetsi ndi zero komwe kuli pa mfundo P, pakati pa machaji onse awiri.

Zodziwika:

Chaji A (q _A ) = + 20 μC = +20 x 10 ⁻⁶ C

Chaji B (q _B ) = +40 μC = +40 x 10 ⁻⁶ C

k = 9 x 10 ⁹ Nm ² C ⁻²

Mtunda pakati pa chaji A ndi chaji B = 20 cm

Mtengo pakati pa mtengo A ndi mfundo P (r _AP ) = a

Mtunda pakati pa cholipiritsa B ndi mfundo P (r _BP ) = 20 – a

Kufunidwa: Kukula kwa mphamvu yamagetsi ndi zero komwe kuli pa….

Yankho:

Kukula kwa mphamvu yamagetsi yopangidwa ndi mphamvu A pa mfundo P

Chaji A ndi yabwino kotero kuti njira ya malo olumikizira magetsi ili kutali ndi chaji A (kumanja).

Kukula kwa mphamvu yamagetsi yopangidwa ndi mphamvu B pa mfundo P:

Chaji B ndi yabwino kotero kuti njira ya malo olumikizira magetsi ili kutali ndi chaji B (kumanzere).

Munda wonse wamagetsi pa mfundo P = 0:

Timagwiritsa ntchito njira ya quadratic kuti tidziwe a.

Kukula kwa mphamvu yamagetsi ndi zero komwe kuli pa 8 cm kuchokera pa chaji A kapena 12 cm kuchokera pa chaji B.

[irp]

5. Kutengera chithunzi chomwe chili pansipa, w apa pali mfundo P kotero kuti gawo lamagetsi pa mfundo P ndi zero? (k = 9 x 10 ⁹ Nm ² C ⁻² , 1 μC = 10 ⁻⁶ C)

Anakonza

To werengerani mphamvu yamagetsi pa mfundo P, poganiza kuti pa mfundo P pali mtengo wabwino woyesera. Q₁ ali ndi chiyembekezo ndipo Q₂ ndi yoipa, chifukwa chake mfundo P iyenera kukhala kumanja kwa Q₂ kapena kumanzere kwa Q₁Ngati mfundo P ili kumanzere kwa Q₁; mphamvu yamagetsi yopangidwa ndi Q₁ pamalo pomwe P ili kumanzere (kutali ndi Q₁ndi mphamvu yamagetsi yopangidwa ndi Q₂ pamalo P kumanja (kulowera ku Q₁). Kulunjika kwa munda wamagetsi kuli moyang'anizana kotero kuti minda iwiri yamagetsi imasiyana kotero kuti mphamvu ya munda wamagetsi pamalo P ndi zero.

Zodziwika:

Q ₁ = +9 μC = +9 x 10 ⁻⁶ C

Q ₂ = -4 μC = -4 x 10 ⁻⁶ C

k = 9 x 10 ⁹ Nm ² C ⁻²

Mtunda pakati pa chaji 1 ndi chaji 2 = 3 cm

Mtunda pakati pa Q ₁ ndi mfundo P (r _1P ) = a

Mtunda pakati pa Q ₂ ndi mfundo P (r _2P ) = 3 + a

Kufunidwa: malo a mfundo P kotero kuti mphamvu yamagetsi pa mfundo P ikhale zero

Yankho:

Point P ili kumanzere kwa Q ₁.

Mphamvu yamagetsi yopangidwa ndi Q1 _pa mfundo P:

Mtengo woyeserera ndi wabwino ndipo Q ₁ ndi wabwino kotero kuti njira ya magetsi ili kumanzere.

Mphamvu yamagetsi yopangidwa ndi Q2 _pa mfundo P:

Mtengo woyeserera ndi wabwino ndipo Q2 _ndi yoipa kotero kuti mbali ya magetsi ili kumanja.

Malo ogwiritsira ntchito magetsi pa mfundo A:

Gwiritsani ntchito fomula ya quadratic kuti mudziwe a:

a = -1.25, b = -13.5, c = -20.25

Mtunda pakati pa Q ₂ ndi mfundo P (r _2P ) = 3 + a = 3 – 1.8 = 1.2 cm.

Point P ili kumanja kwa 1.2 cm kuchokera ku Q ₁.

[irp]

Werengani zambiri

1. Ma point awiri, Q_A = +8 μC ndi Q_B = -5 μC, zimalekanitsidwa ndi mtunda r = 10 cm. Kodi kukula kwa mphamvu yamagetsi. K yokhazikika = 8.988 x 10⁹ Nm²C^-2 = 9x10 pa⁹ Nm²C^-2.

Zodziwika:

Chaji A (q _A ) = +8 μC = +8 x 10 ^-6 C

Chaji B (q _B ) = -5 μC = -5 x 10 ^-6 C

k = 9 x 10 ⁹ Nm ² C ⁻²

Mtunda pakati pa zolipiritsa A ndi B (r AB ₎ = 10 cm = 0.1 m

Kufunidwa : Kukula kwa mphamvu yamagetsi

Yankho:

Fomula ya lamulo la Coulomb :

Kukula kwa mphamvu yamagetsi:

[irp]

2. Tinthu tating'onoting'ono tiwiri tomwe timayatsidwa monga momwe tawonetsera pachithunzi pansipa. Q _P = +10 μC ndi Q _q = +20 μC zimalekanitsidwa ndi mtunda r = 10 cm. Kodi kukula kwa mphamvu yamagetsi ndi kotani?

Zodziwika:

Chaji P (Q _P ) = +10 μC = +10 x 10 ^-6 C

Chaji Q (Q _Q ) = +20 μC = +20 x 10 ^-6 C

k = 9 x 10 ⁹ Nm ² C ⁻²

Mtunda pakati pa ma chaji P ndi Q (r _PQ ) = 12 cm = 0.12 m = 12 x 10 ^-2 m

Kufunidwa: Kukula kwa mphamvu yamagetsi

Yankho:

[irp]

3. Tinthu tating'onoting'ono titatu tayikidwa pamzere monga momwe chithunzi chili pansipa chikusonyezera. Chaji A = -5 μC, chaji B = +10 μC ndi chaji C = -12 μC. Werengani mphamvu yamagetsi yokhazikika pa tinthu tating'onoting'ono B chifukwa cha machaji ena awiri.

Zodziwika:

Chaji A (q _A ) = -5 μC = -5 x 10 ^-6 C

Chaji B (q _B ) = +10 μC = +10 x 10 ^-6 C

Chaji C (q _C ) = -12 μC = -12 x 10 ^-6 C

k = 9 x 10 ⁹ Nm ² C ⁻²

Mtunda pakati pa tinthu tating'onoting'ono A ndi B (r _AB ) = 6 cm = 0.06 m = 6 x 10 ^-2 m

Mtunda pakati pa tinthu tating'onoting'ono B ndi C (r _BC ) = 4 cm = 0.04 m = 4 x 10 ^-2 m

Kufunidwa: Kukula ndi momwe mphamvu yamagetsi yokhazikika imayendera pa tinthu tating'onoting'ono B

Yankho:

Mphamvu yonse pa tinthu B ndi kuchuluka kwa mphamvu ya F _BA yomwe imagwiritsidwa ntchito pa tinthu B ndi tinthu A ndipo mphamvu ya F _BC yomwe imagwiritsidwa ntchito pa tinthu B ndi tinthu C.

Mphamvu ya F _BA yomwe imagwiritsidwa ntchito pa tinthu B ndi tinthu A:

 

Kulunjika kwa mphamvu yamagetsi kumaloza ku tinthu A (malo kupita kumanzere).

Mphamvu ya F _BC yomwe imagwiritsidwa ntchito pa tinthu B ndi tinthu A:

 

Kulunjika kwa mphamvu yamagetsi kumaloza ku tinthu C (kuloza kumanja).

Mphamvu yamagetsi yokhazikika pa tinthu tating'onoting'ono B :

F _B = F _AB – F _BC = 675 N – 125 N = 550 Newtons.

Kulunjika kwa mphamvu yamagetsi ya net static pa tinthu B kumasonyeza tinthu C (kumasonyeza kumanja).

[irp]

4. +Q ₁ = 10 μC, +Q ₂ = 50 μC ndi Q ₃ zalekanitsidwa monga momwe zasonyezedwera pachithunzi chili pansipa. Kodi mphamvu ya electrostatic pa tinthu 3 ndi yotani ngati mphamvu ya electrostatic pa tinthu 2 ndi zero?

Zodziwika:

Chaja 1 (q ₁ ) = +10 μC = +10 x 10 ^-6 C

Chaja 2 (q ₂ ) = +50 μC = +50 x 10 ^-6 C

Mtunda pakati pa ma chaji 1 ndi 2 (r ₁₂ ) = 2 cm = 0.02 m = 2 x 10 ^-2 m

Mtunda pakati pa cholipiritsa 2 ndi cholipiritsa 3 (r ₂₃ ) = 6 cm = 0.06 m = 6 x 10 ^-2 m

Mphamvu yamagetsi yokhazikika pa tinthu 2 (F ₂ ) = 0

Akufuna : ndalama 3 (q ₃ )

Yankho:

Mphamvu yonse pa tinthu 2 ndi kuchuluka kwa mphamvu ya F ₂₁ yomwe imagwiritsidwa ntchito pa tinthu 2 ndi tinthu 1 ndipo mphamvu ya F ₂₃ yomwe imagwiritsidwa ntchito pa tinthu 2 ndi tinthu 3.

Mphamvu F ₂₁ yomwe imagwiritsidwa ntchito pa tinthu 2 ndi tinthu 1:

Kulunjika kwa mphamvu yamagetsi kumaloza ku tinthu 3 (kuloza kumanja).

Mphamvu F₂₃ yogwiritsidwa ntchito pa tinthu 2 ndi tinthu 3: 

Kulunjika kwa mphamvu yamagetsi kumaloza ku tinthu 1 (malo kupita kumanzere).

Mphamvu yonse ya electrostatic pa tinthu 2 = 0:

Werengani zambiri

1. Chinthu chokhala ndi nthawi ya inertia ya 2 kg m ² chimazungulira pa 1 rad/s. Kodi mphamvu ya angular ya chinthucho ndi yotani ?

Zodziwika:

Nthawi ya kulephera (I) = 2 kg m ²

Liwiro la angular ( ω ) = 1 rad/s

Kufunidwa: Angular momentum (L)

Yankho:

Fomula ya angular momentum:

L = Ine ω

L = angular momentum (kg m ² /s), I = mphindi ya inertia (kg m ² ), ω = angular speed (rad/s)

Mphamvu ya angular:

L = I ω = (2)(1) = 2 kg m ² /s

[irp]

2. Pulley ya silinda ya 2 kg yokhala ndi utali wa 0.1 m imazungulira pa liwiro lokhazikika la 2 rad/s. Kodi mphamvu ya pulley ya angular ndi yotani?

Zodziwika:

Kulemera kwa pulley (m) = 2 kg g

Utali wa pulley (r) = 0.1 m

Liwiro la angular (ω) = 2 r ad/s

Kufunidwa: Mphamvu ya angular

Yankho:

Fomula ya mphindi ya inertia ya silinda yolimba:

Ine = 1/2 mr ²

I = mphindi ya kulephera (kg m ² ), m = kulemera (kg), r = utali wozungulira (m)

Nthawi ya kutopa:

I = 1/2 (2)(0.1) ² = (1)(0.01) = 0.01 kg m ²

Liwiro la angular:

L = I ω = ( 0.01 )( 2 ) = 0.02 kg m ² /s

[irp]

3. Chipilala chofanana cha makilogalamu awiri chokhala ndi utali wa mamita 0.2 chimazungulira pa 4 rad/s. Kodi mphamvu ya mpira ndi yotani?

Zodziwika:

Kulemera kwa mpira (m) = 2 kg

Utali wa mpira (r) = 0.2 m

Liwiro la angular (ω) = 4 ra d/s

Kufunidwa: Mphamvu ya angular

Yankho:

Fomula ya mphindi ya inertia ya malo ofanana:

Ine = (2/5) mr ²

I = mphindi t ya inertia (kg m ² ), m = kulemera (kg), r = utali wozungulira (m)

Nthawi ya inertia ya malo ofanana:

I = (2/5)(2)(0.2) ² = (4/5)(0.04) = 0.032 kg m ²

Mphamvu ya angular ya mlengalenga:

L = I ω = ( 0.032 )( 4 ) = 0.128 kg m ² /s

[irp]

4. Tinthu tating'onoting'ono ta 1-kg timazungulira pa liwiro lokhazikika la 2 rad/s. Kodi liwiro la angular ndi lotani ngati radius ya bwalo ndi 10 cm?

Zodziwika:

Kulemera kwa chinthu (m) = 1 kg g

Utali wozungulira wa bwalo (r) = 10 cm = 10/100 = 0.1 m

Liwiro la angular (ω) = 2 rad/ s

Kufunidwa: Mphamvu ya angular

Yankho:

Fomula ya mphindi ya inertia ya tinthu tating'onoting'ono:

Ine = mr ² = (1)(0.1) ² = (1)(0.01) = 0.01 kg m ²

Mphamvu ya angular:

L = I ω = (0.01)(2) = 0.02 kg m ² /s

Werengani zambiri

1. Chinthu chili ndi nthawi ya inertia ya 1 kg m ² chimazungulira pa liwiro lokhazikika la 2 rad/s. Kodi mphamvu ya kayendedwe ka chinthucho ndi yotani ?

Zodziwika:

Nthawi ya inertia (I) = 1 kg m ²

Liwiro la angular ( ω) = 2 rad/s

Kufunidwa: Mphamvu ya kinetic yozungulira (K E )

Yankho:

Fomula ya mphamvu ya kinetic yozungulira:

KE = 1/2 I ω ²

KE = mphamvu ya kinetic yozungulira (kg m²/s²), Ine = mphindi ya kusakhala ndi mphamvu (kg m²), ω = liwiro la angular (rad/s)

Mphamvu ya kinetic yozungulira:

KE = 1/2 I ω ² = 1/2 (1) (2) ² = 1/2 (1) (4) = 2 Joules

[irp]

2. Pulley ya silinda ya makilogalamu 20 yokhala ndi utali wa mamita 0.2 imazungulira pa liwiro lokhazikika la 4 rad/s. Kodi mphamvu ya kinetic ya pulley ndi yotani?

Zodziwika:

Kulemera kwa pulley ya silinda (m) = 20 kg g

Utali wa silinda (r) = 0.2 m

Liwiro la angular (ω) = 4 ra d/s

Kufunidwa: Kodi mphamvu ya kinetic yozungulira ndi chiyani?

Yankho;

Fomula ya mphindi ya inertia ya silinda:

Ine = 1/2 mr ²

I = mphindi ya inertia ( kg m ² ), m = kulemera (kg), r = radius (mita)

Nthawi ya inertia ya pulley ya silinda:

I = 1/2 (20)(0.2) ² = (10)(0.04) = 0.4 kg m ²

Mphamvu ya kinetic yozungulira ya pulley:

KE = 1/2 I ω ² = 1/2 (0.4) (4) ² = (0.2) (16) = 3.2 Joules

[irp]

3. Mpira wa A- 10 kg wokhala ndi utali wa 0.1 m umazungulira pa nthawi yokhazikika ya 10 rad/s. Kodi mphamvu ya kinetic ya mpirawo ndi yotani?

Zodziwika:

Kulemera kwa mpira (m) = 10 kg

Utali wa mpira (r) = 0.1 m

Liwiro la angular (ω) = 10 r ad/s

Kufunidwa: Mphamvu ya kayendedwe ka kayendedwe ka zinthu

Yankho:

Fomula ya mphindi ya inertia:

Ine = (2/5) mr ²

I = mphindi ya kulephera (kg m ² ), m = kulemera (kg), r = utali wozungulira (m)

Nthawi ya kusakhazikika kwa mpira:

I = (2/5)(10)(0.1) ² = (4)(0.01) = 0.04 kg m ²

Mphamvu ya kinetic yozungulira ya mpira:

K E = 1/2 I ω ² = 1/2 (0.04) (10) ² = (0.02) (100) = 2 Joules

[irp]

4. Tinthu tating'onoting'ono ta 0.5- kg timazungulira pa liwiro lokhazikika la 2 rad/s. Kodi mphamvu ya kayendedwe ka tinthu tating'onoting'ono ndi yotani ngati utali wa bwalo ndi 10 cm?

Zodziwika:

Kulemera kwa tinthu tating'onoting'ono (m) = 0.5 kg g

Utali wa mpira (r) = 10 cm = 10/100 = 0.1 m

Liwiro la angular (ω) = 2 rad/ s

Kufunidwa: Mphamvu ya kayendedwe ka kayendedwe ka zinthu

Yankho:

Nthawi ya inertia ya tinthu tating'onoting'ono:

Ine = mr ² = (0.5)(0.1) ² = (0.5)(0.01) = 0.005 kg m ²

Mphamvu ya kinetic yozungulira:

K E = 1/2 I ω ² = 1/2 (0.005) (2) ² = 1/2 (0.005) (4) = (0.005) (2) = 0.01 Joule

Werengani zambiri

1. Mphamvu F imagwiritsidwa ntchito pa chingwe chozunguliridwa ndi pulley ya silinda. Mphamvu yake ndi 2 N m ndipo nthawi ya inertia ndi 1 kg m ² , kodi kuthamanga kwa silinda ndi kotani ?

Zodziwika:

Mphamvu ( τ ) = 2 N m

Nthawi ya inertia (I) = 1 kg m ²

Kufunidwa: Kuthamanga kwa angular kwa silinda

Yankho:

Στ = I α

Στ = torque ya ukonde, I = mphindi ya inertia, α = kuthamanga kwa angular

Kuthamanga kwa silinda mozungulira:

α = Στ / I = 2 / 1 = 2 rad/s ²

[irp]

2. Mphamvu F imagwiritsidwa ntchito pa chingwe chozunguliridwa ndi pulley ya silinda. Kukula kwa mphamvu ndi 10 N, utali wa silinda ndi 0.2 m ndipo nthawi ya inertia ndi 1 kg m 2, Kodi kuthamanga kwa silinda ndi kotani ?

Zodziwika:

Mphamvu (F) = 10 N

Utali wa silinda (R) = 0.2 m

Nthawi ya inertia (I) = 1 kg m ²

Kufunidwa: Kuthamanga kwa silinda mozungulira.

Yankho:

τ = FR

τ = torque, F = mphamvu, R = radius ya silinda

Makokedwe:

τ = FR = (1 0 N) (0.2 m) = 2 N m

Στ = I α

Στ = torque ya ukonde, I = mphindi ya inertia, α = kuthamanga kwa angular

Kuthamanga kwa silinda mozungulira:

α = Στ / I = 2 / 1 = 2 rad/s ²

[irp]

3. Mphamvu F imagwiritsidwa ntchito pa chingwe chozunguliridwa ndi pulley ya silinda. Kukula kwa mphamvu ndi 10 N, utali wa silinda ndi 0.2 m ndipo kulemera kwa silinda ndi 20 kg m ^2, . Kodi kuthamanga kwa silinda ndi kotani?

Zodziwika:

Mphamvu (F) = 10 N

Utali wa silinda (R) = 0.2 m

Kulemera kwa silinda (M) = 20 kg

Kufunidwa: Kuthamanga kwa silinda ya angular

Yankho:

τ = FR = (1 0 N) (0.2 m) = 2 N m

Nthawi ya kutopa:

I = 1⁄2 MR ² = 1⁄2 (20)(0.2) ² = 1⁄2 (20)(0.04) = 0.4 kg m ²

Kuthamanga kwa silinda mozungulira:

α = Στ / I = 2 / 0.4 = 5 rad/s ²

[irp]

4. Chipika cha 1 kg chomwe chimapachikidwa pa chingwe chozunguliridwa ndi pulley ya silinda. Nthawi ya inertia ya pulley ndi 1 kg m ² ndipo utali wa pulley ndi 0.2 m. Kodi kuthamanga kwa angular kwa pulley ndi chiyani? Kuthamanga chifukwa cha mphamvu yokoka ndi 10 m/s ².

Zodziwika:

Nthawi ya kulephera kwa pulley (I) = 1 kg m ²

Kulemera kwa chipika (m) = 1 kg

Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s ²

Kulemera (w) = mg = (1 kg)(10 m/s ² ) = 10 kg m/s ² = 10 N

Utali wa pulley (R) = 0.2 m

Kufunidwa: Kuthamanga kwa ngodya

Yankho:

Makokedwe:

τ = FR = w R = (1 0 N) (0.2 m) = 2 N m

Nthawi ya kutopa:

I = 1 kg m ²

Kuthamanga kwa angular:

α = Στ / I = 2 / 1 = 2 rad/s ²

[irp]

5. Chipika cha 1 kg chomwe chimapachikidwa pa chingwe chozunguliridwa ndi pulley ya silinda. Kulemera kwa pulley ndi 20 kg ndipo utali wa pulley ndi 0,2 m. Kodi kuthamanga kwa angular kwa pulley ndi kuthamanga kwa free fall kwa chipikacho ndi chiyani? Kuthamanga chifukwa cha mphamvu yokoka ndi 10 m/s ².

Zodziwika:

Kulemera kwa pulley (M) = 20 kg

Utali wa pulley (R) = 0,2 m

Kulemera kwa chipika (m) = 1 kg

Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s ²

Kulemera (w) = mg = (1 kg)(10 m/s ² ) = 10 kg m/s ² = 10 N

Kufunidwa: kuthamanga kwa ngodya kwa pulley ndi kuthamanga kwa kugwa kwaulere kwa block.

Yankho:

Mphamvu ya mphamvu:

τ = FR = w R = (1 0 N) (0.2 m) = 2 N m

Nthawi ya inertia ya pulley ya silinda:

I = 1⁄2 MR ² = 1⁄2 (20)(0.2) ² = (10)(0.04) = 0.4 kg m ²

Kuthamanga kwa angular kwa pulley:

α = Στ / I = 2 / 0.4 = 5 rad/s ²

Kuthamanga kwa kugwa kwaulere kwa block:

a = R α = (0.2)(5) = 1 m/s ²

Werengani zambiri

Nthawi ya inertia ya tinthu tating'onoting'ono

1. Mpira wa magalamu 100 wolumikizidwa kumapeto kwa chingwe chokhala ndi kutalika kwa masentimita 30. Kodi nthawi ya kulephera kwa mpirawo ndi yotani pa mzere wozungulira wa AB? Musanyalanyaze kulemera kwa chingwe.

Zodziwika:

Mzere wozungulira pa AB

Mpira wolemera (m) = magalamu 100 = 100/1000 = 0.1 kg

Mtunda pakati pa mpira ndi mzere wozungulira (r) = 30 cm = 0.3 m

Kufunidwa: Nthawi ya kutopa kwa mpira (I)

Yankho:

Ine = mr ² = (0.1 kg)(0.3 m) ²

I = (0.1 kg)(0.09 ^m2 )

I = 0.009 kg m ²

[irp]

2. Mpira wa magalamu 100, m ₁ , ndi mpira wa magalamu 200, m ₂ , wolumikizidwa ndi ndodo yotalika masentimita 60. Kulemera kwa ndodo sikunyalanyazidwa. Mzere wozungulira uli pakati pa ndodo. Kodi nthawi ya kusakhazikika kwa mpira ndi yotani pa mzere wozungulira?

Zodziwika:

Kulemera kwa mpira 1 (m ₁ ) = magalamu 100 = 100/1000 = 0.1 kg

Mtunda wa mpira 1 ndi mzere wozungulira (r ₁ ) = 30 cm = 30/100 = 0.3 m

Kulemera kwa mpira (m ₂ ) = 200 magalamu = 200/1000 = 0.2 kg

Mtunda wa mpira 2 ndi mzere wozungulira (r ₂ ) = 30 cm = 30/100 = 0.3 m

Ankafuna: mphindi ya inertia ya mipira

Yankho:

Ine = m ₁ r ₁ ² + m ₂ r ₂ ²

I = (0.1 kg)( 0.3 m) ² + (0.2 kg)( 0.3 m) ²

I = (0.1 kg)( 0.09 m2 ⁾ + (0.2 kg)( 0.09 ^m2 )

I = 0.009 kg m ² + 0.018 kg m ²

I = 0.027 kg m ²

[irp]

3. Mpira wa magalamu 200, m ₁ ndi mpira wa magalamu 100, m _2, wolumikizidwa ndi ndodo yotalika masentimita 60. Musanyalanyaze kulemera kwa ndodo. Mzere wozungulira uli pa mpira m _2. Kodi nthawi ya kusakhazikika kwa mipira ndi chiyani? Musanyalanyaze kulemera kwa ndodo.

Zodziwika:

Kulemera kwa mpira 1 (m ₁ ) = 2 00 magalamu = 200/1000 = 0.2 kg

Mtunda pakati pa mpira 1 ndi mzere wozungulira (r ₁ ) = 60 cm = 60/100 = 0.6 m

Kulemera kwa mpira 2 (m ₂ ) = magalamu 100 = 100/1000 = 0.1 kg

Mtunda pakati pa mpira 2 ndi mzere wozungulira (r ₂ ) = 0 m

Akufuna: Nthawi ya kusasangalala kwa mipira

Yankho:

Ine = m ₁ r ₁ ² + m ₂ r ₂ ²

I = (0.2 kg)( 0,6 m) ² + (0.2 kg)(0 ) ²

I = (0.2 kg)( 0.36 ^m2 ) + 0

I = 0.072 kg m ²

[irp]

4. Kulemera kwa mpira uliwonse ndi magalamu 100, olumikizidwa ndi chingwe. Kutalika kwa chingwe ndi 60 cm ndipo m'lifupi mwa chingwe ndi 30 cm. Kodi nthawi ya kusagwira bwino kwa mpira ndi yotani pa mzere wozungulira? Musanyalanyaze kulemera kwa chingwe.

Zodziwika:

Kulemera kwa mpira = m ₁ = m ₂ = m ₃ = m ₄ = 1 00 magalamu = 100/1000 = 0.1 kg

Mtunda pakati pa mpira ndi mzere wozungulira (r ₁ ) = 30 cm = 30/100 = 0.3 m

Mtunda pakati pa mpira 2 ndi mzere wozungulira (r ₂ ) = 30 cm = 30/100 = 0.3 m

Mtunda pakati pa mpira 3 ndi mzere wozungulira (r ₃ ) = 30 cm = 30/100 = 0.3 m

Mtunda pakati pa mpira 4 ndi mzere wozungulira (r ₄ ) = 30 cm = 30/100 = 0.3 m

Kudziwika: Nthawi ya inertia

Yankho:

Ine = m₁ r₁² +m₂ r₂² +m₃ r₃² +m₄ r₄²

I = (0.1 kg)( 0.3 m) ² + (0.1 kg)( 0.3 m) ² + (0.1 kg)(0.3 m) 2 + (0.1 kg)(0.3 m) ² + (0.1 kg)(0.3 m) ²

I = (0.1 kg)( 0.09 m2 ⁾ + (0.1 kg)(0.09 m2 ⁾ + (0.1 kg)(0.09 m2 ⁾ + (0.1 kg)(0.09 ^m2 )

I = 0.036 kg m ²

[irp]

Nthawi ya inertia ya chinthu cholimba

5. Kodi ndodo yofanana yolemera makilogalamu awiri ndi kutalika kwa mamita awiri ndi chiyani? Mzere wozungulira uli pakati pa ndodo.

Zodziwika:

Kulemera kwa ndodo (M) = 2 kg

Kutalika kwa ndodo (L) = 2 m

Kufunidwa: Nthawi ya kusakhala ndi mphamvu

Yankho:

Fomula ya mphindi ya inertia pamene mzere wozungulira uli pakati pa ndodo yayitali yofanana:

Ine = (1/12) ML ²

I = (1/12) (2 kg)( 2 m) ²

I = (1/12) (2 kg)(4 ^m2 )

I = (1/12)(8 kg ^m2 )

I = 8/12 kg m ²

I = 2/3 kg m ²

[irp]

6. Kodi ndodo yofanana yolemera makilogalamu awiri ndi kutalika kwa mamita awiri imakhala ndi nthawi yotani? Mzere wozungulira uli kumapeto kwa ndodo.

Zodziwika:

Kulemera kwa ndodo (M) = 2 kg

Kutalika kwa ndodo yolimba (L) = 2 m

Kufunidwa: Nthawi ya kusakhala ndi mphamvu

Yankho:

Fomula ya mphindi ya inertia pamene mzere wozungulira uli kumapeto kwa ndodo:

Ine = (1/3) ML ²

I = (1/3) (2 kg)( 2 m) ²

I = (1/3) (2 kg)(4 ^m2 )

I = (1/3)(8 kg ^m2 )

I = 8/3 kg m ²

[irp]

7. Silinda yolimba ya makilogalamu 10 yokhala ndi utali wa mamita 0.1. Mzere wozungulira uli pakati pa silinda yolimba, yomwe yawonetsedwa pachithunzi chili pansipa. Kodi nthawi ya inertia ya silinda ndi yotani?

Zodziwika:

Kulemera kwa silinda yolimba (M) = 10 kg

Utali wa silinda (L) = 0.1 m

Kufunidwa: Nthawi ya inertia

Kufunidwa: Nthawi ya inertia

Yankho:

Fomula ya mphindi ya inertia pamene mzere wozungulira uli pakati pa silinda:

Ine = (1/2) MR ²

I = (1/2) (10 kg)(0.1 m) ²

I = (1/2) (10 kg)(0.01 ^m2 )

I = (1/2)(0.1 kg ^m2 )

I = 0.05 kg m ²

8. Chipilala chofanana cha makilogalamu 20 chokhala ndi kutalika kwa 0.1 m. Mzere wozungulira womwe uli pakati pa chipilalacho wawonetsedwa pachithunzi chili pansipa.

Zodziwika:

Kulemera kwa mbulunga (M) = 20 kg

Utali wa mlengalenga (L) = 0.1 m

Kufunidwa: mphindi ya inertia

Yankho:

Fomula ya mphindi ya inertia pamene mzere wozungulira uli pakati pa bwalo:

Ine = (2/5) MR ²

I = (2/5)(20 kg)(0.1 m) ²

I = (2/5)(20 kg)(0.01 ^m2 )

I = (2/5)(0.2 kg ^m2 )

I = 0.4/5 kg m ²

I = 0.08 kg m ²

[irp]

9. Mbale yopyapyala yolemera makilogalamu awiri yokhala ndi kutalika kwa mamita 0.5 ndi m'lifupi mwa mamita 0.2. Mzere wozungulira uli pakati pa mbale yopyapyala yomwe yawonetsedwa pachithunzi chili pansipa. Kodi nthawi ya kulephera kwa mzera ndi yotani?

Zodziwika:

Kulemera kwa mbale yozungulira (M) = 2 kg

Kutalika kwa mbale (a) = 0.5 m

M'lifupi mwa mbale (b) = 0.2 m

Kufunidwa: Nthawi ya Kusakhazikika

Yankho:

Fomula ya mphindi ya inertia pamene mzere wozungulira uli pakati pa mbale:

Ine = (1/12 ) M (a ² + b ² )

Ine = (1/12)(2)(0.5 ² + 0.2 ² )

Ine = (2/12)(0.25 + 0.04)

Ine = (1/6)(0.29)

I = 0.29/6 kg m ²

Werengani zambiri