Physics

1. A capacitor yeplate yakafanana ane kutanga kugona C, mvumo yenzvimbo yakasununguka is ε_o, 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 5ε_o, simba rekupedzisira re capacitor yeparallel-plate chii.

Zvinozivikanwa:

Kugona kwe capacitor = C

Tmvumo yenzvimbo yakasununguka = ε_o

Pnzvimbo yekunonoka =A

The mufambo pakati pemaplate = d

Kuda: Kugona kwe capacitor (C)

Solution:

2. Iyo capacitor ine simba guru zvichibva pamufananidzo uri pazasi is...

Solution:

Fomura ye capacitor yeplate yakafanana:

Kugona kwema capacitor:

Iyo capacitor ine capacitor yakakura kupfuura dzosey i capacitor C_3.

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 ne2 ndiko…

Zvinozivikanwa:

Capacitor 1:

Nzvimbo yepamusoro = 2A

Daro riri pakati pemaplate =d₁

Capacitor 2:

Nzvimbo yepamusoro =A

Daro riri pakati pemaplate = 2 d₁

Kuda: Kuenzanisa kugona kwema capacitor 1 ne2

Solution:

5.

Sarudza kuenzanisa kugona kwe Ma capacitor eparallel-plate I neII.

Solution:

Kuenzanisa kugona kwe Ma capacitor eparallel-plate I neII:

6. Ma capacitor maviri akafanana anoratidzwa mumufananidzo uri pazasi.

Kana A₁ = ½ A₂ d₂ = 3 d₁ ipapo ona chiyero chesimba re parallel-plate capacitor pakati pemufananidzo wechipiri nemufananidzo wekutanga.

Zvinozivikanwa:

Capacitor yeplate yakafanana I:

A₁ = 1

d₁ = 1

Capacitor yeplate yakafanana II:

A₂ = 2

d₂ = 3

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

Solution:

Capacitor yeplate yakafanana I:

Capacitor yeplate yakafanana II:

Tchiyero chesimba re parallel-plate capacitor II neI:

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1. Sarudza iyo kugona kwemagetsi panzvimbo iri pa1 cm kubva pachaji 5.0 μC. Chikamu cheCoulomb (k) = 9 x 10⁹ Nm²C^-2, 1 μC = 10^-6 C.

Zvinozivikanwa:

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

murandu (q) = 5.0 μC = 5.0 x 10^-6 C

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

Zvaidiwa: Kugona kwemagetsi (V)

Solution:

Kugona kwemagetsi:

Simba remagetsi riri 4.5 X 10⁶ Volt

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.

Zvinozivikanwa:

murandu Q₁ = -5.0 μC = -5.0 x 10^-6 C

The mufambo yepoindi A kubva Q₁ = 10 cm = 0.1 m = 10^-1 m

murandu Q₂ = 6.0 μC = 6.0 x 10^-6 C

Kureba kwenzvimbo a kubva Q₂ = 10 cm = 0.1 m = 10^-1 m

Nguva dzose yaCoulomb (k) = 9 x 10⁹ Nm²C^-2

Zvaidiwa: Simba remagetsi panzvimbo A

Solution:

Simba remagetsi 1 :

Simba remagetsi 2 :

Simba remagetsi panzvimbo A :

V = V₂ - V₁

V = (54 - 45) x 10⁴

V = 9 x 10⁴

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.

Zvinozivikanwa:

murandu Q₁ = -5.0 μC = -5.0 x 10^-6 C

Kureba kwepoindi A kubva Q₁ = 40 cm = 0.4 m = 4 x 10^-1 m

murandu Q₂ = 6.0 μC = 6.0 x 10^-6 C

Kureba kwepoindi A kubva Q₂ = 50 cm = 0.5 m = 5 x 10^-1 m

Nguva dzose yaCoulomb (k) = 9 x 10⁹ Nm²C^-2

Zvaidiwa: Simba remagetsi panguva A

Solution:

Simba remagetsi 1 :

Simba remagetsi 2 :

Simba remagetsi panzvimbo A :

V = V₁ + V₂

V = (-11.25 + 10.8) x 10⁴

V = -0.45 x 10⁴

V = -4.5 x 10³

Simba remagetsi panzvimbo A riripo -4.5 x 10³ Volt

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1. Electron inokurumidziswa kubva pakuzorora kuburikidza nemusiyano we 12 V. Chii chiri kuchinja mu simba remagetsi ye erekitironi?

Zvinozivikanwa:

The charge pa erekitironi (e) = -1.60 x 10^-19 Coulomb

Kugona kwemagetsi = voltage (V) = 12 Volt

Kuda: Kuchinja kwesimba remagetsi remaerekitironi (ΔPE)

Solution:

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

Chiratidzo chekusiya chinoratidza kuti simba rinogona kuderera.

2. Maplate maviri akafanana anochajwa. Kupatsanurwa kwemaplate acho i2 cm uye hukuru hwe munda wemagetsi Pakati pemaplates pane 500 Volt/meter. Chii chinochinja simba ringangoitika reproton kana rakurumidza kubva paplate ine positive charged kuenda paplate ine negative charge.

Zvinozivikanwa:

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

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

Mutengo weproton = +1.60 x 10^-19 Coulomb

Zvaidiwa: 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^-18 Joule

3. Mapoinzi maviri ekuchaja akaparadzaniswa nedaro re10 cm. Kuchaja panzvimbo A =+9 μC uye muripo papoindi B = -4 μC. k = 9 x 10⁹ Nm²C^-2, 1 μC = 10^-6 C. Chii chinochinja pamagetsi anogona kushaikwa panhamba B kana akakurumidza kusvika panhamba A?

Zvinozivikanwa:

Mari A (q)₁) = +9 μC = +9 x 10^-6 C

murandu B (q₁) = -4 μC = -4 x 10^-6 C

k = 9 x 10⁹ Nm²C^-2

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

Zvaidiwa: Kuchinja kwesimba remagetsi (ΔEP)

Solution:

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1. Yunifomu munda wemagetsi E = 8000 N/C inopfuura nepakati penzvimbo yakati sandara ine sikweya A = 10 m². Sarudza iyo kuyerera kwemagetsi.

Zvinozivikanwa:

Hukuru hwesimba remagetsi (E) = 8000 N/C

Nzvimbo (A) = 10 m²

θ = 0^o (kona iri pakati penzira yemagetsi nemutsetse wakadhirowewa wakatwasuka kunzvimbo yacho)

Kuda: Kuyerera kwemagetsi (Φ)

Solution:

Fomura yemagetsi ekufambisa:

Φ = EA cos q

Φ = kuyerera kwemagetsi (Nm²/C), E = munda wemagetsi (N/C), A = nzvimbo (m²), q = kona iri pakati pemutsetse wemagetsi nemutsetse wenguva dzose.

Kuyerera kwemagetsi:

Φ = EA cos q = (8000)(10)(cos 0) = (8000)(10)(1)) = 80,000 = 8 x 10⁴ Nm²/C

2. Munda wemagetsi wakaenzana E = 5000 N/C unopfuura nepakati penzvimbo yakati sandara yesikweya A = 2 m². Sarudza kuti magetsi anoyerera sei.

Zvinozivikanwa:

Munda wemagetsi (E) = 5000 N/C

Nzvimbo (A) = 2 m²

θ = 60^o (kona iri pakati penzira yemagetsi nemutsetse wakadhirowewa wakatwasuka kunzvimbo yacho)

Zvaidiwa: Kuyerera kwemagetsi (Φ)

Solution:

Kuyerera kwemagetsi:

Φ = EA cos q = (5000)(2)(cos 60) = (5000)(2)(0.5)= = 5000 = 5 x 10³ Nm²/C

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

Zvinozivikanwa:

Nharaunda yebhora (r) = 0.5 m

Kuchaja kwemagetsi (Q) = 10 μC = 10 x 10^-6 C

Zvaidiwa: Kuyerera kwemagetsi (Φ)

Solution:

Munda wemagetsi:

E = kq/r²

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

E = (90 x 10)³) / 0,25

E = 360 x 10³

E = 3.60 x 10⁵ N / C.

Nzvimbo yepamusoro:

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

Kuyerera kwemagetsi:

Mitsetse yemagetsi yakatwasuka panzvimbo yacho, zvekuti kona iri pakati penzira yemagetsi nemutsetse wakadhirowewa wakatarisana nenzvimbo yacho, ndiyo 0^o.

Φ = EA cos q

Φ = (3.60 X 10⁵)(3.14)(cos 0)

Φ = (11.304 x 10⁵)(1)

Φ = 11.304 x 10⁵

Φ = 1.13 x 10⁶ Nm²/C

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1. Verenga hukuru uye gwara remunda wemagetsi panzvimbo A iri pa5 cm kubva pane imwe poindi yekubhadhara Q = + 10 μC. k = 9 x 10⁹ Nm²C^-2, 1 μC = 10^-6 C)

Zvinozivikanwa:

Kuchaja kwemagetsi (Q) = + 10 μC = + 10 x 10^-6 C

The mufambo pakati penzvimbo A nenzvimbo yekuchaja Q (r)_A) = 5 cm = 0.05 m = 5 x 10^-2 m

k = 9 x 10⁹ Nm²C^-2

Kuda: Hukuru negwara re munda wemagetsi panguva A

Solution:

Kutungamira kwemunda wemagetsi panzvimbo A:

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

2. Verenga hukuru negwara remagetsi panzvimbo P iri pa10 cm kubva papoindi yekuchaja Q = -20 μC. k = 9 x 10⁹ Nm²C^-2, 1 μC = 10^-6 C.

Zvinozivikanwa:

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

Daro riri pakati penzvimbo P nechaji yemagetsi (r)_P) = 10 cm = 0.1 m = 1 x 10^-1 m

k = 9 x 10⁹ Nm²C^-2

Kuda: Hukuru uye kutungamira kwemunda wemagetsi panzvimbo P

Solution:

Kutungamira kwemunda wemagetsi panzvimbo A:

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

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?

Zvinozivikanwa:

Mari A (q)_A) = -2 μC = -2 x 10^-6 C

Muripo 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 pechaji B nepoindi P (r)_BP) = 20 cm = 0.2 m = 2 x 10^-1 m

Zvaidiwa: Hukuru uye kutungamira kwesimba remagetsi panzvimbo P.

Solution:

Chaji A haina kunaka saka divi remagetsi riri ku Q_A (kuruboshwe).

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 10⁵)

E = 13.5 x 10⁵ N / C.

Kutungamira kwesimba remagetsi kunongedzera kuQ_A (kuruboshwe).

4. Hukuru hwesimba remagetsi harisi zero pa…

Chaji A yakanaka uye chaji B yakanaka zvekuti hukuru hwesimba remagetsi huri pa zero panzvimbo P, pakati pemhosva mbiri idzi.

Zvinozivikanwa:

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

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

k = 9 x 10⁹ Nm²C^-2

Daro riri pakati pemari A uye mhosva yacho B = 20 cm

Mari iri pakati pechaji A nepoindi P (r_AP) = a

Daro riri pakati pechaji B nepoindi P (r_BP) = 20 – a

Zvaidiwa: Hukuru hwesimba remagetsi harisi zero riri pa….

Solution:

Hukuru hwesimba remagetsi rinogadzirwa nechaji A panzvimbo P

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

Hukuru hwesimba remagetsi rinogadzirwa nechaji B panzvimbo P:

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

Munda wemagetsi wese panzvimbo P = 0:

Tinoshandisa fomura yequadratic kuti tizive a.

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

5Zvichibva pamufananidzo uri pazasi, wheino poindi P zvekuti munda wemagetsi papoindi P uri zero? (k = 9 x 10⁹ Nm²C^-2, 1 μC = 10^-6 C)

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:

Q₁ = +9 μC = +9 x 10^-6 C

Q₂ = -4 μC = -4 x 10^-6 C

k = 9 x 10⁹ Nm²C^-2

Daro riri pakati pekuchaja 1 nekuchaja 2 = 3 cm

Kureba pakati peQ₁ uye poindi P (r)_1P) = a

Kureba pakati peQ₂ uye poindi P (r)_2P) = 3 + a

Zvaidiwa: nzvimbo yepoindi P kuitira kuti munda wemagetsi panzvimbo P uri zero

Solution:

PPoindi P iri kuruboshwe rweQ₁.

Munda wemagetsi wakagadzirwa naQ₁ panzvimbo P:

Mari yekuyedza iri positive uye Q₁ zvakanaka zvekuti divi remagetsi riri kuruboshwe.

Munda wemagetsi wakagadzirwa naQ₂ panzvimbo P:

Mari yekuyedza iri positive uye Q₂ haina kunaka zvekuti divi remagetsi riri kurudyi.

Munda wemagetsi weNet panzvimbo A:

Shandisa fomura yequadratic kuti uone a :

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

Kureba pakati peQ₂ uye poindi P (r)_2P) = 3 + a = 3 – 1.8 = 1.2 cm.

Poindi P iri kurudyi rwe1.2 cm kubva paQ₁.

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1. Kuchaja mapoinzi maviri, Q_A = +8 μC uye Q_B = -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.

Zvinozivikanwa:

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

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

k = 9 x 10⁹ Nm²C^-2

The mufambo pakati pechaji A neB (r)_AB) = 10 cm = 0.1 m

Wanted : Hukuru hwesimba remagetsi

Solution:

Fomura ye Mutemo weCoulomb :

Hukuru hwesimba remagetsi:

2. Zvidimbu zviviri zvakachajwa sezvakaratidzwa pamufananidzo uri pazasi._P = +10 μC uye Q_q = +20 μC zvakaparadzaniswa nechinhambwe r = 10 cm. Simba remagetsi rinoshanduka chii?

Zvinozivikanwa:

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

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

k = 9 x 10⁹ Nm²C^-2

Daro riri pakati pemari P neQ (r_PQ) = 12 cm = 0.12 m = 12 x 10^-2 m

Zvaidiwa: Thukuru hwesimba remagetsi

Solution:

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.

Zvinozivikanwa:

Mari A (q)_A) = -5 μC = -5 x 10^-6 C

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

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

k = 9 x 10⁹ Nm²C^-2

Kureba pakati pezvikamu A na B (r)_AB) = 6 cm = 0.06 m = 6 x 10^-2 m

Daro riri pakati pezvikamu B naC (r)_BC) = 4 cm = 0.04 m = 4 x 10^-2 m

Zvaidiwa: Hukuru uye gwara resimba remagetsi rinotenderera pachikamu B

Solution:

Simba remagetsi pachikamu B ndiro huwandu hwesimba remagetsi F_BA inoshandiswa pachikamu B nechikamu A nesimba F_BC inoshandiswa pachikamu B nechikamu C.

Simba F_BA inoshandiswa pachikamu B nechikamu A:

 

Kutungamira kwesimba remagetsi kunongedzera kuchinhu A (nongedzo kuruboshwe).

Simba F_BC inoshandiswa pachikamu B nechikamu A:

 

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 Newtons.

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

4. +Q₁ = 10 μC, +Q₂ = 50 μC uye Q₃ zvakaparadzaniswa sezvakaratidzwa mumufananidzo uri pazasi. Chii chinonzi electrostatic charge pachikamu 3 kana simba re electrostatic force riri pachikamu 2 riri zero?

Zvinozivikanwa:

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

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

Kureba pakati pemari 1 ne2 (r)₁₂) = 2 cm = 0.02 m = 2 x 10^-2 m

Daro riri pakati pekuchaja 2 nekuchaja 3 (r)₂₃) = 6 cm = 0.06 m = 6 x 10^-2 m

Simba remagetsi rinogara riri pachikamu chechipiri (F)₂= = 0

Wanted : muripo 3 (q)₃)

Solution:

Simba guru riri pachikamu chechipiri ndiro vector huwandu hwesimba F₂₁ inoshandiswa pachikamu chechipiri nechikamu 1 uye simba F₂₃ inoshandiswa pachikamu chechipiri nechikamu chechitatu.

Simba F₂₁ inoshandiswa pachikamu chechipiri nechikamu 1:

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:

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1. Chinhu chine nguva ye inertia of 2 makirogiramu m² inotenderera pa 1 rad/s. Chii angular kukurumidza yechinhu chacho?

Zvinozivikanwa:

Nguva yeinertia (I) = 2 kg m²

Kumhanya kwekona (ω) = 1 rad/s

Zvaidiwa: Angular momentum (L)

Solution:

Fomura ye angular momentum:

L = Ini ω

L= angular kukurumidza (kg m²/s), ini = nguva ye inertia (kg m²), ω = kumhanya kwekona (rad/s)

Mwenje wekona:

L = Ini ω = (2)(1) = 2 kg m²/s

2. A zana-kg pulley yesilinda ine nharaunda ye 0.1 M inotenderera nekumhanya kwekona kunogara kuripo kwe2 rad/s. Chii chinonzi angular momentum yepulley?

Zvinozivikanwa:

Misa yepulley (m) = 2 kg

Nharaunda yePulley (r) = 0.1 m

Kumhanya kwekona (ω) = 2 rad/s

Zvaidiwa: Angular momentum

Solution:

Fomura yenguva yekusagadzikana kwesimbi yakasimba:

I = 1/2 mr²

I = nguva ye inertia (kg m²), m = uremu (kg), r = radius (m)

Nguva yekusaita basa:

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

Kumhanya kwekona:

L = Ini ω = (0.01)(2) = 0.02 kg m²/s

3. Chipembere chakaenzana che2-kg chine dhayamita ye 0.2 M inotenderera pa 4 rad/s. Chii chinonzi angular momentum yebhora?

Zvinozivikanwa:

Misa yebhora (m) = 2 kg

Nharaunda yebhora (r) = 0.2 m

Kumhanya kwekona (ω) = 4 rad/s

Zvaidiwa: Angular momentum

Solution:

Fomura yenguva yekusagadzikana kwechikamu chimwe chete:

I = (2/5) Va.²

Ini = nguvat yekusagadzikana (kg m²), m = huremu (kg), r = radius (m)

Nguva yekusagadzikana kwenzvimbo imwechete:

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

Mwenje wekona webhora:

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

4. A 1 kg chidimbu chinotenderera nekumhanya kwakasimba kwe 2 rad/s. Chii chinonzi kona yekumhanya kana radius yedenderedzwa iri 1?0 cm.

Zvinozivikanwa:

Misa yechinhu (m) = 1 kg

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

Kumhanya kwekona (ω) = 2 rad/s

Zvaidiwa: Angular momentum

Solution:

Fomura yenguva yekusagadzikana kwezvikamu:

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

Mwenje wekona:

L = I ω = (0.01)(2) = 0.02 kg m²/s

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1. Chinhu chine nguva ye inertia ye 1 kg m² inotenderera nekumhanya kwekona kunogara kuripo kwe 2 rad/s. Chii simba rekufamba kwekinetic yechinhu chacho?

Zvinozivikanwa:

Nguva yekusagadzikana (I) = 1 kg m²

The angular velocity (ω) = 2 rad/s

Kuda: Simba rekinetic rinotenderera (KE)

Solution:

Fomura yesimba rinotenderera rekinetic:

KE = 1/2 I ω²

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

Simba rekinetic rinotenderera:

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

2. A 20-kg chipuri chesirinda ine radius ye 0.2 m inotenderera nekumhanya kwakasimba kwe 4 rad/s. Chii chinonzi rotational kinetic energy yepulley?

Zvinozivikanwa:

Misa yepulley yesilinda (m) = 20 kg

Nharaunda yesirindi (r) = 0.2 m

Kumhanya kwekona (ω) = 4 rad/s

Zvaidiwa: Chii chinonzi simba rekinetic rinotenderera

Mhinduro;

Fomura yenguva yekusagadzikana kwe cylinder:

I = 1/2 mr²

I = nguva yekusaita basa (kg m²), m = huremu (kg), r = radius (mita)

Nguva yekusashanda kwepulley yesilinda:

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

Simba rekutenderera kwepulley:

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

3. A-10 makirogiramu bhora rine nharaunda ye 0.1 M inotenderera nechiyero chisingachinji che 10 rad/s. Chii chinonzi kinetic energy yebhora?

Zvinozivikanwa:

Misa yebhora (m) = 10 kg

Nharaunda yebhora (r) = 0.1 m

Angular velocity (ω) = 10 rad/s

Zvaidiwa: Simba rekinetic rinotenderera

Solution:

Fomura yenguva yekusagadzikana:

I = (2/5) Va.²

I = nguva ye inertia (kg m²), m = huremu (kg), r = radius (m)

Nguva yekusaita basa kwebhora:

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

Simba rekufamba kwebhora:

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

4. A 0.5-makirogiramu ezvikamu zvinotenderera nekumhanya kwakafanana kwe 2 rad/s. Chii chinonzi rotational kinetic energy yechinhu ichi kana radius yedenderedzwa iri? 10 cm.

Zvinozivikanwa:

Misa chezvimedu (m) = 0.5 kg

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

Kumhanya kwekona (ω) = 2 rad/s

Zvaidiwa: Simba rekinetic rinotenderera

Solution:

Nguva yekusashanda zvakanaka kwezvikamu:

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

Simba rekinetic rinotenderera:

KE = 1/2 I ω² = 1/2 (0.005)(2)² = 1/2 (0.005)(4) = (0.005)(2) = 0.01 Joule

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1. Simba F rinoiswa patambo yakaputirwa papure yesilinda. torsion is 2 N m uye nguva ye inertia is 1 makirogiramu m², chii chinonzi angular acceleration yesirindi.

Zvinozivikanwa:

Torque (τ) = 2 N m

Nguva yekusaita basa (I) = 1 kg m²

Kuda: Kukurumidza kwe silinda kwekona

Solution:

Στ = Ini α

Στ = torque yakakwana, I = nguva yekusagadzikana, α = kukurumidza kwekona

Kukurumidza kwe silinda kwekona:

α = Στ / I = 2 / 1 = 2 rad/s²

2. Simba F rinoiswa patambo yakaputirwa papulley yesilinda. Hukuru hwesimba iri i10 N, nharaunda yesirinjiri ndeye 0.2 m uye nguva yekusashanda zvakanaka ndeye 1 makirogiramu m2, WKo kukurumidza kwe silinda kwekona ndiko chii?

Zvinozivikanwa:

Simba (F) = 10 N

Nharaunda yesirinji (R) = 0.2 m

Nguva yekusaita basa (I) = 1 kg m²

Kuda: Kukurumidza kwe silinda kwekona.

Solution:

τ = FR

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

Torque:

τ = FR = (10 N(0.2 m) = 2 N m

Στ = Ini α

Στ = torque yakakwana, I = nguva yekusagadzikana, α = kukurumidza kwekona

Kukurumidza kwe silinda kwekona:

α = Στ / I = 2 / 1 = 2 rad/s²

3. Simba F rinoiswa patambo yakaputirwa papure yesilinda. Hukuru hwesimba i10 N, nharaunda yesirinjiri i 0.2 m uye huremu hwesirinjiri i 20 kg m^2,. Thengowani ndiyo kona yekumhanyisa silinda.

Zvinozivikanwa:

Simba (F) = 10 N

Nharaunda yesirinji (R) = 0.2 m

Huremu hwesirinda (M) = 20 kg

Zvaidiwa: Kumhanyisa kwe silinda kwekona

Solution:

τ = FR = (10 N(0.2 m) = 2 N m

Nguva yekusaita basa:

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

Kukurumidza kwe silinda kwekona:

α = Στ / I = 2 / 0.4 = 5 rad/s²

4. Chivharo che 1-kg chakarembera patambo chakaputirwa papulley yesilinda. Nguva yekusashanda kwepulley i1 kg m² uye nharaunda yepulley ndeye 0.2 m. Chii chinonzi angular acceleration yepulley. Kuwedzera nekuda kwegiravhiti iri 10 m/s².

Zvinozivikanwa:

Nguva yekusashanda kwepulley (I) = 1 kg m²

Misa yebhuroko (m) = 1 kg

Kukurumidza kunokonzerwa negiravhiti (g) = 10 m/s²

uremu (w) = mg = (1 kg)(10 m/s²) = 10 kg m/s² = 10N

Nharaunda yepulley (R) = 0.2 m

Zvaidiwa: Kumhanyisa kwekona

Solution:

Torque:

τ = FR = w R = (10 N(0.2 m) = 2 N m

Nguva yekusaita basa:

I = 1 kg m²

Kukurumidzisa kwekona:

α = Στ / I = 2 / 1 = 2 rad/s²

5. Chivharo che 1-kg chakarembera patambo chakaputirwa papulley yesilinda. Huremu hwepulley i20 kg uye nharaunda yepulley ndeye 0,2 m. Chii chinonzi angular acceleration yepulley uye free-fall kukurumidza kwebhokisi. Kukurumidza kunokonzerwa negiravhiti i10 m/s².

Zvinozivikanwa:

Huremu hwepulley (M) = 20 kg

Nharaunda yepulley (R) = 0,2 m

Huremu hwebhuroko (m) = 1 kg

Kukurumidza kunokonzerwa negiravhiti (g) = 10 m/s²

Huremu (w) = mg = (1 kg)(10 m/s²) = 10 kg m/s² = 10N

Zvaidiwa: kukurumidza kwekona kwepulley uye kukurumidza kwekuwa kwebhuroko.

Solution:

Torque:

τ = FR = w R = (10 N(0.2 m) = 2 N m

Nguva yekusashanda kwepulley yesilinda:

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

Kukurumidza kwekona kwepulley:

α = Στ / I = 2 / 0.4 = 5 rad / s²

Kukurumidza kwekuwa kwebhuroko:

a = R α = (0.2)(5) = 1 m/s²

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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.

Zvinozivikanwa:

Kutenderera kwe axis pa AB

Misa bhora (m) = magiramu zana = 100/1000 = 0.1 kg

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

Kuda: Nguva yekusaita basa kwebhora (I)

Solution:

Ini = Va.² = (0.1 kg)(0.3 m)²

I = (0.1 kg)(0.09 m²)

I = 0.009 kg m²

2. Bhora remagiramu zana, m₁, uye bhora remagiramu mazana maviri, m₂, yakabatana netsvimbo ine urefu hwemasendimita makumi matanhatu. Huremu hwetsvimbo hahuna hanya. Mutsetse wekutenderera uri pakati petsvimbo. Ndeipi nguva yekusagadzikana kwebhora pamusoro pemutsetse wekutenderera?

Zvinozivikanwa:

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

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

Huremu hwebhora (m₂) = magiramu 200 = 200/1000 = 0.2 kg

The mufambo yebhora 2 uye axis yekutenderera (r)₂) = 30 cm = 30/100 = 0.3 m

Zvaidiwa: nguva yekusagadzikana kwemabhora

Mhinduro:

Ini = 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 M²) + (0.2 kg)(0.09 M²)

I = 0.009 kg m² + 0.018 kg m²

I = 0.027 kg m²

3. Bhora remagiramu zana, m₁ uye bhora remagiramu zana, m_2, yakabatana netsvimbo ine urefu hwemasendimita makumi matanhatu. Usafuratira huremu hwetsvimbo. Nzvimbo yekutenderera iri pabhora m₂Chii chinonzi nguva yekusashanda zvakanaka kwemabhora. Usatarisa huremu hwetsvimbo.

Zvinozivikanwa:

Huremu hwebhora 1 (m)₁= = 2Magiramu zana = 00/1000 = 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) = magiramu 100 = 100/1000 = 0.1 kg

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

Zvaidiwa: Nguva yekusagadzikana kwemabhora

Solution:

Ini = m₁ r₁² +m₂ r₂²

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 m²

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.

Zvinozivikanwa:

Huremu hwebhora = m₁ = m₂ = m₃ = m₄ = 1Magiramu zana = 00/1000 = 0.1 kg

Daro riri pakati pebhora ne axis yekutenderera (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

Zvinozivikanwa: Nguva yeinertia

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

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 m²

Nguva yekusagadzikana kwechinhu chakasimba

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

Zvinozivikanwa:

Huremu hwetsvimbo (M) = 2 kg

Kureba kwetsvimbo (L) = 2 m

Kuda: Nguva yeinertia

Solution:

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

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

Zvinozivikanwa:

Huremu hwetsvimbo (M) = 2 kg

Kureba kwetsvimbo yakasimba (L) = 2 m

Kuda: Nguva yeinertia

Solution:

Fomura yenguva yekusagadzikana apo axis yekutenderera iri pamugumo mumwe wetsvimbo:

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

Zvinozivikanwa:

Huremu hwesirinda yakasimba (M) = 10 kg

Nharaunda yesirinji (L) = 0.1 m

Kuda: Nguva yekusagadzikana

Kuda: Nguva yekusagadzikana

Solution:

Fomura yenguva yekusagadzikana apo axis yekutenderera iri pakati pesilinda:

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

Zvinozivikanwa:

Huremu hwebhora (M) = 20 kg

Nharaunda yebhora (L) = 0.1 m

Kuda: nguva yekusaita chinhu

Solution:

Fomura yenguva yekusagadzikana apo axis yekutenderera iri pakati pebhora:

Ini = (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. 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:

Huremu hweplate rectangular (M) = 2 kg

Kureba kweplate (a) = 0.5 m

Upamhi hweplate (b) = 0.2 m

Zvaidiwa: Nguva yeinertia

Solution:

Fomura yenguva yekusagadzikana apo axis yekutenderera iri pakati peplate:

Ini = (1/12) M (a² + b²)

Ini = (1/12)(2)(0.5)² + 0.2²)

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

Ini = (1/6)(0.29)

I = 0.29/6 kg m²

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