Ma capacitor eparallel-plate - matambudziko nemhinduro

1. A capacitor yeplate yakafanana ane kutanga kugona C, mvumo yenzvimbo yakasununguka is εo, nzvimbo yeplate is A, daro riri pakati pemaplate is d. Kanae nzvimbo yeplate yakawedzera ka4, daro riri pakati peplate inova 2d uye mvumo yenzvimbo yakasununguka is 5εo, simba rekupedzisira re capacitor yeparallel-plate chii.

Zvinozivikanwa:

Kugona kwe capacitor = C

Kubvumidzwa kwenzvimbo yakasununguka = ​​ε o

Nzvimbo yekunonoka P = A

Daro riri pakati pemaplate = d

Zvinodiwa: Kugona kwe capacitor (C)

Solution:

Ma capacitor eparallel-plate - matambudziko nemhinduro 1

[irp]

2. Capacitor ine simba guru zvichibva pamufananidzo uri pazasi ndeiyi …

Ma capacitor eparallel-plate - matambudziko nemhinduro 2

Solution:

Fomura ye capacitor yeplate yakafanana:

Ma capacitor eparallel-plate - matambudziko nemhinduro 3

Kugona kwema capacitor:

Ma capacitor eparallel-plate - matambudziko nemhinduro 4

Capacitor ine simba guru re y i capacitor C3.

[irp]

3.

Funga nezvezvinhu zvinotevera!
(1) Dielectric constant
(2) The musiyano ungangoitika pakati pemaplate
(3) Ndiro thick
(4) Nzvimbo yepamusoro yeplate
(5) Daro riri pakati pemaplate
(6) Huwandu hwe electric charge
Zvinhu zvinokanganisa kugona kwemaplate akafanana ma capacitor ari…

Solution:

(1), (4) uye (5)

4. Kuenzanisa kugona kwe capacitor 1 ne 2 ndiko…

Ma capacitor eparallel-plate - matambudziko nemhinduro 5Zvinozivikanwa:

Muchina we1:

Nzvimbo yepamusoro = 2A

Daro riri pakati pemaplate = d 1

Muchina we2:

Nzvimbo yepamusoro = A

Daro riri pakati pemaplate = 2 d 1

Zvinodiwa: Kuenzanisa kugona kwema capacitor 1 ne2

Solution:

Ma capacitor eparallel-plate - matambudziko nemhinduro 6

[irp]

5.

Ma capacitor eparallel-plate - matambudziko nemhinduro 15

Sarudza kuenzanisa kugona kweParallel-plate capacitor I neII.

Solution:

Ma capacitor eparallel-plate - matambudziko nemhinduro 16

Kuenzanisa kugona kweParallel -plate capacitors I neII:

Ma capacitor eparallel-plate - matambudziko nemhinduro 17

[irp]

6. Ma capacitor maviri akafanana anoratidzwa mumufananidzo uri pazasi.

Kana A 1 = ½ A 2 uye d 2 = 3 d 1 , sarudza chiyero chesimba re capacitor yeplate yakafanana pakati pemufananidzo 2 nemufananidzo 1.

Ma capacitor eparallel-plate - matambudziko nemhinduro 18

Zvinozivikanwa:

Capacitor yeplate yakafanana I:

A 1 = 1

d 1 = 1

Capacitor yeplate yakafanana II:

A 2 = 2

d 2 = 3

Zvinodiwa: chiyero chesimba re capacitor yeplate yakafanana pakati pemufananidzo 2 nemufananidzo 1

Solution:

Capacitor yeplate yakafanana I:

Ma capacitor eparallel-plate - matambudziko nemhinduro 19

Capacitor yeplate yakafanana II:

Chiyero chesimba re capacitors dzeparallel-plate II neI:

Ma capacitor eparallel-plate - matambudziko nemhinduro 20

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Matambudziko emagetsi - matambudziko nemhinduro

1. Tsvaga simba remagetsi panzvimbo iri pa1 cm kubva pakuchaja 5.0 μ C. Coulomb constant (k) = 9 x 10 9 Nm 2 C −2 , 1 μC = 10 −6 C.

Zvinozivikanwa:

Nhambwe kubva pakuchaja (r) = 1 cm = 1/100 m = 0.01 m = 10 -2 m

Chaji (q) = 5.0 μ C = 5.0 x 10 -6 C

Chimiro cheCoulomb (k) = 9 x 10 9 Nm 2 C −2

Zvinodiwa: Simba remagetsi (V)

Solution:

Kugona kwemagetsi:

Matambudziko emagetsi nemhinduro 1

Simba remagetsi i4.5 x 10 6 Volts

[irp]

2. murandu Q1 = 5.0 μC uye kuchaja Q2 = 6.0 μC. Nguva dzose yaCoulomb (k) = 9 x 109 Nm2C-2, 1 μC = 10-6 C. Poindi A iri pakati pemhosva. Sarudza simba remagetsi panzvimbo A.

Matambudziko emagetsi nemhinduro 2

Zvinozivikanwa:

Chaji Q 1 = -5.0 μ C = -5.0 x 10 -6 C

Kureba kwenzvimbo A kubva paQ 1 = 10 cm = 0.1 m = 10 -1 m

Chaji Q 2 = 6.0 μ C = 6.0 x 10 -6 C

Kureba kwenzvimbo a kubva kuQ 2 = 10 cm = 0.1 m = 10 -1 m

Nguva dzose yaCoulomb (k) = 9 x 10 9 Nm 2 C −2

Zvinodiwa: Simba remagetsi panzvimbo A

Solution:

Simba remagetsi 1 :

Matambudziko emagetsi nemhinduro 3

Simba remagetsi 2 :

Matambudziko emagetsi nemhinduro 4

Simba remagetsi panzvimbo A :

V = V 2 – V 1

V = (54 - 45) x 10 4

V = 9 x 10 4

[irp]

3. murandu q1 = 5.0 μC uye kuchaja q2 = 6.0 μC. Nguva dzose yaCoulomb (k) = 9 x 109 Nm2C-2, 1 μC = 10-6 C. Sarudza simba remagetsi panzvimbo A.

Matambudziko emagetsi nemhinduro 5Zvinozivikanwa:

Chaji Q 1 = -5.0 μ C = -5.0 x 10 -6 C

Kureba kwenzvimbo A kubva kuQ 1 = 40 cm = 0.4 m = 4 x 10 -1 m

Chaji Q 2 = 6.0 μ C = 6.0 x 10 -6 C

Kureba kwenzvimbo A kubva kuQ 2 = 50 cm = 0.5 m = 5 x 10 -1 m

Nguva dzose yaCoulomb (k) = 9 x 10 9 Nm 2 C −2

Zvinodiwa: Simba remagetsi panzvimbo A

Solution:

Simba remagetsi 1 :

Matambudziko emagetsi nemhinduro 6

Simba remagetsi 2 :

Matambudziko emagetsi nemhinduro 7

Simba remagetsi panzvimbo 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

Simba remagetsi panzvimbo A i -4.5 x 10 3 Volts

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Simba remagetsi rinogona kushandiswa - matambudziko nemhinduro

1. Erekitironi inokurumidziswa kubva pakuzorora kuburikidza nemusiyano we potential we 12 V. Chii chinonzi shanduko mu electric potential energy ye erekitironi?

Simba remagetsi rinogona kushandiswa - matambudziko nemhinduro 2Zvinozivikanwa:

Mutengo we erekitironi (e) = -1.60 x 10 -19 Coulomb

Simba remagetsi = voltage (V) = 12 Volts

Zvinodiwa: Kuchinja kwesimba remagetsi remaerekitironi (ΔPE)

Solution:

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

Chiratidzo chekusiya chinoratidza kuti simba rinogona kuderera.

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2. Maplate maviri akafanana anochajwa. Kupatsanurwa kwemaplate i2 cm uye hukuru hwesimba remagetsi pakati peplate i500 Volt/meter. Chii chinochinja simba ringangoitika reproton kana rakurumidza kubva paplate ine chaji yakanaka kuenda paplate ine chaji yakaipa.

Simba remagetsi rinogona kushandiswa - matambudziko nemhinduro 2Zvinozivikanwa:

Hukuru hwesimba remagetsi pakati pemaplate (E) = 500 Volt/mita

Kureba pakati pemaplate (s) = 2 cm = 0,02 m

Kuchaja paproton = +1.60 x 10 -19 Coulombs

Zvinodiwa: Kuchinja kwesimba remagetsi (ΔPE)

Solution:

Kugona kwemagetsi:

V = E s

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

V = 10 Volt

Kuchinja kwesimba remagetsi:

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. Mapoinzi maviri anopatsanurwa nedaro re 10 cm. Chaja papoinzi A = +9 μC uye chaja papoinzi B = -4 μC. k = 9 x 10 9 Nm 2 C −2 , 1 μC = 10 −6 C. Chii chinochinja musimba remagetsi rinogoneka pakuchaja papoinzi B kana rikakurumidza kusvika papoinzi A?

Simba remagetsi rinogona kushandiswa - matambudziko nemhinduro 3

Zvinozivikanwa:

Chaja A (q 1 ) = +9 μC = +9 x 10 −6 C

Chaja B (q 1 ) = -4 μC = -4 x 10 −6 C

k = 9 x 10 9 Nm 2 C −2

Nhambwe iri pakati pemari A neB (r) = 10 cm = 0.1 m = 10 -1 m

Zvinodiwa: Kuchinja kwesimba remagetsi (ΔEP)

Solution:

Simba remagetsi rinogona kushandiswa - matambudziko nemhinduro 4

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Kuyerera kwemagetsi - matambudziko nemhinduro

1. Munda wemagetsi wakaenzana E = 8000 N/C unopfuura nepakati penzvimbo yakati sandara ine sikweya A = 10 m2 . Tsvaga kuti magetsi ari kufamba sei.

Kuyerera kwemagetsi munzvimbo nenzvimbo dzakavharwa - matambudziko nemhinduro 1Zvinozivikanwa:

Hukuru hwesimba remagetsi (E) = 8000 N/C

Nzvimbo (A) = 10 m 2

θ = 0 o (kona iri pakati pegwara remagetsi nemutsetse wakadhirowewa wakatarisana nenzvimbo yacho)

Zvinodiwa: Kuyerera kwemagetsi ( Φ)

Solution:

Fomura yemagetsi ekufambisa:

Φ = EA cos q

Φ = flux yemagetsi ( Nm 2 /C) , E = munda wemagetsi (N/C), A = nzvimbo (m 2 ), q = kona iri pakati pemutsetse wemagetsi nemutsetse wakajairika.

Kuyerera kwemagetsi:

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

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2. Munda wemagetsi wakaenzana E = 5000 N/C unopfuura nepakati penzvimbo yakati sandara ine sikweya A = 2 m 2. Tsvaga kuti magetsi ari kufamba sei.

Kuyerera kwemagetsi munzvimbo nenzvimbo dzakavharwa - matambudziko nemhinduro 2Zvinozivikanwa:

Munda wemagetsi (E) = 5000 N/C

Nzvimbo (A) = 2 m 2

θ = 60 o (kona iri pakati pegwara remagetsi nemutsetse wakadhirowewa wakatarisana nenzvimbo yacho)

Zvinodiwa: Kuyerera kwemagetsi ( Φ)

Solution:

Kuyerera kwemagetsi:

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

[irp]

3. Bhora rakasimba rine 0.5 metres radius rine 10 μC electric charge pakati paro. Tsvaga kuti flux yemagetsi inopfuura nepabhora rakasimba.

Kuyerera kwemagetsi munzvimbo nenzvimbo dzakavharwa - matambudziko nemhinduro 3Zvinozivikanwa:

Nharaunda yebhora (r) = 0.5 m

Chaja yemagetsi (Q) = 10 μC = 10 x 10 -6 C

Zvinodiwa: Kuyerera kwemagetsi ( Φ)

Solution:

Munda wemagetsi:

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

Nzvimbo yepamusoro:

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

Kuyerera kwemagetsi:

Mitsetse yemagetsi yakatarisana nenzvimbo, zvekuti kona iri pakati pegwara remagetsi nemutsetse wakadhonzwa wakatarisana nenzvimbo, i0 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

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Hukuru uye divi reminda yemagetsi - matambudziko nemhinduro

1. Verenga hukuru negwara remagetsi panzvimbo A iri pa5 cm kubva papoindi yekuchaja Q = +10 μC. k = 9 x 10 9 Nm 2 C −2 , 1 μC = 10 −6 C)

Zvinozivikanwa:

Chaja yemagetsi (Q) = +10 μC = +10 x 10 -6 C

Daro riri pakati penzvimbo A nechaji yepoindi Q (r A ) = 5 cm = 0.05 m = 5 x 10 -2 m

k = 9 x 10 9 Nm 2 C −2

Zvinodiwa: Hukuru uye kwakanangana nemagetsi panzvimbo A

Solution:

Hukuru uye divi reminda yemagetsi - matambudziko nemhinduro 1

Kutungamira kwemunda wemagetsi panzvimbo A:

Chaji yemagetsi yakanaka saka divi remagetsi riri kure nechaji yemagetsi uye mapoinzi A.

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2. Verenga hukuru negwara remagetsi panzvimbo P iri pa10 cm kubva papoindi yekuchaja Q = -2 0 μC. k = 9 x 10 9 Nm 2 C −2 , 1 μC = 10 −6 C.

Zvinozivikanwa:

Chaja yemagetsi (q) = -20 μC = -20 x 10 -6 C

Nhambwe iri pakati penzvimbo P nechaji yemagetsi (r P ) = 10 cm = 0.1 m = 1 x 10 -1 m

k = 9 x 10 9 Nm 2 C −2

Zvinodiwa: Hukuru uye kwakanangana nemagetsi panzvimbo P

Solution:

Hukuru uye divi reminda yemagetsi - matambudziko nemhinduro 2

Kutungamira kwemunda wemagetsi panzvimbo A:

Chaji yemagetsi haina kunaka saka divi remagetsi rinoenda kune chaji yemagetsi.

[irp]

3. Mapoinzi maviri anopatsanurwa nedaro remasendimita makumi mana. Ndeipi nzvimbo yemagetsi iri pakati pemapoinzi maviri aya uye divi rayo riri papi P pakati pemapoinzi maviri aya, kureva kuti 20 cm kubva papoinzi A?

Hukuru uye divi reminda yemagetsi - matambudziko nemhinduro 3

Zvinozivikanwa:

Chaja A (q A ) = -2 μC = -2 x 10 -6 C

Chaja B (q B ) = + 4 μC = +4 x 10 -6 C

Daro riri pakati pekuchaja A nepoindi P (r AP ) = 20 cm = 0.2 m = 2 x 10 -1 m

Daro riri pakati pekuchaja B nepoindi P (r BP ) = 20 cm = 0.2 m = 2 x 10 -1 m

Zvinodiwa: Hukuru uye divi remagetsi panzvimbo P.

Solution:

Hukuru uye divi reminda yemagetsi - matambudziko nemhinduro 4

Chaji A haina kunaka zvekuti divi remagetsi riri paQ A (kuruboshwe).

Hukuru uye divi reminda yemagetsi - matambudziko nemhinduro 5

Chaji B yakanaka zvekuti divi renzvimbo dzemagetsi riri kure neQ B (kuruboshwe).

Huwandu hwemagetsi ari panzvimbo A:

E = E A + E B

E = (4.5 x 10 5 ) + (9 x 10 5 )

E = 13.5 x 10 5 N/C

Kutungamira kwesimba remagetsi kunongedzera kuQ A (kuruboshwe).

[irp]

4. Hukuru hwesimba remagetsi harisi zero pa…

Hukuru uye divi reminda yemagetsi - matambudziko nemhinduro 6

Chaja A iri positive uye chaja B iri positive zvekuti hukuru hwesimba remagetsi huri zero riri panzvimbo P, pakati pechaja dzese dziri mbiri.

Zvinozivikanwa:

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

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

k = 9 x 10 9 Nm 2 C −2

Daro riri pakati pechaji A nechaji B = 20 cm

Mutengo uri pakati pechaji A nepoindi P (r AP ) = a

Daro riri pakati pekuchaja B nepoindi P (r BP ) = 20 – a

Zvinodiwa: Hukuru hwesimba remagetsi harisi zero riri pa….

Solution:

Hukuru hwesimba remagetsi rinogadzirwa nechaji A panzvimbo P

Hukuru uye divi reminda yemagetsi - matambudziko nemhinduro 7

Chaji A yakanaka zvekuti divi renzvimbo dzemagetsi riri kure nechaji A (kurudyi).

Hukuru hwesimba remagetsi rinogadzirwa nechaji B panzvimbo P:

Hukuru uye divi reminda yemagetsi - matambudziko nemhinduro 8

Chaji B yakanaka zvekuti divi renzvimbo dzemagetsi riri kure nechaji B (kuruboshwe).

Munda wemagetsi wese panzvimbo P = 0:

Hukuru uye divi reminda yemagetsi - matambudziko nemhinduro 9

Tinoshandisa fomura yequadratic kuti tizive a.

Hukuru uye divi reminda yemagetsi - matambudziko nemhinduro 10

Hukuru hwesimba remagetsi harisi zero riri pa 8 cm kubva pachaji A kana 12 cm kubva pachaji B.

[irp]

5. Zvichibva pamufananidzo uri pazasi, w pano pane poindi P kuitira kuti munda wemagetsi papoindi P uve zero? (k = 9 x 10 9 Nm 2 C −2 , 1 μC = 10 −6 C)

Hukuru uye divi reminda yemagetsi - matambudziko nemhinduro 11

mhinduro

To verenga simba remagetsi panzvimbo P, zvichifungidzirwa kuti panzvimbo P pane muripo wekuyedza wakanaka. Q1 zvakanaka uye Q2 iri negative, saka poindi P inofanira kunge iri kurudyi rweQ2 kana kuruboshwe rweQ1Kana poindi P iri kuruboshwe rweQ1; munda wemagetsi unogadzirwa naQ1 panzvimbo P iri kuruboshwe (kure neQ)1) uye simba remagetsi rinogadzirwa neQ2 panzvimbo P kurudyi (kuna Q1). Kwakanangana nemunda wemagetsi kwakatarisana kuitira kuti minda miviri yemagetsi iparadzane kuitira kuti simba remunda wemagetsi panzvimbo P rive zero.

Zvinozivikanwa:

Mubvunzo 1 = +9 μC = +9 x 10 −6 C

Mubvunzo 2 = -4 μC = -4 x 10 −6 C

k = 9 x 10 9 Nm 2 C −2

Daro riri pakati pekuchaja 1 nekuchaja 2 = 3 cm

Daro riri pakati peQ 1 nepoindi P (r 1P ) = a

Daro riri pakati peQ 2 nepoindi P (r 2P ) = 3 + a

Zvinodiwa: nzvimbo yepoindi P kuitira kuti munda wemagetsi papoindi P uve zero

Solution:

Poindi P iri kuruboshwe rweQ1.

Munda wemagetsi wakagadzirwa neQ 1 panzvimbo P:

Hukuru uye divi reminda yemagetsi - matambudziko nemhinduro 12

Chaji yekuyedza iri positive uye Q 1 iri positive zvekuti divi remagetsi riri kuruboshwe.

Munda wemagetsi wakagadzirwa neQ 2 panzvimbo P:

Hukuru uye divi reminda yemagetsi - matambudziko nemhinduro 13

Chaji yekuyedza iri positive uye Q2 iri negative zvekuti divi remagetsi riri kurudyi.

Munda wemagetsi weNet panzvimbo A:

Hukuru uye divi reminda yemagetsi - matambudziko nemhinduro 14

Shandisa fomura yequadratic kuti uone a :

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

Hukuru uye divi reminda yemagetsi - matambudziko nemhinduro 15

Daro riri pakati peQ 2 nepoindi P (r 2P ) = 3 + a = 3 – 1.8 = 1.2 cm.

Poindi P iri kurudyi rwe1.2 cm kubva paQ 1.

[irp]

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Mutemo waCoulomb - matambudziko nemhinduro

1. Kuchaja mapoinzi maviri, QA = +8 μC uye QB = -5 μC, dzakaparadzaniswa nechinhambwe r = 10 cm. Ukuru hwe simba remagetsi. Iyo k isingachinji = 8.988 x 109 Nm2C-2 = 9 x gumi9 Nm2C-2.

Mutemo waCoulomb - matambudziko nemhinduro 1

Zvinozivikanwa:

Chaja A (q A ) = +8 μC = +8 x 10 -6 C

Chaja B (q B ) = -5 μC = -5 x 10 -6 C

k = 9 x 10 9 Nm 2 C −2

Nhambwe iri pakati pechaja A neB (r AB ) = 10 cm = 0.1 m

Zvinodiwa : Hukuru hwesimba remagetsi

Solution:

Fomura yemutemo waCoulomb :

Mutemo waCoulomb - matambudziko nemhinduro 2

Hukuru hwesimba remagetsi:

Mutemo waCoulomb - matambudziko nemhinduro 16

[irp]

2. Zvidimbu zviviri zvine chaji sezvakaratidzwa pamufananidzo uri pazasi. Q P = +10 μC uye Q q = +20 μC zvakaparadzaniswa nedaro r = 10 cm. Chii chinonzi hukuru hwesimba remagetsi.

Mutemo waCoulomb - matambudziko nemhinduro 4

Zvinozivikanwa:

Chaja P (Q P ) = +10 μC = +10 x 10 -6 C

Chaja Q (Q Q ) = +20 μC = +20 x 10 -6 C

k = 9 x 10 9 Nm 2 C −2

Nhambwe iri pakati pechaji P neQ (r PQ ) = 12 cm = 0.12 m = 12 x 10 -2 m

Zvinodiwa: Hukuru hwesimba remagetsi

Solution:

Mutemo waCoulomb - matambudziko nemhinduro 15

[irp]

3. Zvidimbu zvitatu zvakachajwa zvakarongwa mumutsara sezvakaratidzwa mumufananidzo uri pazasi. Chaji A = -5 μC, chaji B = +10 μC uye chaji C = -12 μC. Verenga simba remagetsi rinogara riripo pachikamu B nekuda kwezvimwe zviviri zvinochajwa.

Mutemo waCoulomb - matambudziko nemhinduro 6

Zvinozivikanwa:

Chaja A (q A ) = -5 μC = -5 x 10 -6 C

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

Chaja C (q C ) = -12 μC = -12 x 10 -6 C

k = 9 x 10 9 Nm 2 C −2

Nhambwe iri pakati pezvikamu A naB (r AB ) = 6 cm = 0.06 m = 6 x 10 -2 m

Nhambwe iri pakati pezvikamu B naC (r BC ) = 4 cm = 0.04 m = 4 x 10 -2 m

Zvinodiwa: Hukuru uye gwara resimba remagetsi pachikamu B

Solution:

Simba guru riri pachikamu B ndiro huwandu hwesimba reF BA rinoiswa pachikamu B nechikamu A uye simba reF BC rinoiswa pachikamu B nechikamu C.

Simba raF BA rinoshandiswa pachikamu B nechikamu A:

 

Mutemo waCoulomb - matambudziko nemhinduro 14

Kutungamira kwesimba remagetsi kunongedzera kuchinhu A (nongedzo kuruboshwe).

Simba raF BC rinoshandiswa pachikamu B nechikamu A:

 

Mutemo waCoulomb - matambudziko nemhinduro 13

Kutungamira kwesimba remagetsi kunongedzera kuchikamu C (nongedzo kurudyi).

Simba remagetsi rinogara riri pachikamu B :

F B = F AB – F BC = 675 N – 125 N = 550 maNewton.

Kutungamira kwesimba remagetsi pachikamu B kunongedzera kuchikamu C (kunongedzera kurudyi).

[irp]

4. +Q 1 = 10 μC, +Q 2 = 50 μC uye Q 3 zvakaparadzaniswa sezvakaratidzwa mumufananidzo uri pazasi. Chii chinonzi electrostatic charge pachikamu 3 kana simba re electrostatic pachikamu 2 riri zero.

Mutemo waCoulomb - matambudziko nemhinduro 9

Zvinozivikanwa:

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

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

Nhambwe iri pakati pemachaji 1 ne2 (r 12 ) = 2 cm = 0.02 m = 2 x 10 -2 m

Nhambwe iri pakati pechaji 2 nechaji 3 (r 23 ) = 6 cm = 0.06 m = 6 x 10 -2 m

Simba remagetsi rinogara riri pachikamu chechipiri (F2 ) = 0

Zvinodiwa : muripo 3 (q 3 )

Solution:

Simba remagetsi pachikamu chechipiri ihuwandu hwesimba F 21 rakashandiswa pachikamu chechipiri nechikamu chekutanga uye simba F 23 rakashandiswa pachikamu chechipiri nechikamu chechipiri.

Simba F 21 rakashandiswa pachikamu chechipiri nechikamu 1:

Mutemo waCoulomb - matambudziko nemhinduro 10

Kutungamira kwesimba remagetsi kunongedzera kuchikamu 3 (nongedza kurudyi).

Simba F23 inoshandiswa pachikamu chechipiri nechikamu 3: 

Kutungamira kwesimba remagetsi kunongedzera kuchikamu 1 (nongedzo kuruboshwe).

Simba remagetsi rinogara riri pachikamu 2 = 0:

Mutemo waCoulomb - matambudziko nemhinduro 11

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Kufamba kweAngular - matambudziko nemhinduro

1. Chinhu chine nguva yekusashanda zvakanaka ye 2 kg m 2 chinotenderera pa 1 rad/s. Chii chinonzi angular momentum yechinhu chacho?

Zvinozivikanwa:

Nguva yekusaita basa (I) = 2 kg m 2

Kumhanya kwekona ( ω ) = 1 rad/s

Zvinodiwa: Angular momentum (L)

Solution:

Fomura ye angular momentum:

L = I ω

L = angular momentum (kg m 2 /s), I = nguva yekusaita basa (kg m 2 ), ω = angular speed (rad/s)

Mwenje wekona:

L = I ω = (2)(1) = 2 kg m 2 /s

[irp]

2. Pureyi yesimbi inorema 2 kg ine radius ye 0.1 m inotenderera nekumhanya kwakafanana kwe 2 rad/s. Chii chinonzi angular momentum yepureyi?

Kufamba kweAngular - matambudziko nemhinduro 1Zvinozivikanwa:

Huremu hwepulley (m) = 2 kg g

Nharaunda yepulley (r) = 0.1 m

Kumhanya kwekona (ω) = 2 r ad/s

Zvinodiwa: Angular momentum

Solution:

Fomura yenguva yekusagadzikana kwesimbi yakasimba:

Ini = 1/2 mr 2

I = nguva yekusaita basa (kg m 2 ), m = huremu (kg), r = radius (m)

Nguva yekusaita basa:

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

Kumhanya kwekona:

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

[irp]

3. Bhora rinorema 2 kg rine dhayamita ye 0.2 m rinotenderera pa 4 rad/s. Chii chinonzi angular momentum yebhora?

Kufamba kweAngular - matambudziko nemhinduro 2Zvinozivikanwa:

Huremu hwebhora (m) = 2 kg

Nharaunda yebhora (r) = 0.2 m

Kumhanya kwekona (ω) = 4 ra d/s

Zvinodiwa: Angular momentum

Solution:

Fomura yenguva yekusagadzikana kwechikamu chimwe chete:

Ini = (2/5) mr 2

I = nguva t yekusashanda (kg m 2 ), m = uremu (kg), r = dhayasi (m)

Nguva yekusagadzikana kwenzvimbo imwechete:

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

Mwenje wekona webhora:

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

[irp]

4. Chidimbu che1-kg chinotenderera nekumhanya kwakafanana kwe2 rad/s. Chii chinonzi kumhanya kwekona kana radius yedenderedzwa iri 10 cm?

Zvinozivikanwa:

Huremu hwechinhu (m) = 1 kg g

Radiyo yedenderedzwa (r) = 10 cm = 10/100 = 0.1 m

Kumhanya kwekona (ω) = 2 rad/ s

Zvinodiwa: Angular momentum

Solution:

Fomura yenguva yekusagadzikana kwezvikamu:

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

Mwenje wekona:

L = I ω = (0.01)(2) = 0.02 kg m 2 /s

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Simba reKinetic rinotenderera - matambudziko nemhinduro

1. Chinhu chine nguva yekusashanda kwesimba ye1 kg m 2 chinotenderera nekumhanya kwakasimba kwe2 rad/s. Chii chinonzi rotational kinetic energy yechinhu chacho?

Zvinozivikanwa:

Nguva yekusaita basa (I) = 1 kg m 2

Kumhanya kwekona ( ω) = 2 rad/s

Zvinodiwa: Simba rekufamba kwemhepo (K E )

Solution:

Fomura yesimba rinotenderera rekinetic:

KE = 1/2 I ω 2

KE = simba rekinetic rinotenderera (kg m2/s2), ini = nguva yekusagadzikana (kg m2), ω = kumhanya kwekona (rad/s)

Simba rekinetic rinotenderera:

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

[irp]

2. Pulley ine huremu hwemakirogiramu makumi maviri ine radius ye 0.2 m inotenderera nekumhanya kwakafanana kwe 4 rad/s. Chii chinonzi rotational kinetic energy yepulley?

Simba rekufamba-famba rekinetic - matambudziko nemhinduro 1Zvinozivikanwa:

Huremu hwepureni yesirinda (m) = 20 kg g

Radiyo yesirinji (r) = 0.2 m

Kumhanya kwekona (ω) = 4 ra d/s

Zvinodiwa: Chii chinonzi simba rekinetic rinotenderera

Mhinduro;

Fomura yenguva yekusagadzikana kwe cylinder:

Ini = 1/2 mr 2

I = nguva yekusashanda ( kg m2 ) , m = uremu (kg), r = dhayasi (mita)

Nguva yekusashanda kwepulley yesilinda:

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

Simba rekutenderera kwepulley:

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

[irp]

3. Bhora reA- 10 kg rine radius ye 0.1 m rinotenderera pa constant ye 10 rad/s. Chii chinonzi kinetic energy yebhora?

Zvinozivikanwa:

Huremu hwebhora (m) = 10 kg

Nharaunda yebhora (r) = 0.1 m

Kumhanya kwekona (ω) = 10 r ad/s

Zvinodiwa: Simba rekufamba kwemhepo rinotenderera

Solution:

Fomura yenguva yekusagadzikana:

Ini = (2/5) mr 2

I = nguva yekusaita basa (kg m 2 ), m = huremu (kg), r = radius (m)

Nguva yekusaita basa kwebhora:

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

Simba rekufamba kwebhora:

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

[irp]

4. Chidimbu che 0.5- kg chinotenderera nekumhanya kwakafanana kwe 2 rad/s. Chii chinonzi rotational kinetic energy yechidimbu kana radius yedenderedzwa iri 10 cm?

Zvinozivikanwa:

Huremu hwechinhu (m) = 0.5 kg g

Radiyo yebhora (r) = 10 cm = 10/100 = 0.1 m

Kumhanya kwekona (ω) = 2 rad/ s

Zvinodiwa: Simba rekufamba kwemhepo rinotenderera

Solution:

Nguva yekusashanda zvakanaka kwezvikamu:

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

Simba rekinetic rinotenderera:

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

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Kutenderera kwemamiriro ezvinhu - matambudziko nemhinduro

1. Simba F rinoiswa patambo yakaputirwa papulley yesilinda. Torque yacho ndeye 2 N m uye nguva yekusashanda zvakanaka ndeye 1 kg m 2 , chii chinonzi angular acceleration yesilinda.

Kutenderera kwemamiriro ezvinhu - matambudziko nemhinduro 1Zvinozivikanwa:

Torque ( τ ) = 2 N m

Nguva yekusaita basa (I) = 1 kg m 2

Zvinodiwa: Kukurumidza kwe silinda kwekona

Solution:

Στ = I α

Στ = mambure torque, I = chinguva che inertia, α = angular kukwidza

Kukurumidza kwe silinda kwekona:

α = Στ / I = 2 / 1 = 2 rad/s 2

[irp]

2. Simba F rinoiswa patambo yakaputirwa papulley yesirinda. Hukuru hwesimba i10 N, radius yesirinda i0.2 m uye nguva yekusashanda i1 kg m 2, Chii chinonzi angular acceleration yesirinda?

Kutenderera kwemamiriro ezvinhu - matambudziko nemhinduro 2Zvinozivikanwa:

Simba (F) = 10 N

Nharaunda yesirinji (R) = 0.2 m

Nguva yekusaita basa (I) = 1 kg m 2

Zvinodiwa: Kukurumidza kwe silinda kwekona.

Solution:

τ = FR

τ = torque, F = simba, R = nharaunda yesirinji

Torque:

τ = FR = (1 0 N)(0.2 m) = 2 N m

Στ = I α

Στ = mambure torque, I = chinguva che inertia, α = angular kukwidza

Kukurumidza kwe silinda kwekona:

α = Στ / I = 2 / 1 = 2 rad/s 2

[irp]

3. Simba F rinoiswa patambo yakaputirwa papulley yesirinda. Hukuru hwesimba i10 N, radius yesirinda i0.2 m uye huremu hwesirinda i20 kg m 2, . Chii chinonzi angular acceleration yesirinda.

Kutenderera kwemamiriro ezvinhu - matambudziko nemhinduro 3Zvinozivikanwa:

Simba (F) = 10 N

Nharaunda yesirinji (R) = 0.2 m

Huremu hwesirinda (M) = 20 kg

Zvinodiwa: Kukurumidza kwe silinda kwekona

Solution:

τ = FR = (1 0 N)(0.2 m) = 2 N m

Nguva yekusaita basa:

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

Kukurumidza kwe silinda kwekona:

α = Στ / I = 2 / 0.4 = 5 rad/s 2

[irp]

4. Chivharo che 1-kg chakarembera kubva patambo yakaputirwa papulley yesilinda. Nguva yekusashanda kwepulley i 1 kg m 2 uye radius yepulley i 0.2 m. Chii chinonzi angular acceleration yepulley. Kukurumidza kunokonzerwa negiravhiti i 10 m/s 2.

Kutenderera kwemamiriro ezvinhu - matambudziko nemhinduro 4Zvinozivikanwa:

Nguva yekusashanda kwepulley (I) = 1 kg m 2

Huremu hwebhuroko (m) = 1 kg

Kukurumidza kunokonzerwa negiravhiti (g) = 10 m/s 2

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

Nharaunda yepulley (R) = 0.2 m

Zvinodiwa: Kukurumidza kwekona

Solution:

Torque:

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

Nguva yekusaita basa:

I = 1 kg m 2

Kukurumidzisa kwekona:

α = Στ / I = 2 / 1 = 2 rad/s 2

[irp]

5. Chivharo che 1-kg chakarembera kubva patambo yakaputirwa papulley yesilinda. Huremu hwepulley i 20 kg uye radius yepulley i 0,2 m. Chii chinonzi angular acceleration yepulley uye free fall acceleration yebhuroko. Kukurumidza kunokonzerwa negravity i 10 m/s 2.

Kutenderera kwemamiriro ezvinhu - matambudziko nemhinduro 5Zvinozivikanwa:

Huremu hwepulley (M) = 20 kg

Nharaunda yepulley (R) = 0,2 m

Huremu hwebhuroko (m) = 1 kg

Kukurumidza kunokonzerwa negiravhiti (g) = 10 m/s 2

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

Zvinodiwa: kukurumidza kwekona kwepulley uye kukurumidza kwekuwa kwebhuroko.

Solution:

Torque:

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

Nguva yekusashanda kwepulley yesilinda:

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

Kukurumidza kwekona kwepulley:

α = Στ / I = 2 / 0.4 = 5 rad/s 2

Kukurumidza kwekuwa kwebhuroko:

a = R α = (0.2)(5) = 1 m/s 2

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Nguva yekusagadzikana kwezvikamu uye miviri yakaoma - matambudziko nemhinduro

Nguva yekusagadzikana kwechikamu

1. Bhora remagiramu zana rakabatana kune rimwe divi retambo ine hurefu hwemasendimita makumi matatu. Ndeipi nguva yekusashanda kwebhora pamusoro pechikamu chekutenderera AB? Usafuratira huremu hwetambo.

Nguva yekusagadzikana kwezvikamu uye miviri yakaoma - matambudziko nemhinduro 1Zvinozivikanwa:

Kutenderera kwe axis pa AB

Bhora rehuremu (m) = magiramu zana = 100/1000 = 0.1 kg

Daro riri pakati pebhora ne axis yekutenderera (r) = 30 cm = 0.3 m

Kudiwa: Nguva yekusaita basa kwebhora (I)

Solution:

Ini = mr 2 = (0.1 kg)(0.3 m) 2

I = (0.1 kg)(0.09 m2 )

I = 0.009 kg m 2

[irp]

2. Bhora remagiramu zana, m 1 , nebhora remagiramu mazana maviri, m 2 , zvakabatana netsvimbo ine hurefu hwemasendimita makumi matanhatu. Huremu hwetsvimbo hahuna hanya. Akisi yekutenderera iri pakati petsvimbo. Ndeipi nguva yekusagadzikana kwebhora pamusoro peakisi yekutenderera?

Nguva yekusagadzikana kwezvikamu uye miviri yakaoma - matambudziko nemhinduro 2Zvinozivikanwa:

Huremu hwebhora 1 (m 1 ) = 100 magiramu = 100/1000 = 0.1 kg

Daro rebhora 1 uye axis yekutenderera (r 1 ) = 30 cm = 30/100 = 0.3 m

Huremu hwebhora (m 2 ) = 200 magiramu = 200/1000 = 0.2 kg

Daro rebhora 2 uye axis yekutenderera (r 2 ) = 30 cm = 30/100 = 0.3 m

Kudiwa: nguva yekusagadzikana kwemabhora

Mhinduro:

Ini = 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. Bhora remagiramu 200, m 1 uye bhora remagiramu 100, m 2, rakabatanidzwa netsvimbo ine hurefu hwemasendimita 60. Usafuratira huremu hwetsvimbo. Mutsetse wekutenderera uri pabhora m 2. Chii chinonzi nguva yekusashanda kwemabhora? Usafuratira huremu hwetsvimbo.

Nguva yekusagadzikana kwezvikamu uye miviri yakaoma - matambudziko nemhinduro 3Zvinozivikanwa:

Huremu hwebhora 1 (m 1 ) = 2 00 magiramu = 200/1000 = 0.2 kg

Daro riri pakati pebhora 1 ne axis yekutenderera (r 1 ) = 60 cm = 60/100 = 0.6 m

Huremu hwebhora 2 (m 2 ) = 100 magiramu = 100/1000 = 0.1 kg

Daro riri pakati pebhora 2 ne axis yekutenderera (r2 ) = 0 m

Kudiwa: Nguva yekusagadzikana kwemabhora

Solution:

Ini = 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. Huremu hwebhora rega rega hunosvika magiramu zana, hwakabatana netambo. Kureba kwetambo ndeye 60 cm uye upamhi hwetambo ndeye 30 cm. Ndeipi nguva yekusashanda kwebhora pamusoro pechikamu chekutenderera. Usafuratira huremu hwetambo.

Nguva yekusagadzikana kwezvikamu uye miviri yakaoma - matambudziko nemhinduro 4Zvinozivikanwa:

Huremu hwebhora = m 1 = m 2 = m 3 = m 4 = 1 00 magiramu = 100/1000 = 0.1 kg

Daro riri pakati pebhora nechikamu chekutenderera (r 1 ) = 30 cm = 30/100 = 0.3 m

Daro riri pakati pebhora 2 ne axis yekutenderera (r 2 ) = 30 cm = 30/100 = 0.3 m

Daro riri pakati pebhora 3 ne axis yekutenderera (r 3 ) = 30 cm = 30/100 = 0.3 m

Daro riri pakati pebhora 4 ne axis yekutenderera (r 4 ) = 30 cm = 30/100 = 0.3 m

Inozivikanwa: Nguva yekusagadzikana

Solution:

Ini = 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]

Nguva yekusagadzikana kwechinhu chakasimba

5. Chii chinonzi nguva yekusashanda kwetsvimbo yakaenzana ine hurefu hwe2 kg ine hurefu hwe2 m. Chikamu chekutenderera chiri pakati petsvimbo.

Nguva yekusagadzikana kwezvikamu uye miviri yakaoma - matambudziko nemhinduro 5Zvinozivikanwa:

Huremu hwetsvimbo (M) = 2 kg

Kureba kwetsvimbo (L) = 2 m

Zvinodiwa: Nguva yekusaita basa

Solution:

Fomura yenguva yekusagadzikana apo axis yekutenderera iri pakati petsvimbo refu yakafanana:

Ini = (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. Chii chinotora nguva yekusashanda kwetsvimbo yakaenzana ine hurefu hwe2 kg ine hurefu hwe2 m? Chikamu chekutenderera chiri pamucheto wetsvimbo.

Nguva yekusagadzikana kwezvikamu uye miviri yakaoma - matambudziko nemhinduro 6Zvinozivikanwa:

Huremu hwetsvimbo (M) = 2 kg

Kureba kwetsvimbo yakasimba (L) = 2 m

Zvinodiwa: Nguva yekusaita basa

Solution:

Fomura yenguva yekusagadzikana apo axis yekutenderera iri pamugumo mumwe wetsvimbo:

Ini = (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. Sirinda yakasimba ye10-kg ine radius ye 0.1 m. Nzvimbo yekutenderera iri pakati pesirinda yakasimba, inoratidzwa mumufananidzo uri pazasi. Ndeipi nguva yekusashanda kwesirinda?

Nguva yekusagadzikana kwezvikamu uye miviri yakaoma - matambudziko nemhinduro 7Zvinozivikanwa:

Huremu hwesirinda yakasimba (M) = 10 kg

Nharaunda yesirinji (L) = 0.1 m

Zvinodiwa: Nguva yekusaita basa

Zvinodiwa: Nguva yekusaita basa

Solution:

Fomura yenguva yekusagadzikana apo axis yekutenderera iri pakati pesilinda:

Ini = (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. Dura rakafanana rinorema 20 kg rine urefu hwe 0.1 m. Mutsetse wekutenderera uri pakati pedura unoratidzwa mumufananidzo uri pazasi.

Nguva yekusagadzikana kwezvikamu uye miviri yakaoma - matambudziko nemhinduro 8Zvinozivikanwa:

Huremu hwebhora (M) = 20 kg

Nharaunda yebhora (L) = 0.1 m

Zvinodiwa: nguva yekusaita basa

Solution:

Fomura yenguva yekusagadzikana apo axis yekutenderera iri pakati pebhora:

Ini = (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. Ndiro yakatetepa ye 2 kg ine hurefu hwe 0.5 m uye upamhi hwe 0.2 m. Nzvimbo yekutenderera iri pakati pendiro yakatetepa inoratidzwa mumufananidzo uri pazasi. Ndeipi nguva yekusashanda kwendiro?

Zvinozivikanwa:

Nguva yekusagadzikana kwezvikamu uye miviri yakaoma - matambudziko nemhinduro 9Huremu hweplate rectangular (M) = 2 kg

Kureba kweplate (a) = 0.5 m

Upamhi hweplate (b) = 0.2 m

Zvinodiwa: Nguva yeKusagadzikana

Solution:

Fomura yenguva yekusagadzikana apo axis yekutenderera iri pakati peplate:

I = (1/12 ) M (a 2 + b 2 )

Ini = (1/12)(2)(0.5 2 + 0.2 2 )

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

Ini = (1/6)(0.29)

I = 0.29/6 kg m 2

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