Nā pilikia i hoʻoponopono ʻia ma ke ʻano Physics kumu

1. A capacitor pā-like i loiloi mua ka mana C, ka permittivity o kahi kūʻokoʻa is ε_o, wahi pā is A, ka mamao ma waena o nā papa is d. Ināe ua hoʻonui ʻia ka ʻāpana o ka pā i 4 mau manawa, ʻo ka mamao ma waena o nā pā lilo i 2d a ka permittivity o kahi ākea kūʻokoʻa ʻo 5 kēiaε_o, he aha ka mana hope loa o ka capacitor parallel-plate.

ʻIke ʻia:

Ka mana o ka capacitor = C

Tka permittivity o kahi ākea kūʻokoʻa = ε_o

Pwahi lohi =A

ka mamao ma waena o nā papa = d

Makemake: Ka mana o ka capacitor (C)

Lōlā:

2. ʻO ka capacitor nona ka mana nui loa e pili ana i ke kiʻi ma lalo nei is...

Lōlā:

ʻO ke ʻano o ka capacitor parallel-plate:

Ka mana o nā capacitors:

ʻO ka capacitor nona ka capacitor nui loaʻO y ka capacitor C_3.

3.

E noʻonoʻo i nā kumu aʻe!
(1) Paʻa mau o ka dielectric
(2)ʻO ʻokoʻa hiki ma waena o nā papa
(3) Pā tʻokiʻoki
(4) Ka ʻili o ka pā
(5) Ka mamao ma waena o nā papa
(6) Ka nui o uku uila
Nā mea e pili ana i ka hiki o nā papa like ʻO nā capacitors…

Lōlā:

(1), (4) a me (5)

4. ʻO ka hoʻohālikelike ʻana o ka mana o ka capacitor 1 a me 2…

ʻIke ʻia:

ʻO ka mea koho 1:

ʻĀpana ʻili = 2A

Ka mamao ma waena o nā papa =d₁

ʻO ka mea koho 2:

ʻĀpana ʻili =A

Ka mamao ma waena o nā papa = 2 lā₁

Makemake: ʻO ka hoʻohālikelike ʻana o ka mana o nā capacitors 1 a me 2

Lōlā:

5.

E hoʻoholo i ka hoʻohālikelike ʻana o ka hiki o Nā capacitors pā like ʻole I a me II.

Lōlā:

Hoʻohālikelike ʻana i ka hiki o Nā capacitors pā like ʻole I a me II:

6. ʻElua mau capacitors pā like i hōʻike ʻia ma ke kiʻi ma lalo nei.

Inā ʻo A₁ = ½ A₂ e d₂ = 3 lā₁ alaila, hooholo ka lakio o nā hiki o ke ʻano like-pā capacitor ma waena o ke kiʻi 2 a me ke kiʻi 1.

ʻIke ʻia:

Ka mea hoʻopili pā-like I:

A₁ = 1

d₁ = 1

Ka mea hoʻopili pā like II:

A₂ = 2

d₂ = 3

Makemake: ka lakio o nā mana o ka capacitor parallel-plate ma waena o ke kiʻi 2 a me ke kiʻi 1

Lōlā:

Ka mea hoʻopili pā-like I:

Ka mea hoʻopili pā like II:

Tka lakio o nā hiki o ke ʻano likepā capacitor II a me I:

heluhelu hou

1. E hoʻoholo i ka hiki ke uila ma kahi kiko i loaʻa ma 1 kenimika mai kahi hoʻouku 5.0 μC. ʻO ke kūpaʻa Coulomb (k) = 9 x 10⁹ Nm²C^-2, 1 μC = 10^-6 C.

ʻIke ʻia:

Ka mamao mai ka uku ʻana (r) = 1 kenimika = 1/100 m = 0.01 m = 10^-2 m

kauoha (q) = 5.0 μC = 5.0 x 10^-6 C

Paʻa Coulomb (k) = 9 x 10⁹ Nm²C^-2

Makemake ʻia: Ka hiki ke uila (V)

Lōlā:

Ka hiki ke uila:

ʻO ka hiki ke uila 4.5 m 10⁶ Volt

2. kauoha Q₁ = 5.0 μC a hoʻouku Q₂ = 6.0 μC. ʻO ke kūpaʻa o Coulomb (k) = 9 x 10⁹ Nm²C^-2, 1 μC = 10^-6 C. Aia ke kiko A ma waena o nā uku. E hoʻoholo i ka hiki ke uila ma ke kiko A.

ʻIke ʻia:

kauoha Q₁ = -5.0 μC = -5.0 x 10^-6 C

ka mamao o ke kiko A mai Q₁ = 10 kenimika = 0.1 m = 10^-1 m

kauoha Q₂ = 6.0 μC = 6.0 x 10^-6 C

Ka mamao o ke kiko a mai Q₂ = 10 kenimika = 0.1 m = 10^-1 m

ʻO ke kūpaʻa o Coulomb (k) = 9 x 10⁹ Nm²C^-2

Makemake ʻia: Ka hiki ke uila ma ke kiko A

Lōlā:

Ka hiki ke uila 1 :

Ka hiki ke uila 2 :

Ka hiki ke uila ma ke kiko A :

V = V₂ - V₁

V = (54 – 45) x 10⁴

V = 9 x 10⁴

3. kauoha q₁ = 5.0 μC a hoʻouku q₂ = 6.0 μC. ʻO ke kūpaʻa o Coulomb (k) = 9 x 10⁹ Nm²C^-2, 1 μC = 10^-6 C. E hoʻoholo i ka hiki ke uila ma ke kiko A.

ʻIke ʻia:

kauoha Q₁ = -5.0 μC = -5.0 x 10^-6 C

Ka mamao o ke kiko A mai Q₁ = 40 kenimika = 0.4 m = 4 x 10^-1 m

kauoha Q₂ = 6.0 μC = 6.0 x 10^-6 C

Ka mamao o ke kiko A mai Q₂ = 50 kenimika = 0.5 m = 5 x 10^-1 m

ʻO ke kūpaʻa o Coulomb (k) = 9 x 10⁹ Nm²C^-2

Makemake ʻia: Ka hiki ke uila ma kahi kiko A

Lōlā:

Ka hiki ke uila 1 :

Ka hiki ke uila 2 :

Ka hiki ke uila ma ke kiko A :

V = V₁ + V₂

V = (-11.25 + 10.8) x 10⁴

V = -0.45 x 10⁴

V = -4.5 x 10³

ʻO ka hiki ke uila ma ke kiko A -4.5 x 10³ Volt

heluhelu hou

1. Hoʻolalelale ʻia kahi uila mai ka hoʻomaha ma o kahi ʻokoʻa hiki o 12 V. He aha ka loli o ikehu hiki ke uila o ka uila?

ʻIke ʻia:

ka haawe ma luna o kahi uila (e) = -1.60 x 10^-19 ʻO Coulomb

Ka hiki ke uila = anakahi uila (V) = 12 Volt

Makemake: ʻO ka loli o ka ikehu hiki ke uila o ka electron (ΔPE)

Lōlā:

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

Hōʻike ka hōʻailona minus e emi ana ka ikehu hiki.

2. Ua hoʻouka ʻia ʻelua mau papa like. ʻO ka mamao ma waena o nā papa he 2 cm a ʻo ka nui o kahua uila ma waena o nā papa he 500 Volt/mika. He aha ka loli o ka ikehu hiki o ka proton i ka wā e hoʻolalelale ʻia ai mai ka papa i hoʻopiʻi maikaʻi ʻia i ka papa i hoʻopiʻi maikaʻi ʻole ʻia.

ʻIke ʻia:

ʻO ka nui o ke kahua uila ma waena o nā papa (E) = 500 Volt/mika

ka mamao ma waena o nā papa (s) = 2 kenimika = 0,02 m

ʻO ke kumukūʻai ma luna o ka proton = +1.60 x 10^-19 ʻO Coulomb

Makemake ʻia: Ka loli o ka ikehu hiki ke uila (ΔPE)

Lōlā:

Ka hiki ke uila:

V = E s

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

V = 10 Volt

Ka loli o ka ikehu hiki ke uila:

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. Ua hoʻokaʻawale ʻia nā uku kiko ʻelua ma kahi mamao o 10 kenimika. ʻO ka uku ma ke kiko A =+9 μC a me ka hoʻouka ma ke kiko B = -4 μC. k = 9 x 10⁹ Nm²C^-2, 1 μC = 10^-6 C. He aha ka loli o ka ikehu hiki ke uila o ka uku ma ke kiko B inā e hoʻolalelale ʻia i ke kiko A?

ʻIke ʻia:

Hoʻopiʻi A (q₁) = +9 µC = +9 x 10^-6 C

kauoha B (q₁) = -4 μC = -4 x 10^-6 C

k = 9 x 10⁹ Nm²C^-2

ʻO ka mamao ma waena o nā uku A a me B (r) = 10 kenimika = 0.1 m = 10^-1 m

Makemake ʻia: Ka loli o ka ikehu hiki ke uila (ΔEP)

Lōlā:

heluhelu hou

1. He ʻaʻahu like kahua uila E = 8000 N/C e hele ana ma waena o kahi ʻāpana huinahā pālahalaha A = 10 m². E hoʻoholo i ka kahe uila.

ʻIke ʻia:

ʻO ka nui o ke kahua uila (E) = 8000 N/C

ʻĀpana (A) = 10 m²

θ = 0^o (ke kihi ma waena o ke kuhikuhi o ke kahua uila a me kahi laina i kaha ʻia i kū pololei i ka ʻāpana)

Makemake: Kahe uila ((Φ)

Lōlā:

ʻO ke ʻano o ka flux uila:

Φ = EA cos q

Φ = kahe uila (Nm²/C), E = kahua uila (N/C), A = wahi (m²), q = ke kihi ma waena o ka laina kahua uila me ka laina maʻamau.

Kahe uila:

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

2. ʻO kahi kahua uila like E = 5000 N/C e hele ana ma kahi ʻāpana huinahā pālahalaha A = 2 m². E hoʻoholo i ke kahe uila.

ʻIke ʻia:

Kahua uila (E) = 5000 N/C

ʻĀpana (A) = 2 m²

θ = 60^o (ke kihi ma waena o ke kuhikuhi o ke kahua uila a me kahi laina i kaha ʻia i kū pololei i ka ʻāpana)

Makemake ʻia: Kahe uila ((Φ)

Lōlā:

Kahe uila:

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

3. He pōpō paʻa me ka radius 0.5 mika he 10 μC ka uku uila ma kona kikowaena. E hoʻoholo i ke kahe uila e hele ana ma o ka pōpō paʻa.

ʻIke ʻia:

Ka laulā o ka pōpō (r) = 0.5 m

Kela uila (Q) = 10 μC = 10 x 10^-6 C

Makemake ʻia: Kahe uila ((Φ)

Lōlā:

Kahua uila:

E = kq/r²

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

E = (90 x 10³) / 0,25

E = 360 x 10³

E = 3.60 x 10⁵ N / C

ʻĀpana ʻili:

A=4 pi r² = 4 (3.14)(0.5)² = (12.56)(0.25) = 3.14 mika²

Kahe uila:

Kū pololei nā laina kahua uila i ka ʻāpana, no laila ʻo ke kihi ma waena o ke kuhikuhi o ke kahua uila a me kahi laina i kaha ʻia e kū pono ana i ka ʻāpana, ʻo ia 0^o.

Φ = EA cos q

Φ = (3.60 m 10⁵)(3.14)(cos 0)

Φ = (11.304 x 10⁵)(1)

Φ = 11.304 x 10⁵

Φ = 1.13 x 10⁶ Nm²/C

heluhelu hou

1. E helu i ka ka nui a me ke kuhikuhi o ke kahua uila ma kahi kiko A i loaʻa ma 5 kenimika mai kahi kiko hoʻouku Q = 10 + μC. k = 9 x 10⁹ Nm²C^-2, 1 μC = 10^-6 C)

ʻIke ʻia:

Kela uila (Q) = 10 + µC = 10 + x 10^-6 C

ka mamao ma waena o ke kiko A a me ke kiko hoʻouku Q (r_A) = 5 kenimika = 0.05 m = 5 x 10^-2 m

k = 9 x 10⁹ Nm²C^-2

Makemake: ʻO ka nui a me ke kuhikuhi o ka kahua uila ma kahi kiko A

Lōlā:

ʻO ke kuhikuhi o ke kahua uila ma ke kiko A:

He maikaʻi ka hoʻouku uila no laila ua mamao aku ke kuhikuhi o ke kahua uila mai ka hoʻouku uila a me nā kiko A.

2. E helu i ka nui a me ke kuhikuhi o ke kahua uila ma kahi kiko P i loaʻa ma 10 cm mai kahi hoʻouku kiko Q = -20 μC. k = 9 x 10⁹ Nm²C^-2, 1 μC = 10^-6 C.

ʻIke ʻia:

Uku uila (q) = -20 µC = -20 x 10^-6 C

ʻO ka mamao ma waena o ke kiko P a me ka uku uila (r_P) = 10 kenimika = 0.1 m = 1 x 10^-1 m

k = 9 x 10⁹ Nm²C^-2

Makemake: ʻO ka nui a me ke kuhikuhi o ke kahua uila ma kahi kiko P

Lōlā:

Ke kuhikuhi o ke kahua uila ma ke kiko A:

He maikaʻi ʻole ka hoʻouku uila no laila ke kuhikuhi o ke kahua uila i ka hoʻouku uila.

3. Ua hoʻokaʻawale ʻia nā uku kiko ʻelua e kahi mamao o 40 kenimika. He aha ka nui a me ke kuhikuhi o ke kahua uila ma ke kiko P ma waena o nā uku ʻelua, ʻo ia hoʻi he 20 kenimika mai ke kiko A?

ʻIke ʻia:

Hoʻopiʻi A (q_A) = -2 µC = -2 x 10^-6 C

Hoʻopiʻi B (q_B) = +4 µC = +4 x 10^-6 C

ʻO ka mamao ma waena o ka uku A a me ke kiko P (r_AP) = 20 kenimika = 0.2 m = 2 x 10^-1 m

ʻO ka mamao ma waena o ka uku B a me ke kiko P (r_BP) = 20 kenimika = 0.2 m = 2 x 10^-1 m

Makemake ʻia: ʻO ka nui a me ke kuhikuhi o ke kahua uila ma kahi P.

Lōlā:

He maikaʻi ʻole ke kumukūʻai A i ʻole ke kuhikuhi ʻana o nā kiko o ke kahua uila iā Q_A (ma ka hema).

He maikaʻi ke kumukūʻai B i ʻole e mamao aku ke kuhikuhi o nā kiko o ke kahua uila mai Q_B (ma ka hema).

ʻO ke kahua uila holoʻokoʻa ma ke kiko A:

ʻE = ʻE_A + E._B

E = (4.5 x 10⁵) + (9 x 10⁵)

E = 13.5 x 10⁵ N / C

Kuhikuhi ke kuhikuhi o ke kahua uila iā Q_A (ma ka hema).

4. ʻO ka nui o ke kahua uila he ʻole ma…

He maikaʻi ka hoʻopiʻi A a he maikaʻi ka hoʻopiʻi B no laila aia ka nui o ke kahua uila ma ka ʻole. ma ke kiko P, ma waena o nā uku ʻelua.

ʻIke ʻia:

kauoha ʻA (q_A) = +20 μC = +20 x 10^-6 C

kauoha B (q_B) = +40 μC = +40 x 10^-6 C

k = 9 x 10⁹ Nm²C^-2

Ka mamao ma waena o nā uku A a me ke kumukūʻai B = 20 kenimika

ʻO ke kumukūʻai ma waena o ke kumukūʻai A a me ke kiko P (r_AP) = a

Ka mamao ma waena o ka uku B a me ke kiko P (r_BP) = 20 – a

Makemake ʻia: ʻO ka nui o ke kahua uila he ʻole aia ma….

Lōlā:

ʻO ka nui o ke kahua uila i hana ʻia e ka uku A ma kahi P

He maikaʻi ke kumukūʻai A i ʻole e mamao aku ke kuhikuhi o nā kiko o ke kahua uila mai ka kumukūʻai A (i ka ʻākau).

ʻO ka nui o ke kahua uila i hana ʻia e ka uku B ma kahi P:

He maikaʻi ka hoʻouku B i ʻole e mamao aku ke kuhikuhi o nā kiko kahua uila mai ka hoʻouku B (ma ka hema).

ʻO ke kahua uila holoʻokoʻa ma ke kiko P = 0:

Hoʻohana mākou i ke ʻano haʻilula quadratic e hoʻoholo ai i ka a.

ʻO ka nui o ke kahua uila he ʻole aia ma 8 kenimika mai ka hoʻopiʻi A a i ʻole 12 kenimika mai ka hoʻopiʻi B.

5Ma muli o ke kiʻi ma lalo nei, weia ke kiko P i ʻole ai ke kahua uila ma ke kiko P he ʻole? (k = 9 x 10⁹ Nm²C^-2, 1 μC = 10^-6 C)

pāʻoihana

Te helu i ka ikaika o ke kahua uila ma kahi P, me ka manaʻo ma kahi P aia kahi hoʻouku hoʻāʻo maikaʻi. Q₁ he maikaʻi a ʻo Q₂ he maikaʻi ʻole, no laila pono ke kiko P ma ka ʻākau o Q₂ a i ʻole ma ka hema o Q₁Inā aia ke kiko P ma ka hema o Q₁; ke kahua uila i hana ʻia e Q₁ ma ke kiko ʻo P ma ka hema (mamao aku o Q₁) a me ke kahua uila i hana ʻia e Q₂ ma ke kiko P ma ka ʻākau (e pili ana iā Q₁). ʻOkoʻa ke kuhikuhi o ke kahua uila i hoʻopau ai nā kahua uila ʻelua kekahi i kekahi i ʻole ka ikaika o ke kahua uila ma ke kiko P he ʻole.

ʻIke ʻia:

Q₁ = +9 μC = +9 x 10^-6 C

Q₂ = -4 μC = -4 x 10^-6 C

k = 9 x 10⁹ Nm²C^-2

Ka mamao ma waena o ka hoʻouka kaua 1 a me ka hoʻouka kaua 2 = 3 kenimika

Ka mamao ma waena o Q₁ a me ke kiko P (r_1P) = a

Ka mamao ma waena o Q₂ a me ke kiko P (r_2P) = 3 + a

Makemake ʻia: kahi o ke kiko P i hiki ai ʻole ke kahua uila ma ke kiko P

Lōlā:

PAia ke kiko P ma ka ʻaoʻao hema o Q₁.

ʻO ke kahua uila i hana ʻia e Q₁ ma ke kiko P:

He maikaʻi ka uku hoʻāʻo a ʻo Q₁ he maikaʻi i ʻole ke kuhikuhi o ke kahua uila ma ka hema.

ʻO ke kahua uila i hana ʻia e Q₂ ma ke kiko P:

He maikaʻi ka uku hoʻāʻo a ʻo Q₂ he maikaʻi ʻole i ʻae ʻia ke kuhikuhi o ke kahua uila i ka ʻākau.

Kahua uila ʻupena ma ke kiko A:

E hoʻohana i ke ʻano quadratic e hoʻoholo ai i kahi:

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

Ka mamao ma waena o Q₂ a me ke kiko P (r_2P) = 3 + a = 3 – 1.8 = 1.2 kenimika.

Aia ke kiko P ma ka ʻākau o 1.2 kenimika o Q₁.

heluhelu hou

1. ʻElua mau hoʻopiʻi kiko, Q_A = +8 μC a me Q_B = -5 μC, ua hoʻokaʻawale ʻia e kahi mamao r = 10 cm. He aha ka nui o ka ikaika uilaʻO ke kūpaʻa k = 8.988 x 10⁹ Nm²C^-2 = 9x10⁹ Nm²C^-2.

ʻIke ʻia:

kauoha ʻA (q_A) = +8 μC = +8 x 10^-6 C

Hoʻopiʻi B (q_B) = -5 μC = -5 x 10^-6 C

k = 9 x 10⁹ Nm²C^-2

ka mamao ma waena o ke kumukūʻai A a me B (r_AB) = 10 kenimika = 0.1 m

makemake : Ka nui o ka ikaika uila

Lōlā:

Haʻilula o Kānāwai Coulomb :

Ka nui o ka ikaika uila:

2. ʻElua mau ʻāpana i hoʻouka ʻia e like me ka mea i hōʻike ʻia ma ke kiʻi ma lalo nei. Q_P = +10 μC a me Q_q = +20 µC ua hoʻokaʻawale ʻia e kahi mamao r = 10 cm. He aha ka nui o ka ikaika electrostatic.

ʻIke ʻia:

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

Hoʻopiʻi Q (Q_Q) = +20 μC = +20 x 10^-6 C

k = 9 x 10⁹ Nm²C^-2

Ka mamao ma waena o nā uku P a me Q (r_PQ) = 12 kenimika = 0.12 m = 12 x 10^-2 m

Makemake ʻia: Tka nui o ka ikaika uila

Lōlā:

3. Ua hoʻonohonoho ʻia ʻekolu mau ʻāpana i hoʻopiʻi ʻia ma kahi laina e like me ka mea i hōʻike ʻia ma ke kiʻi ma lalo nei. ʻO ke kumukūʻai A = -5 μC, ʻo ke kumukūʻai B = +10 μC a me ke kumukūʻai C = -12 μC. E helu i ka ikaika electrostatic net ma ka ʻāpana B ma muli o nā kumukūʻai ʻelua ʻē aʻe.

ʻIke ʻia:

Hoʻopiʻi A (q_A) = -5 μC = -5 x 10^-6 C

Hoʻopiʻi B (q_B) = +10 μC = +10 x 10^-6 C

Hoʻopiʻi C (q_C) = -12 μC = -12 x 10^-6 C

k = 9 x 10⁹ Nm²C^-2

ʻO ka mamao ma waena o nā ʻāpana A a me B (r_AB) = 6 kenimika = 0.06 m = 6 x 10^-2 m

ʻO ka mamao ma waena o nā ʻāpana B a me C (r_BC) = 4 kenimika = 0.04 m = 4 x 10^-2 m

Makemake ʻia: ʻO ka nui a me ke kuhikuhi o ka ikaika electrostatic net ma ka ʻāpana B

Lōlā:

ʻO ka ikaika ʻupena ma ka ʻāpana B ka huina vector o ka ikaika F_BA i hoʻokau ʻia ma luna o ka ʻāpana B e ka ʻāpana A a me ka ikaika F_BC i hoʻokau ʻia ma luna o ka ʻāpana B e ka ʻāpana C.

ʻO ka ikaika F_BA i hoʻokau ʻia ma luna o ka ʻāpana B e ka ʻāpana A:

 

Kuhikuhi ke kuhikuhi o ka ikaika electrostatic i ka ʻāpana A (kuhikuhi i ka hema).

ʻO ka ikaika F_BC i hoʻokau ʻia ma luna o ka ʻāpana B e ka ʻāpana A:

 

Kuhikuhi ke kuhikuhi o ka ikaika electrostatic i ka ʻāpana C (kuhikuhi i ka ʻākau).

ʻO ka ikaika electrostatic net ma ka ʻāpana B :

F_B =F_AB - F_BC = 675 N – 125 N = 550 Newtons.

ʻO ke kuhikuhi o ka ikaika electrostatic upena ma ka ʻāpana B e kuhikuhi ana i ka ʻāpana C (e kuhikuhi ana i ka ʻākau).

4. +Q₁ = 10 μC, +Q₂ = 50 μC a me Q₃ ua hoʻokaʻawale ʻia e like me ka mea i hōʻike ʻia ma ke kiʻi ma lalo nei. He aha ka uku electrostatic ma ka ʻāpana 3 inā ʻaʻohe ka ikaika electrostatic net ma ka ʻāpana 2.

ʻIke ʻia:

Hoʻouka 1 (q₁) = +10 μC = +10 x 10^-6 C

Hoʻouka 2 (q₂) = +50 μC = +50 x 10^-6 C

ʻO ka mamao ma waena o nā uku 1 a me 2 (r₁₂) = 2 kenimika = 0.02 m = 2 x 10^-2 m

ʻO ka mamao ma waena o ka uku 2 a me ka uku 3 (r₂₃) = 6 kenimika = 0.06 m = 6 x 10^-2 m

ʻO ka ikaika electrostatic net ma ka ʻāpana 2 (F₂) = 0

makemake : hoʻouka 3 (q₃)

Lōlā:

ʻO ka ikaika upena ma ka ʻāpana 2 ka veme ka huina o ka ikaika F₂₁ i hoʻokau ʻia ma ka ʻāpana 2 e ka ʻāpana 1 a me ka ikaika F₂₃ i hoʻokau ʻia ma luna o ka ʻāpana 2 e ka ʻāpana 3.

ʻO ka ikaika F₂₁ i hoʻokau ʻia ma ka ʻāpana 2 e ka ʻāpana 1:

Kuhikuhi ke kuhikuhi o ka ikaika electrostatic i ka ʻāpana 3 (kuhikuhi i ka ʻākau).

ʻO ka ikaika F₂₃ i hoʻokau ʻia ma ka ʻāpana 2 e ka ʻāpana 3: 

Kuhikuhi ke kuhikuhi o ka ikaika electrostatic i ka ʻāpana 1 (kuhikuhi i ka hema).

ʻO ka ikaika electrostatic net ma ka ʻāpana 2 = 0:

heluhelu hou

1. He mea me ka manawa o ka inertia of 2 kg m² hoʻohuli ma 1 rad/s. He aha ka ka ikaika kihi o ka mea?

ʻIke ʻia:

Manawa o ka inertia (I) = 2 kg m²

Ka wikiwiki kihi (ω) = 1 rad/s

Makemake ʻia: ʻO ka manaʻo kihikihi (L)

Lōlā:

ʻO ke ʻano o ka momentum angular:

L =I ω

L= ka ikaika kihi (kg m²/s), ʻo wau = manawa o ka inertia (kg m²), ω = wikiwiki kihi (rad/s)

ʻO ka momentum angular:

L =I ω = (2)(1) = 2 kg m²/s

2. 2-kg ka pulley cylinder me ka radius o 0.1 ka m hoʻohuli i ka wikiwiki angular mau o 2 rad/s. He aha ka momentum angular o ka pulley?

ʻIke ʻia:

Ka Mass o ka pulley (M) = 2kg

Ka radius o ka pulley (r) = 0.1 mika

Ka wikiwiki kihi (ω) = 2 rhoʻolaha

Makemake ʻia: ʻO ka manaʻo kihikihi

Lōlā:

ʻO ke ʻano o ka manawa o ka inertia no ka cylinder paʻa:

I = 1/2 mr²

I = manawa o ka inertia (kg m²), m = nuipa (kg), r = radius (M)

Manawa o ka inertia:

ʻO wau = 1/2 (2)(0.1)² = (1)(0.01) = 0.01 kg m²

ʻO ka wikiwiki kihi:

L =I ω = (0.01)(2) = 0.02 kg m²/s

3. He poepoe like 2-kg me ka radius o 0.2 ka m hoʻohuli ma 4 rad/s. He aha ka momentum angular o ka pōpō.

ʻIke ʻia:

Ka Mass o ka pōpō (M) = 2 kg

Ka laulā o ka pōpō (r) = 0.2 mika

Ka wikiwiki kihi (ω) = 4 rad/s

Makemake ʻia: ʻO ka manaʻo kihikihi

Lōlā:

ʻO ke ʻano o ka manawa o ka inertia no ka poepoe like:

I = (2/5) Mr.²

ʻO wau = manawat o ka inertia (kg m²), m = ka nuipaʻa (kg), r = radius (M)

ʻO ka manawa o ka inertia no ka poepoe like:

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

ʻO ka momentum angular o ka sphere:

L = I ω = (0.032)(4) = 0.128 kg m²/s

4. A 1 kg wili ka ʻāpana i ka wikiwiki angular mau o 2 rad/s. He aha ka wikiwiki angular inā he 1 ka radius o ka pōʻai0 wm.

ʻIke ʻia:

Ka Mass o ka mea (M) = 1kg

ʻO ke anawaena o ka pōʻai (r) = 10 kenimika = 10/100 = 0.1 mika

Ka wikiwiki kihi (ω) = 2 rad/s

Makemake ʻia: ʻO ka manaʻo kihikihi

Lōlā:

ʻO ke ʻano o ka manawa o ka inertia no nā ʻāpana:

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

Ka ikaika kihi:

L = I ω = (0.01)(2) = 0.02 kg m²/s

heluhelu hou

1. Loaʻa i kahi mea manawa o ka inertia o 1 kg m² hoʻohuli i ka wikiwiki angular mau o 2 rad/s. He aha ka ikehu kinetic wili o ka mea?

ʻIke ʻia:

ʻO ka manawa o ka inertia (I) = 1 kg m²

ka holo wikiwiki angular (ω) = 2 rad / s

Makemake: ʻO ka ikehu kinetic rotational (KE)

Lōlā:

ʻO ke ʻano o ka ikehu kinetic rotational:

KE = 1/2 ʻI ω²

KE = ka ikehu kinetic rotational (kg m²/s²), ʻo wau = ka manawa o ka inertia (kg m²), ω = ka wikiwiki kihi (rad/s)

ʻO ka ikehu kinetic rotational:

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

2. He 20-kg kaʻa wili paukūʻolokaʻa me ka radius o 0.2 m e wili ana i ka wikiwiki angular mau o 4 rad/s. He aha ka ikehu kinetic rotational o ka pulley?

ʻIke ʻia:

Ka Mass o ka pulley cylinder (M) = 20kg

ʻO ke anawaena o ka cylinder (r) = 0.2 mika

Ka wikiwiki kihi (ω) = 4 rad/s

Makemake ʻia: He aha ka ikehu kinetic rotational

Hoʻonā;

ʻO ke ʻano o ka manawa o ka inertia o ka cylinder:

I = 1/2 mr²

I = ka manawa o ka inertia (kg m²), m = ka nuipaʻa (kg), r = radius (mika)

ʻO ka manawa inertia o ka pulley cylinder:

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

ʻO ka ikehu kinetic rotational o ka pulley:

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

3. A-10 kg pōpō me ka radius o 0.1 ka m hoʻohuli ma kahi wikiwiki mau o 10 rad/s. He aha ka ikehu kinetic o ka pōpō.

ʻIke ʻia:

Ka Mass o ka pōpō (M) = 10 kg

Ka laulā o ka pōpō (r) = 0.1 mika

ʻO ka wikiwiki wikiwiki (ω) = 10 rhoʻolaha

Makemake ʻia: ʻO ka ikehu kinetic rotational

Lōlā:

Ke ʻano o ka manawa o ka inertia:

I = (2/5) Mr.²

I = manawa o ka inertia (kg m²), m = ka nuipaʻa (kg), r = radius (M)

Ka manawa o ka inertia o ka pōpō:

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

ʻO ka ikehu kinetic rotational o ka pōpō:

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

4. A 0.5-e wili ana nā ʻāpana kg i ka wikiwiki angular mau o 2 rad/s. He aha ka ikehu kinetic rotational o ka ʻāpana inā ʻo ka radius o ka pōʻai 10 wm.

ʻIke ʻia:

Ka Mass o ka ʻāpana (M) = 0.5kg

ʻO ke anawaena o ka pōpō (r) = 10 kenimika = 10/100 = 0.1 mika

Ka wikiwiki kihi (ω) = 2 rad/s

Makemake ʻia: ʻO ka ikehu kinetic rotational

Lōlā:

Manawa o ka inertia no nā ʻāpana:

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

ʻO ka ikehu kinetic rotational:

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

heluhelu hou

1. Hoʻopili ʻia kahi ikaika F i kahi kaula i wahī ʻia a puni kahi pulley cylinder. ikehu is 2 N m a me ke manawa o ka inertia is 1 kg m², he aha ka hoʻolalelale kihi o ka cylinder.

ʻIke ʻia:

ʻO ka ikehu (τ) = 2 N m

ʻO ka manawa o ka inertia (I) = 1 kg m²

Makemake: ʻO ka wikiwiki angular o ka cylinder

Lōlā:

ʻO Στ =I α

ʻO Στ = ka torque upena, I = ka manawa o ka inertia, α = ka wikiwiki kihi

Ka wikiwiki ʻana o ke kinikini:

α = Στ / I = 2 / 1 = 2 rad/s²

2. Hoʻopili ʻia kahi ikaika F i kahi kaula i wahī ʻia a puni kahi pulley cylinder. ʻO ka nui o ka ikaika he 10 ʻO N, ʻo ke radius o ka cylinder he 0.2 m a ʻo ka manawa o ka inertia 1 kg m2, WʻO ka wikiwiki angular o ka cylinder anei?

ʻIke ʻia:

Ikaika (F) = 10 N

Ka laulā o ka paukūʻolokaʻa (R) = 0.2 m

ʻO ka manawa o ka inertia (I) = 1 kg m²

Makemake: ʻO ka hoʻolalelale angular o ka cylinder.

Lōlā:

τ = FR

τ = torque, F = ikaika, R = radius o ka paukūʻolokaʻa

Torque:

τ = FR = (10 N)(0.2 m) = 2 N m

ʻO Στ =I α

ʻO Στ = ka torque upena, I = ka manawa o ka inertia, α = ka wikiwiki kihi

Ka wikiwiki ʻana o ke kinikini:

α = Στ / I = 2 / 1 = 2 rad/s²

3. Hoʻopili ʻia kahi ikaika F i ke kaula i wahī ʻia a puni kahi pulley cylinder. ʻO ka nui o ka ikaika he 10 ʻO N, ʻo ke anawaena o ka cylinder he 0.2 m a ʻo ke kaumaha o ka cylinder he 20 kg m^2,. WʻO ka wikiwiki angular o ka cylinder ka pāpale.

ʻIke ʻia:

Ikaika (F) = 10 N

Ka laulā o ka paukūʻolokaʻa (R) = 0.2 m

Ka nuipa o ka paukūʻolokaʻa (M) = 20 kg

Makemake ʻia: Ka wikiwiki ʻana o ke kinikini

Lōlā:

τ = FR = (10 N)(0.2 m) = 2 N m

Manawa o ka inertia:

ʻO wau = 1/2 MR² = 1/2 (20)(0.2)² = 1⁄2 (20)(0.04) = 0.4 kg m²

Ka wikiwiki ʻana o ke kinikini:

α = Στ / I = 2 / 0.4 = 5 rad/s²

4. He poloka 1-kg e kau ana mai ke kaula i wahī ʻia a puni kahi pulley cylinder. ʻO ka manawa o ka inertia o ka pulley he 1 kg m² a ʻo ke radius o ka pulley he 0.2 m. He aha ka wikiwiki angular o ka pulley. ʻO ka wikiwiki ma muli o ka umekaumaha he 10 m/s².

ʻIke ʻia:

Ka manawa o ka inertia o ka pulley (I) = 1 kg m²

Ka Mass o ka poloka (m) = 1 kg

Ka wikiwiki ma muli o ke koʻikoʻi (g) = 10 m/s²

Weight (w) = mg = (1 kg)(10 m/s)²) = 10 kg m/s² = 10 N

Ka laulā o ka pulley (R) = 0.2 m

Makemake ʻia: Hoʻolalelale kihi

Lōlā:

Torque:

τ = FR = w R = (10 N)(0.2 m) = 2 N m

Manawa o ka inertia:

ʻO I = 1 kg m²

Hoʻolalelale kihi:

α = Στ / I = 2 / 1 = 2 rad/s²

5. He poloka 1-kg e kau ana mai ke kaula i wahī ʻia a puni kahi pulley cylinder. ʻO ke kaumaha o ka pulley he 20 kg a ʻo ke radius o ka pulley he 0,2 m. He aha ka wikiwiki angular o ka pulley a me ka hāʻule manuahi ka wikiwiki o ka poloka. ʻO ka wikiwiki ma muli o ke koʻikoʻi he 10 m/s².

ʻIke ʻia:

Ka nuipa o ka pulley (M) = 20 kg

Ka laulā o ka pulley (R) = 0,2 m

Ka nuipa o ka poloka (m) = 1 kg

Ka wikiwiki ma muli o ke koʻikoʻi (g) = 10 m/s²

Kaumaha (w) = mg = (1 kg)(10 m/s)²) = 10 kg m/s² = 10 N

Makemake ʻia: ka wikiwiki angular o ka pulley a me ka wikiwiki hāʻule manuahi o ka poloka.

Lōlā:

ʻO ka torque:

τ = FR = w R = (10 N)(0.2 m) = 2 N m

ʻO ka manawa inertia o ka pulley cylinder:

ʻO wau = 1/2 MR² = 1/2 (20)(0.2)² = (10)(0.04) = 0.4 kg m²

ʻO ka wikiwiki kihi o ka pulley:

α = Στ / I = 2 / 0.4 = 5 rad / s²

ʻO ka wikiwiki o ka hāʻule manuahi o ka poloka:

a = R α = (0.2)(5) = 1 m/s²

heluhelu hou

ʻO ka manawa o ka inertia o ka ʻāpana

1. He pōpō 100-kalama i hoʻopili ʻia i kekahi wēlau o ke kaula me ka lōʻihi o 30 kenimika. He aha ka manawa o ka inertia o ka pōpō e pili ana i ke axis o ka wili AB? E hoʻowahāwahā i ke kaumaha o ke kaula.

ʻIke ʻia:

ʻO ke axis o ka wili ma AB

Ka Mass pōpō (m) = 100 grams = 100/1000 = 0.1 kg

ʻO ka mamao ma waena o ka pōpō a me ke koʻi o ka wili (r) = 30 kenimika = 0.3 m

Makemake: Manawa o ka inertia o ka pōpō (I)

Lōlā:

ʻO wau = Mr.² = (0.1 kg)(0.3 mika)²

ʻO wau = (0.1 kg)(0.09 m)²)

ʻO I = 0.009 kg m²

2. He pōpō 100-kalama, m₁, a me kahi pōpō 200-kalama, m₂, i hoʻopili ʻia e kahi koʻokoʻo me ka lōʻihi o 60 cm. Hoʻowahāwahā ʻia ke kaumaha o ke koʻokoʻo. Aia ke axis o ka wili ma ke kikowaena o ke koʻokoʻo. He aha ka manawa o ka inertia o ka pōpō e pili ana i ke axis o ka wili?

ʻIke ʻia:

Ka nuipa o ka pōpō 1 (m₁) = 100 grams = 100/1000 = 0.1 kg

ʻO ka mamao o ka pōpō 1 a me ke axis o ka wili (r₁) = 30 kenimika = 30/100 = 0.3 mika

Ka nuipa o ka pōpō (m₂) = 200 grams = 200/1000 = 0.2 kg

ka mamao o ka pōpō 2 a me ke axis o ka wili (r₂) = 30 kenimika = 30/100 = 0.3 mika

Makemake ʻia: manawa o ka inertia o nā pōpō

Pane:

ʻO wau = m₁ r₁² +m₂ r₂²

ʻO wau = (0.1 kg)(0.3 m)² + (0.2 kg)(0.3 m)²

ʻO wau = (0.1 kg)(0.09 ka m²) + (0.2 kg)(0.09 ka m²)

I = 0.009 kg m² + 0.018 kg m²

I = 0.027 kg m²

3. He pōpō 200-kalama, m₁ a me kahi pōpō 100-gram, m_2, i hoʻopili ʻia e kahi koʻokoʻo me ka lōʻihi o 60 cm. Hoʻowahāwahā i ke kaumaha o ke koʻokoʻo. Aia ke axis o ka wili ma ka pōpō m₂He aha ka manawa o ka inertia o nā pōpō. E hoʻowahāwahā i ka nuipa o ke koʻokoʻo.

ʻIke ʻia:

Ka nuipa o ka pōpō 1 (m₁) = 200 grams = 200/1000 = 0.2 kg

ʻO ka mamao ma waena o ka pōpō 1 a me ke axis o ka wili (r₁) = 60 kenimika = 60/100 = 0.6 mika

Ka nuipa o ka pōpō 2 (m₂) = 100 grams = 100/1000 = 0.1 kg

ʻO ka mamao ma waena o ka pōpō 2 a me ke axis o ka wili (r₂) = 0 mika

Makemake ʻia: Ka manawa o ka inertia o nā pōpō

Lōlā:

ʻO wau = m₁ r₁² +m₂ r₂²

ʻO wau = (0.2 kg)(0,6 m)² + (0.2 kg)(0)²

ʻO wau = (0.2 kg)(0.36 ka m²) + 0

ʻO I = 0.072 kg m²

4. ʻO ke kaumaha o kēlā me kēia pōpō he 100 grams, i hoʻopili ʻia e ke kaula. ʻO ka lōʻihi o ke kaula he 60 cm a ʻo ka laulā o ke kaula he 30 cm. He aha ka manawa o ka inertia o ka pōpō e pili ana i ke axis o ka wili. E hoʻowahāwahā i ke kaumaha o ke kaula.

ʻIke ʻia:

Ka nuipa o ka pōpō = m₁ = m₂ = m₃ = m₄ = 100 grams = 100/1000 = 0.1 kg

ʻO ka mamao ma waena o ka pōpō a me ke koʻi o ka wili (r₁) = 30 kenimika = 30/100 = 0.3 mika

ʻO ka mamao ma waena o ka pōpō 2 a me ke axis o ka wili (r₂) = 30 kenimika = 30/100 = 0.3 mika

ʻO ka mamao ma waena o ka pōpō 3 a me ke axis o ka wili (r₃) = 30 kenimika = 30/100 = 0.3 mika

ʻO ka mamao ma waena o ka pōpō 4 a me ke axis o ka wili (r₄) = 30 kenimika = 30/100 = 0.3 mika

ʻIke ʻia: Manawa o ka inertia

Lōlā:

ʻO wau = m₁ r₁² +m₂ r₂² +m₃ r₃² +m₄ r₄²

ʻO wau = (0.1 kg)(0.3 m)² + (0.1 kg)(0.3 m)² + (0.1 kg)(0.3 mika)² + (0.1 kg)(0.3 mika)²

ʻO wau = (0.1 kg)(0.09 ka m²) + (0.1 kg)(0.09 m²) + (0.1 kg)(0.09 m²) + (0.1 kg)(0.09 m²)

ʻO I = 0.036 kg m²

ʻO ka manawa o ka inertia o kahi mea paʻa

5. He aha ka manawa o ka inertia o kahi koʻokoʻo like 2-kg ka lōʻihi me ka lōʻihi o 2 m. Aia ke axis o ka wili ma ke kikowaena o ke koʻokoʻo.

ʻIke ʻia:

Ka nuipa o ke koʻokoʻo (M) = 2 kg

ʻO ka lōʻihi o ke koʻokoʻo (L) = 2 m

Makemake: Manawa o ka inertia

Lōlā:

ʻO ke ʻano o ka manawa o ka inertia ke kau ʻia ke axis o ka rotation ma ke kikowaena o ke koʻokoʻo lōʻihi like:

ʻO wau = (1/12) ML²

ʻO wau = (1/12) (2 kg)(2 m)²

ʻO wau = (1/12) (2 kg)(4 m)²)

ʻO wau = (1/12)(8 kg m²)

ʻO I = 8/12 kg m²

ʻO I = 2/3 kg m²

6. He aha ka manawa o ka inertia o kahi koʻokoʻo like 2-kg ka lōʻihi me ka lōʻihi o 2 m? Aia ke axis o ka wili ma kekahi wēlau o ke koʻokoʻo.

ʻIke ʻia:

Ka nuipa o ke koʻokoʻo (M) = 2 kg

ʻO ka lōʻihi o ke koʻokoʻo paʻa (L) = 2 m

Makemake: Manawa o ka inertia

Lōlā:

ʻO ke ʻano hana no ka manawa o ka inertia ke kau ʻia ke axis o ka rotation ma kekahi wēlau o ke koʻokoʻo:

ʻO wau = (1/3) ML²

ʻO wau = (1/3) (2 kg)(2 m)²

ʻO wau = (1/3) (2 kg)(4 m)²)

ʻO wau = (1/3)(8 kg m²)

ʻO I = 8/3 kg m²

7. He cylinder paʻa 10-kg me ka radius o 0.1 m. Aia ke axis o ka wili ma ke kikowaena o ka cylinder paʻa, i hōʻike ʻia ma ke kiʻi ma lalo nei. He aha ka manawa o ka inertia o ka cylinder?

ʻIke ʻia:

Ka nuipa o ka paukū paʻa (M) = 10 kg

Ka laulā o ka paukūʻolokaʻa (L) = 0.1 m

Makemake: ʻO ka manawa o ka inertia

Makemake: ʻO ka manawa o ka inertia

Lōlā:

ʻO ke ʻano o ka manawa o ka inertia ke kau ʻia ke axis o ka rotation ma ke kikowaena o ka cylinder:

ʻO wau = (1/2) MR²

ʻO wau = (1/2) (10 kg)(0.1 m)²

ʻO wau = (1/2) (10 kg)(0.01 m)²)

ʻO wau = (1/2)(0.1 kg m²)

ʻO I = 0.05 kg m²

8. He poepoe like he 20-kg me ka lōʻihi o 0.1 m. Ua hōʻike ʻia ke axis o ka wili ma ke kikowaena o ka poepoe ma ke kiʻi ma lalo nei.

ʻIke ʻia:

Ka nuipa o ka poepoe (M) = 20 kg

ʻO ke anawaena o ka poepoe (L) = 0.1 m

Makemake: he manawa o ka inertia

Lōlā:

ʻO ke ʻano o ka manawa o ka inertia ke kau ʻia ke axis o ka rotation ma ke kikowaena o ka poepoe:

ʻO wau = (2/5) MR²

ʻO wau = (2/5)(20 kg)(0.1 m)²

ʻO wau = (2/5)(20 kg)(0.01 m)²)

ʻO wau = (2/5)(0.2 kg m²)

ʻO I = 0.4/5 kg m²

ʻO I = 0.08 kg m²

9. He papa lahilahi huinahā 2-kg me ka lōʻihi o 0.5 m a me ka laulā o 0.2 m. Aia ke axis o ka wili ma ke kikowaena o ka papa huinahā i hōʻike ʻia ma ke kiʻi ma lalo nei. He aha ka manawa o ka inertia o ka huinahā?

ʻIke ʻia:

Ka nuipa o ka papa huinahā (M) = 2 kg

ʻO ka lōʻihi o ka pā (a) = 0.5 m

ʻO ka laulā o ka pā (b) = 0.2 m

Makemake ʻia: Manawa o ka inertia

Lōlā:

ʻO ke ʻano o ka manawa o ka inertia ke kau ʻia ke axis o ka rotation ma ke kikowaena o ka pā:

ʻO wau = (1/12) M (a² + b²)

ʻO wau = (1/12)(2)(0.5² + 0.2²)

ʻO wau = (2/12)(0.25 + 0.04)

ʻO wau = (1/6)(0.29)

ʻO I = 0.29/6 kg m²

heluhelu hou