physics

1. A lub capacitor parallel-plate muaj thawj zaug muaj peev xwm C, qhov permittivity ntawm qhov chaw dawb is ε_o, thaj chaw phaj is A, qhov kev ncua deb ntawm cov phaj is d. Yog tiase thaj tsam ntawm daim phaj nce 4 zaug, qhov deb ntawm cov phaj ua 2d thiab qhov permittivity ntawm free space yog 5ε_o, qhov peev xwm kawg ntawm lub capacitor parallel-plate yog dab tsi.

Paub:

Lub peev xwm ntawm lub capacitor = C

Qhov permittivity ntawm qhov chaw dawb = ε _o

P thaj chaw lig = A

Qhov nrug ntawm cov phaj = d

Tom ntej: Capacitor Muaj Peev Xwm (C)

Tshuaj:

[irp]

2. Lub capacitor uas muaj peev xwm loj tshaj plaws raws li daim duab hauv qab no yog ...

Tshuaj:

Cov mis ntawm lub capacitor parallel-plate:

Lub peev xwm ntawm cov capacitors:

Lub capacitor uas muaj lub peev xwm y loj tshaj plaws yog capacitor C3_.

[irp]

3.

Xav txog cov yam hauv qab no!
(1) Dielectric tas mus li
(2) Tus qhov sib txawv ntawm qhov muaj peev xwm nruab nrab ntawm cov phaj
(3) Phaj thick
(4) Qhov chaw ntawm lub phaj
(5) Qhov deb ntawm cov phaj
(6) Tus nqi ntawm hluav taws xob
Cov yam tseem ceeb uas cuam tshuam rau lub peev xwm ntawm cov phaj sib luag cov capacitors yog…

Tshuaj:

(1), (4) thiab (5)

4. Qhov sib piv ntawm lub peev xwm ntawm lub capacitor 1 thiab 2 yog ...

Paub:

Lub Capacitor 1:

Thaj chaw nto = 2A

Qhov nrug ntawm cov phaj = d ₁

Lub Capacitor 2:

Thaj chaw nto = A

Qhov nrug ntawm cov phaj = 2 d ₁

Xav tau: Kev sib piv ntawm lub peev xwm ntawm cov capacitors 1 thiab 2

Tshuaj:

[irp]

5.

Txheeb xyuas qhov sib piv ntawm lub peev xwm ntawm Parallel-plate capacitor I thiab II.

Tshuaj:

Kev sib piv ntawm lub peev xwm ntawm Parallel-plate capacitors I thiab II:

[irp]

6. Ob lub capacitors parallel-plate uas tau qhia hauv daim duab hauv qab no.

Yog tias A ₁ = ½ A ₂ thiab d ₂ = 3 d ₁ ces txiav txim siab qhov piv ntawm cov peev xwm ntawm lub capacitor parallel-plate ntawm daim duab 2 thiab daim duab 1.

Paub:

Lub capacitor parallel-plate I:

A1 = ₁

d1 = ₁

Lub capacitor phaj sib luag II:

A2 = ₂

d2 = ₃

Xav tau: qhov piv ntawm cov peev xwm ntawm lub capacitor parallel-plate ntawm daim duab 2 thiab daim duab 1

Tshuaj:

Lub capacitor parallel-plate I:

Lub capacitor phaj sib luag II:

Qhov piv ntawm cov peev xwm ntawm cov capacitors parallel-plate II thiab I:

nyeem ntxiv

1. Txheeb xyuas lub zog hluav taws xob ntawm qhov chaw nyob ntawm 1 cm ntawm lub zog them 5.0 μ C. Coulomb tas li (k) = 9 x 10 ⁹ Nm ² C ⁻² , 1 μC = 10 ⁻⁶ C.

Paub:

Qhov nrug ntawm qhov them (r) = 1 cm = 1/100 m = 0.01 m = 10 ^-2 m

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

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

Xav tau: Lub zog hluav taws xob (V)

Tshuaj:

Lub zog hluav taws xob:

Lub zog hluav taws xob yog 4.5 x 10 ⁶ Volts

[irp]

2. them Q₁ = 5.0 μC thiab them nqi Q₂ = 6.0 μC. Coulomb tus nqi tas mus li (k) = 9 x 10⁹ Nm²C^-2, 1 μC = 10^-6 C. Point A nyob nruab nrab ntawm cov nqi. Txheeb xyuas lub zog hluav taws xob ntawm qhov chaw A.

Paub:

Them Q ₁ = -5.0 μ C = -5.0 x 10 ^-6 C

Qhov nrug ntawm qhov chaw A ntawm Q ₁ = 10 cm = 0.1 m = 10 ^-1 m

Tus nqi Q ₂ = 6.0 μ C = 6.0 x 10 ^-6 C

Qhov nrug ntawm qhov taw tes a ntawm Q ₂ = 10 cm = 0.1 m = 10 ^-1 m

Coulomb tus nqi tas mus li (k) = 9 x 10 ⁹ Nm ² C ⁻²

Xav tau: Lub zog hluav taws xob ntawm qhov chaw A

Tshuaj:

Lub zog hluav taws xob 1 :

Lub zog hluav taws xob 2 :

Lub zog hluav taws xob ntawm qhov chaw A :

V = _V2 – _V1

V = (54 – 45) x 10 ⁴

V = 9 x 10 ⁴

[irp]

3. them q₁ = 5.0 μC thiab them nqi q₂ = 6.0 μC. Coulomb tus nqi tas mus li (k) = 9 x 10⁹ Nm²C^-2, 1 μC = 10^-6 C. Txheeb xyuas lub zog hluav taws xob ntawm qhov chaw A.

Paub:

Them Q ₁ = -5.0 μ C = -5.0 x 10 ^-6 C

Qhov nrug ntawm qhov chaw A ntawm Q ₁ = 40 cm = 0.4 m = 4 x 10 ^-1 m

Tus nqi Q ₂ = 6.0 μ C = 6.0 x 10 ^-6 C

Qhov nrug ntawm qhov chaw A ntawm Q ₂ = 50 cm = 0.5 m = 5 x 10 ^-1 m

Coulomb tus nqi tas mus li (k) = 9 x 10 ⁹ Nm ² C ⁻²

Xav tau: Lub zog hluav taws xob ntawm qhov chaw A

Tshuaj:

Lub zog hluav taws xob 1 :

Lub zog hluav taws xob 2 :

Lub zog hluav taws xob ntawm qhov chaw 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

Lub zog hluav taws xob ntawm qhov chaw A yog -4.5 x 10 ³ Volts

nyeem ntxiv

1. Ib lub electron raug nrawm los ntawm qhov so los ntawm qhov sib txawv ntawm 12 V. Qhov kev hloov pauv ntawm lub zog fais fab ntawm lub electron yog dab tsi?

Paub:

Tus nqi ntawm ib lub electron (e) = -1.60 x 10 ^-19 Coulomb

Lub zog hluav taws xob = voltage (V) = 12 Volts

Xav tau: Kev hloov pauv ntawm lub zog hluav taws xob ntawm lub electron (ΔPE)

Tshuaj:

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

Lub cim rho tawm qhia tias lub zog muaj peev xwm txo qis.

[irp]

2. Ob lub phaj sib luag raug them nqi. Qhov sib nrug ntawm cov phaj yog 2 cm thiab qhov loj ntawm lub zog hluav taws xob ntawm cov phaj yog 500 Volt / 'meter'. Qhov kev hloov pauv ntawm lub zog muaj peev xwm ntawm proton thaum raug nrawm los ntawm lub phaj them nqi zoo mus rau lub phaj them nqi tsis zoo yog dab tsi.

Paub:

Qhov loj ntawm lub zog hluav taws xob ntawm cov phaj (E) = 500 Volt/meter

Qhov nrug ntawm cov phaj (s) = 2 cm = 0,02 m

Tus nqi ntawm ib qho proton = +1.60 x 10 ^-19 Coulombs

Xav tau: Kev hloov pauv ntawm lub zog hluav taws xob (ΔPE)

Tshuaj:

Lub zog hluav taws xob:

V = E s

V = (500 Volt/m2)(0.02 m)

V = 10 Volts

Kev hloov pauv ntawm lub zog fais fab:

ΔPE = qV

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. Ob lub ntsiab lus them nqi raug sib cais los ntawm qhov deb ntawm 10 cm. Them rau ntawm qhov chaw A = +9 μC thiab them rau ntawm qhov chaw B = -4 μC. k = 9 x 10 ⁹ Nm ² C ⁻² , 1 μC = 10 ⁻⁶ C. Qhov kev hloov pauv ntawm lub zog fais fab ntawm qhov chaw B yog dab tsi yog tias raug nrawm mus rau qhov chaw A?

Paub:

Them A (q ₁ ) = +9 μC = +9 x 10 ⁻⁶ C

Them B (q ₁ ) = -4 μC = -4 x 10 ⁻⁶ C

k = 9 x 10 ⁹ Nm ² C ⁻²

Qhov nrug ntawm cov nqi A thiab B (r) = 10 cm = 0.1 m = 10 ^-1 m

Xav tau: Kev hloov pauv ntawm lub zog hluav taws xob (ΔEP)

Tshuaj:

nyeem ntxiv

1. Ib lub teb hluav taws xob sib npaug E = 8000 N/C hla dhau ib cheeb tsam tiaj tiaj A = 10 m2 ^. Txheeb xyuas qhov hluav taws xob flux.

Paub:

Qhov loj ntawm lub zog hluav taws xob (E) = 8000 N/C

Cheeb Tsam (A) = 10 m ²

θ = 0 ^o (lub kaum sab xis ntawm qhov kev taw qhia ntawm lub zog hluav taws xob thiab ib txoj kab kos perpendicular rau thaj chaw)

Xav tau: Fais fab flux ( Φ)

Tshuaj:

Cov qauv ntawm cov hluav taws xob flux:

Φ = EA cos q

Φ = hluav taws xob flux ( Nm ² /C) , E = hluav taws xob teb (N/C), A = cheeb tsam (m ² ), q = lub kaum sab xis ntawm kab hluav taws xob teb thiab kab ib txwm.

Fais fab ntws:

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

[irp]

2. Ib lub teb hluav taws xob sib npaug E = 5000 N/C hla dhau ib cheeb tsam tiaj tiaj A = 2 m2 ^. Txheeb xyuas qhov flux hluav taws xob.

Paub:

Lub zog hluav taws xob (E) = 5000 N/C

Cheeb Tsam (A) = 2 m ²

θ = 60 ^o (lub kaum sab xis ntawm qhov kev taw qhia ntawm lub zog hluav taws xob thiab ib txoj kab kos perpendicular rau thaj chaw)

Xav tau: Fais fab flux ( Φ)

Tshuaj:

Fais fab ntws:

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

[irp]

3. Ib lub pob khov kho uas muaj lub vojvoog 0.5 meters muaj lub zog hluav taws xob 10 μC nyob hauv nruab nrab. Txheeb xyuas seb lub zog hluav taws xob hla dhau lub pob khov kho li cas.

Paub:

Lub vojvoog ntawm lub pob (r) = 0.5 m

Lub zog hluav taws xob (Q) = 10 μC = 10 x 10 ^-6 C

Xav tau: Fais fab flux ( Φ)

Tshuaj:

Lub teb hluav taws xob:

E = kq/ ^r2

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

Thaj chaw nto:

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

Fais fab ntws:

Cov kab hluav taws xob teb perpendicular rau thaj chaw, yog li ntawd lub kaum sab xis ntawm qhov kev taw qhia ntawm lub teb hluav taws xob thiab ib txoj kab kos perpendicular rau thaj chaw, yog 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

nyeem ntxiv

1. Xam qhov loj thiab kev coj ntawm lub zog hluav taws xob ntawm qhov chaw A nyob ntawm 5 cm ntawm qhov chaw them Q = +10 μC. k = 9 x 10 ⁹ Nm ² C ⁻² , 1 μC = 10 ⁻⁶ C)

Paub:

Lub zog hluav taws xob (Q) = +10 μC = +10 x 10 ^-6 C

Qhov nrug ntawm qhov chaw A thiab qhov chaw them nqi Q (r _A ) = 5 cm = 0.05 m = 5 x 10 ^-2 m

k = 9 x 10 ⁹ Nm ² C ⁻²

Xav tau: Qhov loj thiab kev coj ntawm lub zog hluav taws xob ntawm qhov chaw A

Tshuaj:

Kev taw qhia ntawm lub zog hluav taws xob ntawm qhov chaw A:

Lub zog hluav taws xob yog qhov zoo yog li ntawd qhov kev taw qhia ntawm lub teb hluav taws xob yog deb ntawm lub zog hluav taws xob thiab cov ntsiab lus A.

[irp]

2. Xam qhov loj thiab kev coj ntawm lub teb hluav taws xob ntawm qhov chaw P nyob ntawm 10 cm ntawm qhov chaw them Q = -2 0 μC. k = 9 x 10 ⁹ Nm ² C ⁻² , 1 μC = 10 ⁻⁶ C.

Paub:

Lub zog hluav taws xob (q) = -20 μC = -20 x 10 ^-6 C

Qhov nrug ntawm qhov chaw P thiab lub zog hluav taws xob (rP ₎ = 10 cm = 0.1 m = 1 x 10 ^-1 m

k = 9 x 10 ⁹ Nm ² C ⁻²

Xav tau: Qhov loj thiab kev coj ntawm lub zog hluav taws xob ntawm qhov chaw P

Tshuaj:

Kev taw qhia ntawm lub zog hluav taws xob ntawm qhov chaw A:

Lub zog hluav taws xob yog negative yog li ntawd lub zog hluav taws xob ntawm lub teb hluav taws xob mus rau lub zog hluav taws xob.

[irp]

3. Ob lub ntsiab lus hluav taws xob raug sib cais los ntawm qhov deb ntawm 40 cm. Qhov loj thiab qhov kev taw qhia ntawm lub zog hluav taws xob ntawm qhov chaw P ntawm ob lub ntsiab lus hluav taws xob, uas yog 20 cm ntawm qhov chaw A yog dab tsi?

Paub:

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

Them B (qB ₎ = + 4 μC = +4 x 10 ^-6 C

Qhov nrug ntawm lub zog them A thiab qhov chaw P (r _AP ) = 20 cm = 0.2 m = 2 x 10 ^-1 m

Qhov nrug ntawm lub zog them B thiab qhov chaw P (r _BP ) = 20 cm = 0.2 m = 2 x 10 ^-1 m

Xav tau: Qhov loj thiab kev coj ntawm lub zog hluav taws xob ntawm qhov chaw P.

Tshuaj:

Tus nqi A yog qhov tsis zoo yog li ntawd qhov kev taw qhia ntawm lub zog hluav taws xob taw tes rau Q _A (mus rau sab laug).

Tus nqi B yog qhov zoo yog li qhov kev taw qhia ntawm cov ntsiab lus hluav taws xob nyob deb ntawm Q _B (mus rau sab laug).

Tag nrho cov hluav taws xob teb ntawm qhov chaw A:

E = E _A + E _B

E = (4.5 x 105 ⁾ + (9 x ¹⁰⁵ )

E = 13.5 x 10 ⁵ N/C

Qhov kev taw qhia ntawm lub zog hluav taws xob taw tes rau Q _A (mus rau sab laug).

[irp]

4. Qhov loj ntawm lub teb hluav taws xob yog xoom ntawm…

Tus nqi A yog qhov zoo thiab tus nqi B yog qhov zoo yog li qhov loj ntawm lub teb hluav taws xob yog xoom nyob ntawm qhov chaw P, ntawm ob qho tib si.

Paub:

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

Tus nqi B (qB ₎ = +40 μC = +40 x 10 ⁻⁶ C

k = 9 x 10 ⁹ Nm ² C ⁻²

Qhov nrug ntawm lub zog A thiab lub zog B = 20 cm

Tus nqi hluav taws xob ntawm tus nqi hluav taws xob A thiab qhov chaw P (r _AP ) = a

Qhov nrug ntawm tus nqi B thiab qhov chaw P (r _BP ) = 20 - a

Xav tau: Qhov loj ntawm lub zog hluav taws xob yog xoom nyob ntawm….

Tshuaj:

Qhov loj ntawm lub zog hluav taws xob uas tsim los ntawm tus nqi A ntawm qhov chaw P

Tus nqi A yog qhov zoo yog li qhov kev taw qhia ntawm cov ntsiab lus hluav taws xob nyob deb ntawm tus nqi A (mus rau sab xis).

Qhov loj ntawm lub zog hluav taws xob uas tsim los ntawm tus nqi B ntawm qhov chaw P:

Tus nqi B yog qhov zoo yog li qhov kev taw qhia ntawm cov ntsiab lus hluav taws xob nyob deb ntawm tus nqi B (mus rau sab laug).

Tag nrho cov hluav taws xob teb ntawm qhov chaw P = 0:

Peb siv cov qauv quadratic los txiav txim siab a.

Qhov loj ntawm lub teb hluav taws xob yog xoom nyob ntawm 8 cm ntawm tus nqi A lossis 12 cm ntawm tus nqi B.

[irp]

5. Raws li daim duab hauv qab no, w ntawm no yog qhov taw tes P yog li ntawd lub teb hluav taws xob ntawm qhov taw tes P yog xoom? (k = 9 x 10 ⁹ Nm ² C ⁻² , 1 μC = 10 ⁻⁶ C)

tshuaj

To xam lub zog hluav taws xob ntawm qhov chaw P, xav tias ntawm qhov chaw P muaj qhov them kuaj zoo. Q₁ yog qhov zoo thiab Q₂ yog qhov tsis zoo, yog li ntawd qhov P yuav tsum nyob rau sab xis ntawm Q₂ los yog sab laug ntawm Q₁Yog tias qhov chaw P nyob rau sab laug ntawm Q₁lub zog hluav taws xob uas tsim los ntawm Q₁ ntawm qhov chaw P nyob rau sab laug (deb ntawm Q₁) thiab lub zog hluav taws xob uas tsim los ntawm Q₂ ntawm qhov chaw P mus rau sab xis (mus rau Q₁). Qhov kev taw qhia ntawm lub zog hluav taws xob yog qhov sib txawv kom ob lub zog hluav taws xob tshem tawm ib leeg kom lub zog hluav taws xob ntawm qhov chaw P yog xoom.

Paub:

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

Qhov nrug ntawm tus nqi 1 thiab tus nqi 2 = 3 cm

Qhov nrug ntawm Q ₁ thiab qhov chaw P (r _1P ) = a

Qhov nrug ntawm Q ₂ thiab qhov chaw P (r _2P ) = 3 + a

Xav tau: qhov chaw ntawm qhov P kom lub zog hluav taws xob ntawm qhov P yog xoom

Tshuaj:

Point P nyob rau sab laug ntawm Q ₁.

Lub teb hluav taws xob tsim los ntawm Q ₁ ntawm qhov chaw P:

Tus nqi sim yog qhov zoo thiab Q ₁ yog qhov zoo yog li qhov kev taw qhia ntawm lub teb hluav taws xob yog mus rau sab laug.

Lub teb hluav taws xob tsim los ntawm Q ₂ ntawm qhov chaw P:

Tus nqi kuaj yog qhov zoo thiab Q ₂ yog qhov tsis zoo yog li qhov kev taw qhia ntawm lub teb hluav taws xob yog mus rau sab xis.

Lub zog hluav taws xob ntawm qhov chaw A:

Siv cov qauv quadratic los txiav txim siab ib qho:

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

Qhov nrug ntawm Q ₂ thiab taw tes P (r _2P ) = 3 + a = 3 – 1.8 = 1.2 cm.

Point P nyob rau ntawm 1.2 cm sab xis ntawm Q ₁.

[irp]

nyeem ntxiv

1. Ob lub ntsiab lus them, Q_A = +8 μC thiab Q_B = -5 μC, sib cais los ntawm qhov deb r = 10 cm. Qhov loj ntawm qhov no yog dab tsi? lub zog hluav taws xobTus nqi tas mus li k = 8.988 x 10⁹ Nm²C^-2 Luas = 9 x 10⁹ Nm²C^-2.

Paub:

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

Them B (qB ₎ = -5 μC = -5 x 10 ^-6 C

k = 9 x 10 ⁹ Nm ² C ⁻²

Qhov nrug ntawm cov nqi A thiab B (r _AB ) = 10 cm = 0.1 m

Xav tau : Qhov loj ntawm lub zog hluav taws xob

Tshuaj:

Cov qauv ntawm Coulomb txoj cai :

Qhov loj ntawm lub zog fais fab:

[irp]

2. Ob lub khoom me me uas raug them raws li qhia hauv daim duab hauv qab no. Q _P = +10 μC thiab Q _q = +20 μC raug sib cais los ntawm qhov deb r = 10 cm. Lub zog electrostatic loj npaum li cas.

Paub:

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

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

k = 9 x 10 ⁹ Nm ² C ⁻²

Qhov nrug ntawm cov nqi P thiab Q (r _PQ ) = 12 cm = 0.12 m = 12 x 10 ^-2 m

Xav tau: Qhov loj ntawm lub zog hluav taws xob

Tshuaj:

[irp]

3. Peb lub khoom me me uas raug them tau teeb tsa ua kab raws li qhia hauv daim duab hauv qab no. Lub zog A = -5 μC, lub zog B = +10 μC thiab lub zog C = -12 μC. Xam lub zog electrostatic net rau ntawm lub khoom me me B vim yog ob lub zog ntxiv.

Paub:

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

Them B (qB ₎ = +10 μC = +10 x 10 ^-6 C

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

k = 9 x 10 ⁹ Nm ² C ⁻²

Qhov nrug ntawm cov khoom me me A thiab B (r _AB ) = 6 cm = 0.06 m = 6 x 10 ^-2 m

Qhov nrug ntawm cov khoom me me B thiab C (r _BC ) = 4 cm = 0.04 m = 4 x 10 ^-2 m

Xav tau: Qhov loj thiab qhov kev taw qhia ntawm lub zog electrostatic net rau ntawm cov khoom me me B

Tshuaj:

Lub zog net rau ntawm lub particle B yog qhov vector sum ntawm lub zog FBA _uas lub particle A siv rau ntawm lub particle B thiab lub zog FBC _uas lub particle C siv rau ntawm lub particle B.

Lub zog FBA _uas lub zog A siv rau ntawm lub khoom B:

 

Qhov kev taw qhia ntawm lub zog electrostatic taw tes rau lub particle A (taw tes rau sab laug).

Lub zog F _BC siv rau ntawm cov khoom me me B los ntawm cov khoom me me A:

 

Qhov kev taw qhia ntawm lub zog electrostatic taw tes rau lub particle C (taw tes rau sab xis).

Lub zog electrostatic net rau ntawm cov khoom B :

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

Qhov kev taw qhia ntawm lub zog electrostatic net rau ntawm cov khoom me me B taw tes rau cov khoom me me C (taw tes rau sab xis).

[irp]

4. +Q ₁ = 10 μC, +Q ₂ = 50 μC thiab Q ₃ raug sib cais raws li qhia hauv daim duab hauv qab no. Yog tias lub zog electrostatic ntawm lub khoom me me 2 yog xoom, tus nqi electrostatic ntawm cov khoom me me 3 yog dab tsi.

Paub:

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

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

Qhov nrug ntawm cov nqi 1 thiab 2 (r ₁₂ ) = 2 cm = 0.02 m = 2 x 10 ^-2 m

Qhov nrug ntawm tus nqi 2 thiab tus nqi 3 (r ₂₃ ) = 6 cm = 0.06 m = 6 x 10 ^-2 m

Lub zog electrostatic net rau ntawm cov khoom me me 2 (F2 ₎ = 0

Xav tau : them 3 (q ₃ )

Tshuaj:

Lub zog net rau ntawm lub particle 2 yog qhov vector sum ntawm lub zog F ₂₁ uas siv rau ntawm lub particle 2 los ntawm lub particle 1 thiab lub zog F ₂₃ uas siv rau ntawm lub particle 2 los ntawm lub particle 3.

Lub zog F ₂₁ siv rau ntawm lub khoom me me 2 los ntawm lub khoom me me 1:

Qhov kev taw qhia ntawm lub zog electrostatic taw tes rau lub khoom me me 3 (taw tes rau sab xis).

Lub zog F₂₃ siv rau ntawm cov khoom me me 2 los ntawm cov khoom me me 3: 

Qhov kev taw qhia ntawm lub zog electrostatic taw tes rau lub khoom me me 1 (taw tes rau sab laug).

Lub zog electrostatic net rau ntawm cov khoom me me 2 = 0:

nyeem ntxiv

1. Ib yam khoom uas muaj lub zog inertia ntawm 2 kg m2 tig ntawm 1 rad/s. ^Lub zog angular ntawm yam khoom yog dab tsi ?

Paub:

Lub sijhawm ntawm inertia (I) = 2 kg m ²

Qhov ceev ntawm lub kaum sab xis ( ω ) = 1 rad/s

Xav tau: Lub zog tig (L)

Tshuaj:

Cov qauv ntawm lub zog angular:

L = Kuv ω

L = lub zog ntawm lub kaum sab xis (kg m2 ^/ s), I = lub zog ntawm inertia (kg m2 ⁾ , ω = qhov ceev ntawm lub kaum sab xis (rad/s)

Lub zog ntawm lub angular:

L = Kuv ω = (2)(1) = 2 kg ^m2 /s

[irp]

2. Ib lub log uas hnyav 2 kg uas muaj lub vojvoog ntawm 0.1 m tig nrog lub kaum sab xis tas li ntawm 2 rad/s. Lub zog ntawm lub log yog dab tsi?

Paub:

Qhov hnyav ntawm lub pulley (m) = 2 k g

Lub vojvoog ntawm lub pulley (r) = 0.1 m

Qhov ceev ntawm lub kaum sab xis (ω) = 2 r ad/s

Xav tau: lub zog angular

Tshuaj:

Cov mis ntawm lub zog ntawm inertia rau lub tog raj kheej khov kho:

Kuv = 1/2 ^m2

Kuv = lub sijhawm ntawm inertia (kg m2 ⁾ , m = pawg (kg), r = radius (m)

Lub sijhawm ntawm inertia:

Kuv = 1/2 (2)(0.1) ² = (1)(0.01) = 0.01 kg ^m2

Qhov ceev ntawm lub kaum sab xis:

L = Kuv ω = ( 0.01 )( 2 ) = 0.02 kg m2 ^/ s

[irp]

3. Ib lub pob kheej kheej hnyav 2-kg uas muaj lub vojvoog ntawm 0.2 m tig ntawm 4 rad/s. Lub zog ntawm lub pob yog dab tsi.

Paub:

Qhov hnyav ntawm lub pob (m) = 2 kg

Lub vojvoog ntawm lub pob (r) = 0.2 m

Qhov ceev ntawm lub kaum sab xis (ω) = 4 ra d/s

Xav tau: lub zog angular

Tshuaj:

Cov mis ntawm lub zog ntawm inertia rau lub sphere sib xws:

Kuv = (2/5) mr ²

Kuv = lub sijhawm t ntawm inertia (kg m2 ⁾ , m = pawg (kg), r = radius (m)

Lub sijhawm ntawm inertia rau lub voj voog sib npaug:

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

Lub zog ntawm lub sphere:

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

[irp]

4. Ib lub khoom me me uas hnyav 1 kg tig nrog lub kaum sab xis tas li ntawm 2 rad/s. Yog tias lub vojvoog radius yog 10 cm, lub kaum sab xis yuav tig li cas.

Paub:

Qhov hnyav ntawm yam khoom (m) = 1 k g

Lub vojvoog ntawm lub vojvoog (r) = 10 cm = 10/100 = 0.1 m

Qhov ceev ntawm lub kaum sab xis (ω) = 2 rad/ s

Xav tau: lub zog angular

Tshuaj:

Cov mis ntawm lub sijhawm ntawm inertia rau cov khoom me me:

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

Lub zog angular:

L = Kuv ω = (0.01)(2) = 0.02 kg m2 ^/ s

nyeem ntxiv

1. Ib yam khoom muaj lub zog inertia ntawm 1 kg m2 tig ntawm qhov ceev ntawm 2 rad/s. ^Lub zog kinetic ntawm yam khoom yog dab tsi ?

Paub:

Lub sijhawm ntawm inertia ⁽ I) = 1 kg m2

Qhov ceev ntawm lub kaum sab xis ( ω) = 2 rad/s

Xav tau: Lub zog kinetic ntawm kev sib hloov ( KE )

Tshuaj:

Cov mis ntawm lub zog kinetic tig:

KE = 1/2 I ω ²

KE = lub zog kinetic ntawm kev sib hloov (kg/m²)²/s²), Kuv = lub sijhawm ntawm inertia (kg/m²)²), ω = qhov ceev ntawm lub kaum sab xis (rad/s)

Lub zog kinetic ntawm kev sib hloov:

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

[irp]

2. Ib lub log uas hnyav 20-kg uas muaj lub vojvoog ntawm 0.2 m tig ntawm qhov ceev ntawm lub kaum sab xis tas li ntawm 4 rad/s. Lub zog kinetic ntawm lub log yog dab tsi?

Paub:

Qhov hnyav ntawm lub tog raj kheej pulley (m) = 20 k g

Lub vojvoog ntawm lub tog raj kheej (r) = 0.2 m

Qhov ceev ntawm lub kaum sab xis (ω) = 4 ra d/s

Xav tau: Lub zog kinetic rotational yog dab tsi

Kev daws teeb meem;

Cov mis ntawm lub sijhawm ntawm inertia ntawm lub tog raj kheej:

Kuv = 1/2 ^m2

Kuv = lub sijhawm ntawm inertia ( kg m2 ⁾ , m = pawg (kg), r = radius (meters)

Lub sijhawm ntawm inertia ntawm lub tog raj kheej pulley:

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

Lub zog kinetic ntawm lub pulley:

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

[irp]

3. A- lub pob hnyav 10 kg uas muaj lub vojvoog ntawm 0.1 m tig ntawm qhov tsis hloov pauv ntawm 10 rad/s. Lub zog kinetic ntawm lub pob yog dab tsi.

Paub:

Qhov hnyav ntawm lub pob (m) = 10 kg

Lub vojvoog ntawm lub pob (r) = 0.1 m

Qhov ceev ntawm lub kaum sab xis (ω) = 10 r ad/s

Xav tau: Lub zog kinetic ntawm kev sib hloov

Tshuaj:

Cov mis ntawm lub sijhawm ntawm inertia:

Kuv = (2/5) mr ²

Kuv = lub sijhawm ntawm inertia (kg m2 ⁾ , m = pawg (kg), r = radius (m)

Lub sijhawm ntawm inertia ntawm lub pob:

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

Lub zog kinetic ntawm lub pob:

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

[irp]

4. Ib lub khoom me me uas hnyav 0.5- kg tig nrog lub kaum sab xis tas li ntawm 2 rad/s. Lub zog kinetic ntawm lub khoom me me yog dab tsi yog tias lub vojvoog radius ntawm lub voj voog yog 10 cm.

Paub:

Qhov hnyav ntawm cov khoom me me (m) = 0.5 k g

Lub vojvoog ntawm lub pob (r) = 10 cm = 10/100 = 0.1 m

Qhov ceev ntawm lub kaum sab xis (ω) = 2 rad/ s

Xav tau: Lub zog kinetic ntawm kev sib hloov

Tshuaj:

Lub sijhawm ntawm inertia rau cov khoom me me:

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

Lub zog kinetic ntawm kev sib hloov:

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

nyeem ntxiv

1. Lub zog F raug siv rau ib txoj hlua khi ib ncig ntawm lub tog raj kheej pulley. Lub torque yog 2 N m thiab lub moment of inertia yog 1 kg m ² , dab tsi yog qhov angular acceleration ntawm lub tog raj kheej.

Paub:

Lub zog tig ( τ ) = 2 N m

Lub sijhawm ntawm inertia (I) = 1 kg ^m2

Tom ntej: Kev ntsuas qhov ceev ntawm lub cylinder

Tshuaj:

Στ = I α

Στ = net torque, I = moment of inertia, α = angular acceleration

Kev nrawm ntawm lub tog raj kheej:

α = Στ / I = 2 / 1 = 2 rad/s ²

[irp]

2. Muaj lub zog F siv rau ib txoj hlua khi ib ncig ntawm lub tog raj kheej. Lub zog loj yog 10 N, lub vojvoog ntawm lub tog raj kheej yog 0.2 m thiab lub zog inertia yog 1 kg m 2, Lub zog nrawm ntawm lub tog raj kheej yog dab tsi ?

Paub:

Lub zog (F) = 10 N

Lub vojvoog ntawm lub tog raj kheej (R) = 0.2 m

Lub sijhawm ntawm inertia (I) = 1 kg ^m2

Xav tau: Qhov kev nrawm ntawm lub cylinder.

Tshuaj:

τ = FR

τ = torque, F = force, R = radius ntawm lub tog raj kheej

Lub zog tig:

τ = FR = (1 0 N)(0.2 m) = 2 N m

Στ = I α

Στ = net torque, I = moment of inertia, α = angular acceleration

Kev nrawm ntawm lub tog raj kheej:

α = Στ / I = 2 / 1 = 2 rad/s ²

[irp]

3. Lub zog F raug siv rau ib txoj hlua khi ib ncig ntawm lub tog raj kheej pulley. Lub zog loj yog 10 N, lub vojvoog ntawm lub tog raj kheej yog 0.2 m thiab qhov hnyav ntawm lub tog raj kheej yog 20 kg m ^2, . Lub kaum sab xis ntawm lub tog raj kheej yog dab tsi .

Paub:

Lub zog (F) = 10 N

Lub vojvoog ntawm lub tog raj kheej (R) = 0.2 m

Qhov hnyav ntawm lub tog raj kheej (M) = 20 kg

Xav tau: Angular acceleration ntawm lub cylinder

Tshuaj:

τ = FR = (1 0 N)(0.2 m) = 2 N m

Lub sijhawm ntawm inertia:

Kuv = 1/2 MR ² = 1/2 (20)(0.2) ² = 1/2 (20)(0.04) = 0.4 kg ^m2

Kev nrawm ntawm lub tog raj kheej:

α = Στ / I = 2 / 0.4 = 5 rad/s ²

[irp]

4. Ib lub thaiv hnyav 1-kg dai ntawm ib txoj hlua khi ib ncig ntawm lub log tsheb. Lub zog ntawm lub log tsheb yog 1 kg m2 thiab lub vojvoog ntawm lub log tsheb yog 0.2 m. Lub zog nrawm ntawm lub log tsheb yog dab tsi? Kev nrawm vim lub ntiajteb txawj nqus ^yog 10 m/ ^s2.

Paub:

Lub sijhawm ntawm inertia ntawm pulley (I) = 1 kg m ²

Qhov hnyav ntawm lub thaiv (m) = 1 kg

Kev nrawm vim lub ntiajteb txawj nqus (g) = 10 m/s ²

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

Lub vojvoog ntawm lub pulley (R) = 0.2 m

Xav tau: Angular acceleration

Tshuaj:

Lub zog tig:

τ = FR = w R = (1 0 N)(0.2 m) = 2 N m

Lub sijhawm ntawm inertia:

Kuv = 1 kg ^m2

Kev nrawm ntawm lub kaum sab xis:

α = Στ / I = 2 / 1 = 2 rad/s ²

[irp]

5. Ib lub thaiv hnyav 1-kg dai ntawm ib txoj hlua khi ib ncig ntawm lub pulley lub tog raj kheej. Qhov hnyav ntawm lub pulley yog 20 kg thiab lub vojvoog ntawm lub pulley yog 0,2 m. Qhov kev nrawm ntawm lub pulley thiab qhov kev nrawm ntawm lub thaiv yog dab tsi ? Kev nrawm vim lub ntiajteb txawj nqus yog 10 m/s ².

Paub:

Qhov hnyav ntawm lub pulley (M) = 20 kg

Lub vojvoog ntawm lub pulley (R) = 0,2 m

Qhov hnyav ntawm lub thaiv (m) = 1 kg

Kev nrawm vim lub ntiajteb txawj nqus (g) = 10 m/s ²

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

Xav tau: qhov kev nrawm ntawm lub pulley thiab qhov kev nrawm ntawm lub caij nplooj zeeg dawb.

Tshuaj:

Lub zog torque:

τ = FR = w R = (1 0 N)(0.2 m) = 2 N m

Lub sijhawm ntawm inertia ntawm lub tog raj kheej pulley:

Kuv = 1/2 MR ² = 1/2 (20)(0.2) ² = (10)(0.04) = 0.4 kg ^m2

Lub angular acceleration ntawm lub pulley:

α = Στ / I = 2 / 0.4 = 5 rad/s ²

Qhov kev nrawm ntawm lub block thaum lub caij nplooj zeeg dawb:

a = R α = (0.2)(5) = 1 m/s ²

nyeem ntxiv

Lub sijhawm ntawm inertia ntawm lub particle

1. Ib lub pob 100-gram txuas rau ib kawg ntawm txoj hlua uas ntev 30 cm. Lub zog ntawm lub pob ncig lub axis ntawm kev tig AB yog dab tsi? Tsis txhob xav txog qhov hnyav ntawm txoj hlua.

Paub:

Lub axis ntawm kev tig ntawm AB

Qhov hnyav ntawm lub pob (m) = 100 grams = 100/1000 = 0.1 kg

Qhov kev ncua deb ntawm lub pob thiab lub axis ntawm kev tig (r) = 30 cm = 0.3 m

Xav tau: Lub sijhawm ntawm inertia ntawm lub pob (I)

Tshuaj:

Kuv = mr ² = (0.1 kg)(0.3 m) ²

Kuv = (0.1 kg) (0.09 ^m2 )

Kuv = 0.009 kg ^m2

[irp]

2. Ib lub pob 100-gram, m ₁ , thiab ib lub pob 200-gram, m ₂ , txuas nrog ib tug pas nrig uas ntev 60 cm. Qhov hnyav ntawm tus pas nrig tsis raug tsis quav ntsej. Lub axis ntawm kev tig yog nyob rau hauv nruab nrab ntawm tus pas nrig. Lub moment of inertia ntawm lub pob ncig lub axis ntawm kev tig yog dab tsi?

Paub:

Qhov hnyav ntawm lub pob 1 (m ₁ ) = 100 grams = 100/1000 = 0.1 kg

Qhov nrug ntawm lub pob 1 thiab lub axis ntawm kev tig (r ₁ ) = 30 cm = 30/100 = 0.3 m

Qhov hnyav ntawm lub pob (m2 ₎ = 200 grams = 200/1000 = 0.2 kg

Qhov nrug ntawm lub pob 2 thiab lub axis ntawm kev tig (r ₂ ) = 30 cm = 30/100 = 0.3 m

Xav tau: lub sijhawm ntawm inertia ntawm cov pob

Lus teb:

Kuv = m ₁ r ₁ ² + m ₂ r ₂ ²

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

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

Kuv = 0.009 kg ^m2 + 0.018 kg ^m2

Kuv = 0.027 kg ^m2

[irp]

3. Ib lub pob 200-gram, m ₁ thiab ib lub pob 100-gram, m _2, txuas nrog ib tug pas nrig uas ntev 60 cm. Tsis txhob xav txog qhov hnyav ntawm tus pas nrig. Lub axis ntawm kev tig yog nyob ntawm lub pob m _2. Lub moment of inertia ntawm cov pob yog dab tsi. Tsis txhob xav txog qhov hnyav ntawm tus pas nrig.

Paub:

Qhov hnyav ntawm lub pob 1 (m ₁ ) = 2 00 grams = 200/1000 = 0.2 kg

Qhov nrug ntawm lub pob 1 thiab lub axis ntawm kev tig (r ₁ ) = 60 cm = 60/100 = 0.6 m

Qhov hnyav ntawm lub pob 2 (m ₂ ) = 100 grams = 100/1000 = 0.1 kg

Qhov nrug ntawm lub pob 2 thiab lub axis ntawm kev sib hloov (r ₂ ) = 0 m

Xav tau: Lub sijhawm ntawm inertia ntawm cov pob

Tshuaj:

Kuv = m ₁ r ₁ ² + m ₂ r ₂ ²

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

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

Kuv = 0.072 kg ^m2

[irp]

4. Qhov hnyav ntawm txhua lub pob yog 100 grams, txuas nrog txoj hlua. Qhov ntev ntawm txoj hlua yog 60 cm thiab qhov dav ntawm txoj hlua yog 30 cm. Lub sijhawm inertia ntawm lub pob ncig lub axis ntawm kev tig yog dab tsi. Tsis txhob xav txog qhov hnyav ntawm txoj hlua.

Paub:

Qhov hnyav ntawm lub pob = m ₁ = m ₂ = m ₃ = m ₄ = 1 00 grams = 100/1000 = 0.1 kg

Qhov nrug ntawm lub pob thiab lub axis ntawm kev sib hloov (r ₁ ) = 30 cm = 30/100 = 0.3 m

Qhov nrug ntawm lub pob 2 thiab lub axis ntawm kev tig (r ₂ ) = 30 cm = 30/100 = 0.3 m

Qhov nrug ntawm lub pob 3 thiab lub axis ntawm kev tig (r ₃ ) = 30 cm = 30/100 = 0.3 m

Qhov nrug ntawm lub pob 4 thiab lub axis ntawm kev tig (r ₄ ) = 30 cm = 30/100 = 0.3 m

Paub: Lub sijhawm ntawm inertia

Tshuaj:

Kuv = m₁ r₁² +m₂ r₂² +m₃ r₃² +m₄ r₄²

Kuv = (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

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

Kuv = 0.036 kg ^m2

[irp]

Lub sijhawm ntawm inertia ntawm ib yam khoom khov kho

5. Lub zog ntawm inertia ntawm ib tug pas nrig ntev 2-kg uas ntev li 2 m yog dab tsi? Lub axis ntawm kev tig nyob rau hauv nruab nrab ntawm tus pas nrig.

Paub:

Qhov hnyav ntawm tus pas nrig (M) = 2 kg

Qhov ntev ntawm tus pas nrig (L) = 2 m

Xav tau: Lub sijhawm ntawm inertia

Tshuaj:

Cov mis ntawm lub sijhawm ntawm inertia thaum lub axis ntawm kev sib hloov nyob rau hauv qhov chaw ntawm lub pas nrig ntev sib xws:

Kuv = (1/12) ML ²

Kuv = (1/12) (2 kg)( 2 m) ²

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

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

Kuv = 8/12 kg ^m2

Kuv = 2/3 kg ^m2

[irp]

6. Lub sijhawm inertia ntawm ib tug pas nrig ntev 2-kg uas ntev li 2 m yog dab tsi? Lub axis ntawm kev tig nyob ntawm ib kawg ntawm tus pas nrig.

Paub:

Qhov hnyav ntawm tus pas nrig (M) = 2 kg

Qhov ntev ntawm tus pas nrig (L) = 2 m

Xav tau: Lub sijhawm ntawm inertia

Tshuaj:

Cov mis rau lub sijhawm ntawm inertia thaum lub axis ntawm kev sib hloov nyob rau ntawm ib kawg ntawm tus pas nrig:

Kuv = (1/3) ML ²

Kuv = (1/3) (2 kg)( 2 m) ²

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

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

Kuv = 8/3 kg ^m2

[irp]

7. Ib lub tog raj kheej khov kho 10-kg nrog lub vojvoog ntawm 0.1 m. Lub axis ntawm kev tig nyob rau hauv nruab nrab ntawm lub tog raj kheej khov kho, qhia nyob rau hauv daim duab hauv qab no. Lub sijhawm ntawm inertia ntawm lub tog raj kheej yog dab tsi?

Paub:

Qhov hnyav ntawm lub tog raj kheej khov kho (M) = 10 kg

Lub vojvoog ntawm lub tog raj kheej (L) = 0.1 m

Xav tau: Lub sijhawm ntawm inertia

Xav tau: Lub sijhawm ntawm inertia

Tshuaj:

Cov mis ntawm lub zog ntawm inertia thaum lub axis ntawm kev sib hloov nyob rau hauv nruab nrab ntawm lub tog raj kheej:

Kuv = (1/2) MR ²

Kuv = (1/2) (10 kg)(0.1 m) ²

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

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

Kuv = 0.05 kg ^m2

8. Ib lub pob kheej kheej hnyav 20-kg ntev li 0.1 m. Lub axis ntawm kev tig nyob rau hauv nruab nrab ntawm lub pob kheej kheej tau qhia nyob rau hauv daim duab hauv qab no.

Paub:

Qhov hnyav ntawm lub pob (M) = 20 kg

Lub vojvoog ntawm lub pob (L) = 0.1 m

Xav tau: lub sijhawm ntawm inertia

Tshuaj:

Cov mis ntawm lub sijhawm ntawm inertia thaum lub axis ntawm kev sib hloov nyob rau hauv qhov chaw ntawm lub sphere:

Kuv = (2/5) MR ²

Kuv = (2/5)(20 kg)(0.1 m) ²

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

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

Kuv = 0.4/5 kg ^m2

Kuv = 0.08 kg ^m2

[irp]

9. Ib lub phaj nyias plaub fab hnyav 2-kg uas ntev 0.5 m thiab dav 0.2 m. Lub axis ntawm kev tig nyob hauv nruab nrab ntawm lub phaj plaub fab uas pom hauv daim duab hauv qab no. Lub sijhawm inertia ntawm lub duab plaub fab yog dab tsi?

Paub:

Qhov hnyav ntawm lub phaj plaub fab (M) = 2 kg

Qhov ntev ntawm lub phaj (a) = 0.5 m

Qhov dav ntawm lub phaj (b) = 0.2 m

Xav tau: Lub sijhawm ntawm Inertia

Tshuaj:

Cov mis ntawm lub zog ntawm inertia thaum lub axis ntawm kev sib hloov nyob rau hauv nruab nrab ntawm lub phaj:

Kuv = (1/ 12 ) M ( ^a2 + ^b2 )

Kuv = (1/12)(2)(0.5 ² + 0.2 ² )

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

Kuv = (1/6)(0.29)

Kuv = 0.29/6 kg ^m2

nyeem ntxiv