Mavuto Othetsedwa mu Fiziki Yoyambira

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

Tchilolezo cha malo omasuka = ε_o

Pdera lochedwa =A

The mtunda pakati pa mbale = d

SE basi: Kutha kwa capacitor (C)

Yankho:

2. Capacitor yomwe ili ndi mphamvu yayikulu kwambiri kutengera chithunzi chomwe chili pansipa is...

Yankho:

Fomula ya capacitor yofanana ndi mbale:

Mphamvu ya ma capacitor:

Capacitor yomwe ili ndi mphamvu yayikulu kwambiriy ndi capacitor C_3.

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:

Wogwira ntchito 1:

Malo apamwamba = 2 A

Mtunda pakati pa mbale =d₁

Wogwira ntchito 2:

Malo apamwamba =A

Mtunda pakati pa mbale = 2 masiku₁

SE basi: Kuyerekeza mphamvu ya ma capacitor 1 ndi 2

Yankho:

5.

Dziwani kufananiza kwa mphamvu ya Ma capacitor a mbale yofanana I ndi II.

Yankho:

Kuyerekeza kwa mphamvu ya Ma capacitor a mbale yofanana I ndi II:

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

Ngati A₁ = ½ A₂ d₂ = 3 masiku₁ ndiye anatsimikiza chiŵerengero cha mphamvu za parallel-chojambulira mbale pakati pa chithunzi 2 ndi chithunzi 1.

Zodziwika:

Kaputeni wa mbale yofanana I:

A₁ = 1

d₁ = 1

Kapitoli wa mbale yofanana II:

A₂ = 2

d₂ = 3

SE basi: 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:

Tchiŵerengero cha mphamvu za parallel-mbale capacitor II ndi I:

Werengani zambiri

1. Sankhani fayilo ya mphamvu yamagetsi pamalo omwe ali pamtunda wa 1 cm kuchokera pa cholipiritsa 5.0 μC. Coulomb yosasintha (k) = 9 x 10⁹ Nm²C^-2, 1 μC = 10^-6 C.

Zodziwika:

Mtunda kuchokera pa cholipiritsa (r) = 1 cm = 1/100 m = 0.01 m = 10^-2 m

kulipiritsa (q) = 5.0 μC = 5.0 x 10^-6 C

Coulomb constant (k) = 9 x 10⁹ Nm²C^-2

Akufuna: Mphamvu yamagetsi (V)

Yankho:

Mphamvu yamagetsi:

Mphamvu yamagetsi ndi 4.5 × 10⁶ Volt

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:

kulipiritsa Q₁ = -5.0 μC = -5.0 x 10^-6 C

The mtunda ya mfundo A kuchokera Q₁ = 10 cm = 0.1 m = 10^-1 m

kulipiritsa Q₂ = 6.0 μC = 6.0 x 10^-6 C

Mtunda wa mfundo a kuchokera Q₂ = 10 cm = 0.1 m = 10^-1 m

Chokhazikika cha Coulomb (k) = 9 x 10⁹ Nm²C^-2

Akufuna: Mphamvu yamagetsi pa mfundo A

Yankho:

Mphamvu yamagetsi 1 :

Mphamvu yamagetsi 2 :

Mphamvu yamagetsi pa mfundo A :

V = V₂ - V₁

V = (54 - 45) x 10⁴

V = 9 x 10⁴

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:

kulipiritsa Q₁ = -5.0 μC = -5.0 x 10^-6 C

Mtunda wa mfundo A kuchokera Q₁ = 40 cm = 0.4 m = 4 x 10^-1 m

kulipiritsa Q₂ = 6.0 μC = 6.0 x 10^-6 C

Mtunda wa mfundo A kuchokera Q₂ = 50 cm = 0.5 m = 5 x 10^-1 m

Chokhazikika cha Coulomb (k) = 9 x 10⁹ Nm²C^-2

Akufuna: Mphamvu yamagetsi pamalopo A

Yankho:

Mphamvu yamagetsi 1 :

Mphamvu yamagetsi 2 :

Mphamvu yamagetsi pa mfundo A :

V = V₁ + V₂

V = (-11.25 + 10.8) x 10⁴

V = -0.45 x 10⁴

V = -4.5 x 10³

Mphamvu yamagetsi pamalo A ndi -4.5 x 10³ Volt

Werengani zambiri

1. Electron imathamanga kuchokera ku mpumulo kudzera mu kusiyana komwe kungatheke kwa 12 V. Kodi kusinthaku ndi kotani? mphamvu zamagetsi ya elekitironi?

Zodziwika:

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

Mphamvu yamagetsi = Voteji (V) = 12 Volt

SE basi: Kusintha kwa mphamvu yamagetsi ya elekitironi (ΔPE)

Yankho:

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

Chizindikiro cha minus chimasonyeza kuti mphamvu zomwe zingatheke zimachepa.

2. Mapepala awiri ofanana ali ndi mphamvu. Kusiyana pakati pa mapepala ndi 2 cm ndipo kukula kwa munda wamagetsi Pakati pa mbale pali 500 Volt/mita. Kodi kusintha kwa mphamvu ya proton kumachitika bwanji ikathamangitsidwa kuchokera ku mbale yomwe yakhala ndi mphamvu yabwino kupita ku mbale yomwe yakhala ndi mphamvu yoipa?

Zodziwika:

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

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

Kuchuluka kwa protoni = +1.60 x 10^-19 Coulomb

Akufuna: 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^-18 Joule

3. Ma charge awiri a nsonga amalekanitsidwa ndi mtunda wa masentimita 10. Ma charge pa nsonga A =+9 μC ndipo mtengo wake udzakhala pa mfundo B = -4 μC. k = 9 x 10⁹ Nm²C^-2, 1 μC = 10^-6 C. Kodi kusintha kwa mphamvu yamagetsi pa point B ndi kotani ngati ikulitsidwa kufika pa point A?

Zodziwika:

Ndalama A (q)₁) = +9 μC = +9 x 10^-6 C

kulipiritsa B (q₁) = -4 μC = -4 x 10^-6 C

k = 9 x 10⁹ Nm²C^-2

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

Akufuna: Kusintha kwa mphamvu yamagetsi (ΔEP)

Yankho:

Werengani zambiri

1. Yunifolomu munda wamagetsi E = 8000 N/C kudutsa m'dera lathyathyathya lalikulu A = 10 m². Sankhani fayilo ya kutuluka kwa magetsi.

Zodziwika:

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

Chigawo (A) = 10 m²

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

SE basi: Kutuluka kwa magetsi (Φ)

Yankho:

Fomula ya flux yamagetsi:

Φ = EA cos q

Φ = mphamvu yamagetsi (Nm²/C), E = malo amagetsi (N/C), A = dera (m²), q = ngodya pakati pa mzere wamagetsi ndi mzere wamba.

Kutuluka kwa magetsi:

Φ = EA cos q = (8000)(10)(chifukwa 0) = (8000)(10)(1)) = 80,000 = 8 X XUMUM⁴ Nm²/C

2. Mphamvu yamagetsi yofanana E = 5000 N/C yodutsa m'dera lathyathyathya lalikulu A = 2 m². Dziwani kuchuluka kwa magetsi.

Zodziwika:

Malo amagetsi (E) = 5000 N/C

Chigawo (A) = 2 m²

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

Akufuna: Kutuluka kwa magetsi (Φ)

Yankho:

Kutuluka kwa magetsi:

Φ = EA cos q = (5000)(2)(chifukwa 60) = (5000)(2)(0.5)= = 5000 = 5 X XUMUM³ Nm²/C

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

mtengo wamagetsi (Q) = 10 μC = 10 x 10^-6 C

Akufuna: Kutuluka kwa magetsi (Φ)

Yankho:

Malo amagetsi:

E = kq/r²

E = (9 x 10⁹ Nm²/C²)(10 × 10^-6 C) / 0.5²

E = (90 x 10³) / 0,25

E = 360 x 10³

E = 3.60 x 10⁵ N / C

Malo ozungulira:

A=4 π r² = 4 (3.14)(0.5)² = (12.56)(0.25) = 3.14 m²

Kutuluka kwa magetsi:

Mizere yamagetsi imazungulira molunjika kuderali, kotero kuti ngodya pakati pa njira yamagetsi ndi mzere wokokedwa mopingasa kuderali, ndi 0^o.

Φ = EA cos q

Φ = (3.60 × 10⁵)(3.14)(chifukwa 0)

Φ = (11.304 x 10⁵) (1)

Φ = 11.304 x 10⁵

Φ = 1.13 x 10⁶ Nm²/C

Werengani zambiri

1. Werengerani kukula ndi komwe magetsi amayendera pamalo A omwe ali pamtunda wa 5 cm kuchokera pamalo pomwe mtengo uyenera kuperekedwa. Q = + 10 μC. k = 9 x 10⁹ Nm²C^-2, 1 μC = 10^-6 C)

Zodziwika:

mtengo wamagetsi (Q) = + 10 μC = + 10 X XUMUM^-6 C

The mtunda pakati pa mfundo A ndi mfundo yolipirira Q (r)_A) = 5 cm = 0.05 m = 5 x 10^-2 m

k = 9 x 10⁹ Nm²C^-2

SE basi: Kukula ndi njira ya munda wamagetsi panthawi 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.

2. Werengani kukula ndi komwe magetsi akuyendera pa mfundo P yomwe ili pa 10 cm kuchokera pa mfundo yomwe yaperekedwa Q = -20 μC. k = 9 x 10⁹ Nm²C^-2, 1 μC = 10^-6 C.

Zodziwika:

Chaji yamagetsi (q) = -20 μC = -20 X XUMUM^-6 C

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

k = 9 x 10⁹ Nm²C^-2

SE basi: Kukula ndi komwe magetsi akuyendera pamalopo P

Yankho:

Kuwongolera kwa magetsi pamalo A:

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

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:

Ndalama A (q)_A) = -2 μC = -2 X XUMUM^-6 C

Cholipiritsa B (q)_B) = +4 μC = +4 X XUMUM^-6 C

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

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

Akufuna: Kukula ndi komwe magetsi ali pa mfundo P.

Yankho:

Chaji A ndi yoipa kotero kuti njira ya malo olumikizira magetsi ikupita ku Q_A (Kumanzere).

Chaji B ndi yabwino kotero kuti komwe kuli malo olumikizira magetsi kuli kutali ndi Q_B (Kumanzere).

Mphamvu yonse yamagetsi pa mfundo A:

E = E_A +E_B

E = (4.5 x 10⁵) + (9 x 10⁵)

E = 13.5 x 10⁵ N / C

Kulunjika kwa munda wamagetsi kumayang'ana ku Q_A (Kumanzere).

4. Kukula kwa mphamvu yamagetsi ndi zero pa…

Chaji A ndi yabwino ndipo chaji B ndi yabwino kotero kuti kukula kwa mphamvu yamagetsi kuli pa zero pa mfundo P, pakati pa milandu yonse iwiri.

Zodziwika:

kulipiritsa A (q)_A) = +20 μC = +20 x 10^-6 C

kulipiritsa B (q)_B) = +40 μC = +40 x 10^-6 C

k = 9 x 10⁹ Nm²C^-2

Mtunda pakati pa zolipiritsa A ndi mlandu 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

Akufuna: 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.

5Kutengera chithunzi chomwe chili pansipa, wApa ndiye mfundo P kotero kuti munda wamagetsi pa mfundo P ndi zero? (k = 9 x 10⁹ Nm²C^-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:

Q₁ = +9 μC = +9 x 10^-6 C

Q₂ = -4 μC = -4 x 10^-6 C

k = 9 x 10⁹ Nm²C^-2

Mtunda pakati pa chaji 1 ndi chaji 2 = 3 cm

Mtunda pakati pa Q₁ ndi mfundo P (r_1P) = a

Mtunda pakati pa Q₂ ndi mfundo P (r_2P) = 3 + a

Akufuna: malo a mfundo P kotero kuti mphamvu yamagetsi pamalo P ndi zero

Yankho:

PPoint P ili kumanzere kwa Q₁.

Mphamvu yamagetsi yopangidwa ndi Q₁ pa mfundo P:

Ndalama yoyeserera ndi yabwino ndipo Q₁ ndi yabwino kotero kuti njira ya magetsi ili kumanzere.

Mphamvu yamagetsi yopangidwa ndi Q₂ pa mfundo P:

Ndalama yoyeserera ndi yabwino ndipo Q₂ ndi yoipa kotero kuti njira 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 Q₂ ndi mfundo P (r_2P) = 3 + a = 3 – 1.8 = 1.2 cm.

Point P ili kumanja kwa Q pa 1.2 cm₁.

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:

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

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

k = 9 x 10⁹ Nm²C^-2

The mtunda pakati pa cholipiritsa A ndi B (r_AB) = 10 cm = 0.1 m

anafuna : Kukula kwa mphamvu yamagetsi

Yankho:

Fomula ya Lamulo la Coulomb :

Kukula kwa mphamvu yamagetsi:

2. Tinthu tating'onoting'ono tiwiri tomwe timayatsidwa monga momwe tawonetsera pachithunzi pansipa._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

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

k = 9 x 10⁹ Nm²C^-2

Mtunda pakati pa zolipiritsa P ndi Q (r_PQ) = 12 cm = 0.12 m = 12 x 10^-2 m

Akufuna: Tmphamvu yamagetsi

Yankho:

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:

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

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

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

k = 9 x 10⁹ Nm²C^-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

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

Yankho:

Mphamvu yonse pa tinthu B ndi chiwerengero cha mphamvu ya vekitala F_BA yogwiritsidwa ntchito pa tinthu B ndi tinthu A ndi mphamvu F_BC yogwiritsidwa ntchito pa tinthu B ndi tinthu C.

Mphamvu F_BA yogwiritsidwa ntchito pa tinthu B ndi tinthu A:

 

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

Mphamvu F_BC yogwiritsidwa 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).

4. +Q₁ = 10 μC, +Q₂ = 50 μC ndi Q₃ 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:

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

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

Mtunda pakati pa zolipiritsa 1 ndi 2 (r₁₂) = 2 cm = 0.02 m = 2 x 10^-2 m

Mtunda pakati pa chaji 2 ndi chaji 3 (r₂₃) = 6 cm = 0.06 m = 6 x 10^-2 m

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

anafuna : cholipiritsa 3 (q₃)

Yankho:

Mphamvu yonse pa tinthu 2 ndi vekitala kuchuluka kwa mphamvu F₂₁ yogwiritsidwa ntchito pa tinthu 2 ndi tinthu 1 ndi mphamvu F₂₃ yogwiritsidwa ntchito pa tinthu 2 ndi tinthu 3.

Mphamvu F₂₁ yogwiritsidwa 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 mphindi ya inertia of 2 makilogalamu m² imazungulira pa 1 rad/s. Kodi mphamvu ya angular cha chinthucho?

Zodziwika:

Mphindi ya inertia (I) = 2 kg m²

Liwiro la ngodya (ω) = 1 rad/s

Akufuna: Angular liwiro (L)

Yankho:

Fomula ya angular momentum:

L = Ine ω

L= mphamvu ya angular (kg m²/s), Ine = mphindi ya inertia (kg m²), ω = liwiro la angular (rad/s)

Mphamvu ya angular:

L = Ine ω = (2)(1) = 2 kg m²/s

2. 2-kg pulley ya silinda yokhala ndi utali wozungulira wa 0.1 mamita imazungulira pa liwiro lokhazikika la angular la 2 rad/s. Kodi angular momentum ya pulley ndi yotani?

Zodziwika:

Misa ya pulley (m) = 2 kg

Utali wozungulira wa Pulley (r) = 0.1 m

Liwiro la ngodya (ω) = 2 rmalonda/magawo

Akufuna: Angular liwiro

Yankho:

Fomula ya mphindi ya inertia ya silinda yolimba:

I = 1/2 mr²

I = mphindi ya inertia (kg m²), m = Unyinji (kg), r = radius (m)

Nthawi ya kutopa:

Ine = 1/2 (2)(0.1)² = (1)(0.01) = 0.01 kg m²

Liwiro la angular:

L = Ine ω = (0.01)(2) = 0.02 kg m²/s

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

Zodziwika:

Misa ya mpira (m) = 2 kg

Ulalo wa mpira (r) = 0.2 m

Liwiro la ngodya (ω) = 4 rad/s

Akufuna: Angular liwiro

Yankho:

Fomula ya mphindi ya inertia ya malo ofanana:

I = (2/5) Bambo.²

Ine = mphindit ya inertia (kg m²), m = kulemera (kg), r = radius (m)

Nthawi ya inertia ya malo ofanana:

Ine = (2/5)(2)(0.2)² = (4/5)(0.04) = 0.032 kg m²

Mphamvu ya angular ya mlengalenga:

L = Ine ω = (0.032)(4) = 0.128 kg m²/s

4. A Kilogalamu imodzi tinthu timazungulira pa liwiro lokhazikika la angular 2 rad/s. Kodi liwiro la angular ndi lotani ngati radius ya bwalo ndi 1?0 masentimita.

Zodziwika:

Misa cha chinthu (m) = 1 kg

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

Liwiro la angular (ω) = 2 rad/s

Akufuna: Angular liwiro

Yankho:

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

I = Bambo.² = (1)(0.1)² = (1)(0.01) = 0.01 kg m²

Mphamvu ya angular:

L = I ω = (0.01)(2) = 0.02 kg m²/s

Werengani zambiri

1. Chinthu chili ndi mphindi ya inertia ya 1 kg m² imazungulira pa liwiro lokhazikika la angular 2 rad/s. Kodi mphamvu ya kayendedwe ka kayendedwe ka zinthu cha chinthucho?

Zodziwika:

Nthawi ya inertia (I) = 1 kg m²

The mathamangitsidwe (ω) = 2 rad / s

SE basi: Mphamvu ya kinetic yozungulira (KE)

Yankho:

Fomula ya mphamvu ya kinetic yozungulira:

KE = 1/2 I ω²

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 ω² = 1/2 (1)(2)² = 1/2 (1)(4) = 2 Joule

2. A 20-kg pulley ya silinda ndi radius ya 0.2 m imazungulira pa liwiro lokhazikika la 4 rad/s. Kodi mphamvu ya kinetic ya pulley yozungulira ndi yotani?

Zodziwika:

Misa ya pulley ya silinda (m) = 20 kg

Utali wa silinda (r) = 0.2 m

Liwiro la angular (ω) = 4 rad/s

Akufuna: Kodi mphamvu ya kinetic yozungulira ndi chiyani?

Yankho;

Fomula ya mphindi ya inertia ya silinda:

I = 1/2 mr²

I = mphindi ya kutopa (makilogalamu m²), m = kulemera (kg), r = radius (mita)

Nthawi ya inertia ya pulley ya silinda:

Ine = 1/2 (20)(0.2)² = (10)(0.04) = 0.4 kg m²

Mphamvu ya kinetic yozungulira ya pulley:

KE = 1/2 I ω² = 1/2 (0.4)(4)² = (0.2)(16) = 3.2 Joule

3. A-10 makilogalamu mpira wokhala ndi utali wa 0.1 mamita imazungulira pa liwiro losasintha la 10 rad/s. Kodi mphamvu ya kinetic ya mpira ndi chiyani?

Zodziwika:

Misa ya mpira (m) = 10 kg

Ulalo wa mpira (r) = 0.1 m

Angular velocity (ω) = 10 rmalonda/magawo

Akufuna: Mphamvu ya kinetic yozungulira

Yankho:

Fomula ya mphindi ya inertia:

I = (2/5) Bambo.²

I = mphindi ya inertia (kg m²), m = kulemera (kg), r = radius (m)

Nthawi ya kusakhazikika kwa mpira:

Ine = (2/5)(10)(0.1)² = (4)(0.01) = 0.04 kg m²

Mphamvu ya kinetic yozungulira ya mpira:

KE = 1/2 I ω² = 1/2 (0.04)(10)² = (0.02)(100) = 2 Joule

4. A 0.5-tinthu ta kg timazungulira pa liwiro lokhazikika la angular 2 rad/s. Kodi mphamvu ya kinetic yozungulira ya tinthu tating'onoting'ono ndi yotani ngati utali wozungulira wa bwalo uli 10 masentimita.

Zodziwika:

Misa ya tinthu tating'onoting'ono (m) = 0.5 kg

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

Liwiro la angular (ω) = 2 rad/s

Akufuna: Mphamvu ya kinetic yozungulira

Yankho:

Nthawi ya inertia ya tinthu tating'onoting'ono:

I = Bambo.² = (0.5)(0.1)² = (0.5)(0.01) = 0.005 kg m²

Mphamvu ya kinetic yozungulira:

KE = 1/2 I ω² = 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. makokedwe is 2 N m ndi mphindi ya inertia is 1 makilogalamu m², ndi chiyani kuthamanga kwa angular ya silinda.

Zodziwika:

Torque (τ) = 2 N m

Nthawi ya inertia (I) = 1 kg m²

SE basi: Kuthamanga kwa angular kwa silinda

Yankho:

Στ = Ine α

Στ = mphamvu yokwanira, I = mphindi ya inertia, α = kuthamanga kwa angular

Kuthamanga kwa silinda mozungulira:

α = Στ / I = 2 / 1 = 2 rad/s²

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 makilogalamu m2, WKodi kuthamanga kwa silinda ndi kotani?

Zodziwika:

Mphamvu (F) = 10 N

Utali wa silinda (R) = 0.2 m

Nthawi ya inertia (I) = 1 kg m²

SE basi: Kuthamanga kwa silinda.

Yankho:

τ = FR

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

Makokedwe:

τ = FR = (10 N(0.2 m) = 2 N m

Στ = Ine α

Στ = mphamvu yokwanira, I = mphindi ya inertia, α = kuthamanga kwa angular

Kuthamanga kwa silinda mozungulira:

α = Στ / I = 2 / 1 = 2 rad/s²

3. Mphamvu F imagwiritsidwa ntchito pa chingwe chozunguliridwa ndi pulley ya silinda. Mphamvu yake ndi 10 N, utali wa silinda ndi 0.2 m ndipo kulemera kwa silinda ndi 20 kg m^2,. Wchipewa ndi liwiro la angular la silinda.

Zodziwika:

Mphamvu (F) = 10 N

Utali wa silinda (R) = 0.2 m

Kulemera kwa silinda (M) = 20 kg

Akufuna: Kuthamanga kwa silinda kozungulira

Yankho:

τ = FR = (10 N(0.2 m) = 2 N m

Nthawi ya kutopa:

Ine = 1⁄2 MR² = 1⁄2 (20)(0.2)² = 1⁄2 (20)(0.04) = 0.4 kg m²

Kuthamanga kwa silinda mozungulira:

α = Στ / I = 2 / 0.4 = 5 rad/s²

4. Chipika cha 1 kg chomwe chapachikidwa pa chingwe chozungulira pulley ya silinda. Nthawi ya kulephera kwa pulley ndi 1 kg m² ndipo utali wa pulley ndi 0.2 m. Kodi kuthamanga kwa angular kwa pulley ndi kotani? Kuthamanga chifukwa cha mphamvu yokoka ndi 10 m/s².

Zodziwika:

Nthawi ya kulephera kwa pulley (I) = 1 kg m²

Misa ya chipika (m) = 1 kg

Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s²

Kunenepa (w) = mg = (1 kg)(10 m/s²) = 10 kg m/s² = 10 n

Utali wa pulley (R) = 0.2 m

Akufuna: Kuthamanga kwa ngodya

Yankho:

Makokedwe:

τ = FR = w R = (10 N(0.2 m) = 2 N m

Nthawi ya kutopa:

I = 1 kg m²

Kuthamanga kwa angular:

α = Στ / I = 2 / 1 = 2 rad/s²

5. Chipika cha 1 kg chomwe chimapachikidwa pa chingwe chozungulira pulley ya silinda. Kulemera kwa pulley ndi 20 kg ndipo utali wa pulley ndi 0,2 m. Kodi kuthamanga kwa angular kwa pulley ndi chiyani? kugwa kwaulere Kuthamanga kwa chipikacho. Kuthamanga chifukwa cha mphamvu yokoka ndi 10 m/s².

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/s²

Kulemera (w) = mg = (1 kg)(10 m/s²) = 10 kg m/s² = 10 n

Akufuna: kuthamanga kwa angular kwa pulley ndi kuthamanga kwa free fall kwa block.

Yankho:

Mphamvu ya mphamvu:

τ = FR = w R = (10 N(0.2 m) = 2 N m

Nthawi ya inertia ya pulley ya silinda:

Ine = 1⁄2 MR² = 1⁄2 (20)(0.2)² = (10)(0.04) = 0.4 kg m²

Kuthamanga kwa angular kwa pulley:

α = Στ / I = 2 / 0.4 = 5 rad / s²

Kuthamanga kwa kugwa kwaulere kwa block:

a = R α = (0.2)(5) = 1 m/s²

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

Misa mpira (m) = magalamu 100 = 100/1000 = 0.1 kg

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

SE basi: 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 m²

2. Mpira wa magalamu 100, m₁, ndi mpira wa magalamu 200, m₂, yolumikizidwa ndi ndodo yotalika masentimita 60. Kulemera kwa ndodo sikunyalanyazidwa. Mzere wozungulira uli pakati pa ndodo. Kodi nthawi ya inertia ya mpira ndi yotani pa mzere wozungulira?

Zodziwika:

Kulemera kwa mpira 1 (m₁) = Magalamu 100 = 100/1000 = 0.1 kg

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

Uzito wa mpira (m₂) = magalamu 200 = 200/1000 = 0.2 kg

The mtunda ya mpira 2 ndi mzere wozungulira (r)₂) = 30 cm = 30/100 = 0.3 m

Akufuna: mphindi ya inertia ya mipira

Yankho:

Ine = m₁ r₁² +m₂ r₂²

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

I = (0.1 kg)(0.09 mamita²) + (0.2 kg)(0.09 mamita²)

I = 0.009 kg m² + 0.018 kg m²

I = 0.027 kg m²

3. Mpira wa magalamu 200, m₁ ndi mpira wa gramu 100, m_2, yolumikizidwa ndi ndodo yotalika masentimita 60. Musanyalanyaze kulemera kwa ndodoyo. Mzere wozungulira uli pa mpira m₂Kodi nthawi ya kusagwira bwino ntchito kwa mipira ndi yotani? Musanyalanyaze kulemera kwa ndodo.

Zodziwika:

Kulemera kwa mpira 1 (m₁= = 2Magalamu 00 = 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 (m₂) = magalamu 100 = 100/1000 = 0.1 kg

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

Akufuna: Nthawi ya inertia ya mipira

Yankho:

Ine = m₁ r₁² +m₂ r₂²

I = (0.2 kg)(0,6 m)² + (0.2 kg)(0)²

I = (0.2 kg)(0.36 mamita²) + 0

I = 0.072 kg m²

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:

Unyinji wa mpira = m₁ = m₂ = m₃ = m₄ = 1Magalamu 00 = 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

Zodziwika: Mphindi 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

I = (0.1 kg)(0.09 mamita²) + (0.1 kg)(0.09 m²) + (0.1 kg)(0.09 m²) + (0.1 kg)(0.09 m²)

I = 0.036 kg m²

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

SE basi: Mphindi ya inertia

Yankho:

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

Ine = (1/12) ML²

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 m²

I = 2/3 kg m²

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

SE basi: Mphindi ya inertia

Yankho:

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

Ine = (1/3) ML²

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 m²

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

SE basi: Nthawi ya inertia

SE basi: Nthawi ya inertia

Yankho:

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

Ine = (1/2) MR²

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 m²

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

SE basi: mphindi ya kutopa

Yankho:

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

Ine = (2/5) MR²

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 m²

I = 0.08 kg m²

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

Akufuna: Mphindi ya inertia

Yankho:

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

Ine = (1/12M (a)² + b²)

Ine = (1/12)(2)(0.5² + 0.2²)

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

Ine = (1/6)(0.29)

I = 0.29/6 kg m²

Werengani zambiri