Ngā Raru Whakaoti i roto i te Ahupūngao Taketake

1. A pūnga pereti-whakarara he tuatahi te kaha C, te āheinga o te wāhi kore utu is ε_o, horahanga pereti is A, te tawhiti i waenga i ngā pereti is d. Mēnāe kua piki ake te horahanga pereti mā te 4 ngā wā, ko te tawhiti i waenga i ngā pereti ka huri hei 2d, ā, te āheinga o te wāhi wātea he 5ε_o, he aha te kaha whakamutunga o te pūnga hiko pereti-whakarara.

Mōhiotia:

Te kaha o te pūnga = C

Te āheinga o te wāhi wātea = ε _o

P horahanga mutunga = A

Te tawhiti i waenga i ngā pereti = d

E hiahiatia ana: Te kaha o te pūnga (C)

Rongoā:

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2. Ko te pūnga hiko kei a ia te kaha nui rawa atu i runga i te whakairoiro i raro nei ko …

Rongoā:

Ko te tātai o te pūnga pereti-whakarara:

Te kaha o ngā pūnga:

Ko te pūnga hiko kei a ia te pūnga hiko y nui rawa ko te pūnga hiko C _3.

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3.

Whakaarohia ngā āhuatanga e whai ake nei!
(1) Pūmau whakapūmau hiko
(2) Ko te rerekētanga pūmanawa i waenganui i ngā pereti
(3) Pereti thīkī
(4) Te horahanga o te mata o te pereti
(5) Te tawhiti i waenganui i ngā pereti
(6) Te nui o utu hiko
Ngā āhuatanga e pā ana ki te kaha o ngā pereti whakarara ko ngā pūnga iahiko he…

Rongoā:

(1), (4) me (5)

4. Ko te whakataurite i te kaha o te pūnga 1 me te 2 ko…

Mōhiotia:

Pūnga 1:

Horahanga mata = 2A

Te tawhiti i waenga i ngā pereti = d ₁

Pūnga 2:

Horahanga mata = A

Te tawhiti i waenga i ngā pereti = 2 d ₁

E hiahiatia ana: Te whakataurite i te kaha o ngā pūnga 1 me te 2

Rongoā:

[irp]

5.

Whakatauhia te whakatairite i te kaha o te pūnga pereti-whakarara I me te II.

Rongoā:

Te whakataurite i te kaha o ngā pūnga iahiko pereti-whakarara I me II:

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6. E rua ngā pūnga pereti-whakarara e whakaaturia ana i te pikitia i raro nei.

Mena ko A ₁ = ½ A ₂ me d ₂ = 3 d ₁ , whakatauhia te ōwehenga o ngā kaha o te pūnga pereti whakarara i waenga i te ahua 2 me te ahua 1.

Mōhiotia:

Pūngao pereti-whakarara I:

A ₁ = 1

d ₁ = 1

Pūngao pereti-whakarara II:

A ₂ = 2

d ₂ = 3

E hiahiatia ana: te ōwehenga o ngā kaha o te pūnga pereti-whakarara i waenga i te ahua 2 me te ahua 1

Rongoā:

Pūngao pereti-whakarara I:

Pūngao pereti-whakarara II:

Te ōwehenga o ngā kaha o ngā pūnga pereti whakarara II me I:

Pānuitia atu

1. Tāutuhia te pūmanawa hiko i tētahi pūwāhi kei te 1 cm mai i tētahi utu 5.0 μC . Te pūmau Coulomb (k) = 9 x 10 ⁹ Nm ² C ⁻² , 1 μC = 10 ⁻⁶ C.

Mōhiotia:

Ko te tawhiti mai i te utu (r) = 1 cm = 1/100 m = 0.01 m = 10 ^-2 m

Utu (q) = 5.0 μ C = 5.0 x 10 ^-6 C

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

E hiahiatia ana: Pūmanawa hiko (V)

Rongoā:

Pūmanawa hiko:

Ko te pūmanawa hiko he 4.5 x ¹⁰⁶ Volts

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2. Akona Q₁ = 5.0 μC me te utu Q₂ = 6.0 μC. Te pūmau o Coulomb (k) = 9 x 10⁹ Nm²C^-2, 1 μC = 10^-6 C. Kei waenganui i ngā utu te Pūwāhi A. Tāutuhia te pūmanawa hiko i te pūwāhi A.

Mōhiotia:

Utu Q ₁ = -5.0 μ C = -5.0 x 10 ^-6 C

Ko te tawhiti o te pūwāhi A mai i Q ₁ = 10 cm = 0.1 m = 10 ^-1 m

Utu Q ₂ = 6.0 μ C = 6.0 x 10 ^-6 C

Ko te tawhiti o te pūwāhi a mai i Q ₂ = 10 cm = 0.1 m = 10 ^-1 m

Te pūmau o Coulomb (k) = 9 x 10 ⁹ Nm ² C ⁻²

E hiahiatia ana: Te pūmanawa hiko i te pūwāhi A

Rongoā:

Pūmanawa hiko 1 :

Pūmanawa hiko 2 :

Pūmanawa hiko i te pūwāhi A :

V = _V2 – _V1

V = (54 – 45) x 10 ⁴

V = 9 x 10 ⁴

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3. Akona q₁ = 5.0 μC me te utu q₂ = 6.0 µC. Te pūmau o Coulomb (k) = 9 x 10⁹ Nm²C^-2, 1 μC = 10^-6 C. Tātaitia te pūmanawa hiko i te pūwāhi A.

Mōhiotia:

Utu Q ₁ = -5.0 μ C = -5.0 x 10 ^-6 C

Ko te tawhiti o te pūwāhi A mai i Q ₁ = 40 cm = 0.4 m = 4 x 10 ^-1 m

Utu Q ₂ = 6.0 μ C = 6.0 x 10 ^-6 C

Ko te tawhiti o te pūwāhi A mai i Q ₂ = 50 cm = 0.5 m = 5 x 10 ^-1 m

Te pūmau o Coulomb (k) = 9 x 10 ⁹ Nm ² C ⁻²

E hiahiatia ana: Te pūmanawa hiko i te pūwāhi A

Rongoā:

Pūmanawa hiko 1 :

Pūmanawa hiko 2 :

Pūmanawa hiko i te pūwāhi A :

_V = _V1 + V2

V = (-11.25 + 10.8) x 10 ⁴

V = -0.45 x ¹⁰³

V = -4.5 x ¹⁰³

Ko te pūmanawa hiko i te pūwāhi A he -4.5 x 10 ³ Volts

Pānuitia atu

1. Ka whakaterea te tere o tētahi irahiko mai i te okioki mā roto i tētahi rerekētanga pūmanawa o te 12 V. He aha te panonitanga o te pūngao pūmanawa hiko o te irahiko?

Mōhiotia:

Ko te utu i runga i te irahiko (e) = -1.60 x 10 ^-19 Coulomb

Pūmanawa hiko = ngaohiko (V) = 12 Volts

E hiahiatia ana: Te huringa o te pūngao pūmanawa hiko o te irahiko (ΔPE)

Rongoā:

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

Ko te tohu tango e tohu ana ka heke te pūngao pūmanawa.

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2. E rua ngā pereti whakarara e utaina ana. Ko te wehenga i waenga i ngā pereti he 2 cm, ā, ko te rahi o te āpure hiko i waenga i ngā pereti he 500 Volt/mita. He aha te huringa o te pūngao pūmanawa o te pūrotene ina whakaterea mai i te pereti utu pai ki te pereti utu kino?

Mōhiotia:

Ko te rahi o te papa hiko i waenganui i ngā pereti (E) = 500 Volt/mita

Ko te tawhiti i waenganui i ngā pereti (s) = 2 cm = 0,02 m

Ko te utu i runga i te porotini = +1.60 x 10 ^-19 Coulombs

E hiahiatia ana: Te huringa o te pūngao pūmanawa hiko (ΔPE)

Rongoā:

Pūmanawa hiko:

V = E s

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

V = 10 Ngāohiko

Te huringa o te pūngao pūmanawa hiko:

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

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3. E wehea ana ngā utu pūwāhi e rua e te tawhiti o te 10 cm. Ko te utu i runga i te pūwāhi A = +9 μC me te utu i runga i te pūwāhi B = -4 μC. k = 9 x 10 ⁹ Nm ² C ⁻² , 1 μC = 10 ⁻⁶ C. He aha te huringa o te kaha hiko o te utu i te pūwāhi B mēnā ka whakaterea ki te pūwāhi A?

Mōhiotia:

Utu A (q ₁ ) = +9 μC = +9 x 10 ⁻⁶ C

Utu B (q ₁ ) = -4 μC = -4 x 10 ⁻⁶ C

k = 9 x 10 ⁹ Nm ² C ⁻²

Ko te tawhiti i waenganui i ngā utu A me B (r) = 10 cm = 0.1 m = 10 ^-1 m

E hiahiatia ana: Te huringa o te pūngao pūmanawa hiko (ΔEP)

Rongoā:

Pānuitia atu

1. Ka haere tētahi papa hiko ōrite E = 8000 N/C mā roto i tētahi horahanga tapawhā papatahi A = 10 m2 ^. Tātaihia te rerenga hiko.

Mōhiotia:

Ko te rahi o te papa hiko (E) = 8000 N/C

Horahanga (A) = 10 ^m²

θ = 0 ^o (te koki i waenganui i te ahunga o te papa hiko me te rārangi kua tuhia poutū ki te horahanga)

E hiahiatia ana: Te rerenga hiko ( Φ)

Rongoā:

Te tātai o te rerenga hiko:

Φ = EA cos q

Φ = te rerenga hiko ( Nm ² /C) , E = te papa hiko (N/C), A = te horahanga (m ² ), q = te koki i waenganui i te rārangi papa hiko me te rārangi noa.

Te rerenga hiko:

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. Ka haere tētahi papa hiko ōrite E = 5000 N/C mā roto i tētahi horahanga tapawhā papatahi A = 2 m2 ^. Tātaihia te rerenga hiko.

Mōhiotia:

Papa hiko (E) = 5000 N/C

Horahanga (A) = 2 ^m²

θ = 60 ^o (te koki i waenganui i te ahunga o te papa hiko me te rārangi kua tuhia poutū ki te horahanga)

E hiahiatia ana: Te rerenga hiko ( Φ)

Rongoā:

Te rerenga hiko:

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

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3. He pōro totoka, he 0.5 mita te whānui, he 10 μC te utu hiko kei waenganui. Tātaihia te rerenga hiko e puta ana i roto i te pōro totoka.

Mōhiotia:

Te whānui o te pōro (r) = 0.5 m

Utu hiko (Q) = 10 μC = 10 x 10 ^-6 C

E hiahiatia ana: Te rerenga hiko ( Φ)

Rongoā:

Mara hiko:

E = kq/ ^r2

E = (9 x 10 ⁹ Nm² /C² ^{) (} 10 x 10 ^-6 C) ^/ 0.5²

E = (90 x ¹⁰³ ) / 0,25

E = 360 x 10 ³

E = 3.60 x 105 ^N /C

Horahanga mata:

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

Te rerenga hiko:

Ka whakarārangi poutū te papa hiko ki te horahanga, nō reira ko te koki i waenganui i te ahunga o te papa hiko me te rārangi kua tuhia poutū ki te horahanga, ko te 0 ^°.

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 106 ^{Nm2 /} C

Pānuitia atu

1. Tātaihia te rahi me te ahunga o te papa hiko i tētahi pūwāhi A kei te 5 cm mai i tētahi utu pūwāhi Q = +10 μC. k = 9 x 10 ⁹ Nm ² C ⁻² , 1 μC = 10 ⁻⁶ C)

Mōhiotia:

Utu hiko (Q) = +10 μC = +10 x 10 ^-6 C

Ko te tawhiti i waenganui i te pūwāhi A me te utu pūwāhi Q (r _A ) = 5 cm = 0.05 m = 5 x 10 ^-2 m

k = 9 x 10 ⁹ Nm ² C ⁻²

E hiahiatia ana: Te rahi me te ahunga o te papa hiko i te pūwāhi A

Rongoā:

Ko te ahunga o te papa hiko i te pūwāhi A:

He pai te utu hiko, nō reira kei tawhiti atu te ahunga o te mara hiko i te utu hiko, ā, kei ngā pūwāhi A anō hoki.

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2. Tātaihia te rahi me te ahunga o te papa hiko i tētahi pūwāhi P kei te 10 cm mai i tētahi utu pūwāhi Q = -2 0 μC. k = 9 x 10 ⁹ Nm ² C ⁻² , 1 μC = 10 ⁻⁶ C.

Mōhiotia:

Utu hiko (q) = -20 μC = -20 x 10 ^-6 C

Ko te tawhiti i waenganui i te pūwāhi P me te utu hiko (r _P ) = 10 cm = 0.1 m = 1 x 10 ^-1 m

k = 9 x 10 ⁹ Nm ² C ⁻²

E hiahiatia ana: Te rahi me te ahunga o te papa hiko i te pūwāhi P

Rongoā:

Ko te ahunga o te papa hiko i te pūwāhi A:

He kino te utu hiko, nō reira te ahunga o te āpure hiko ki te utu hiko.

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3. E 40 cm te tawhiti e wehea ana e ngā utu pūwāhi e rua. He aha te rahi me te ahunga o te papa hiko i te pūwāhi P i waenganui i ngā utu e rua, arā, 20 cm te tawhiti mai i te pūwāhi A?

Mōhiotia:

Utu A (q _A ) = -2 μC = -2 x 10 ^-6 C

Utu B (q _B ) = + 4 μC = +4 x 10 ^-6 C

Ko te tawhiti i waenganui i te utunga A me te pūwāhi P (r _AP ) = 20 cm = 0.2 m = 2 x 10 ^-1 m

Ko te tawhiti i waenganui i te utu B me te pūwāhi P (r _BP ) = 20 cm = 0.2 m = 2 x 10 ^-1 m

E hiahiatia ana: Te rahi me te ahunga o te āpure hiko i te pūwāhi P.

Rongoā:

He kino te utunga A, nō reira ko te ahunga o ngā pūwāhi o te mara hiko kei te taha o Q _A (ki te taha mauī).

He pai te utunga B, nō reira kei tawhiti atu te ahunga o ngā pūwāhi o te mara hiko i a QB ₍ ki te taha mauī).

Ko te papa hiko katoa i te pūwāhi A:

E = _EA + _EB

E = (4.5 x 10 ⁵ ) + (9 x 10 ⁵ )

E = 13.5 x 10 ⁵ N/C

E anga ana te ahunga o te papa hiko ki Q _A (ki te taha mauī).

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4. Kore te rahi o te papa hiko i te…

He pai te utu A, he pai hoki te utu B, nō reira ko te rahi o te āpure hiko he kore kei te pūwāhi P, i waenganui i ngā utu e rua.

Mōhiotia:

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

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

k = 9 x 10 ⁹ Nm ² C ⁻²

Ko te tawhiti i waenganui i te utu A me te utu B = 20 cm

Ko te utu i waenganui i te utu A me te pūwāhi P (r _AP ) = a

Ko te tawhiti i waenganui i te utunga B me te pūwāhi P (r _BP ) = 20 – a

E hiahiatia ana: Ko te rahi o te papa hiko he kore kei te….

Rongoā:

Te rahi o te āpure hiko i hangaia e te utunga A i te pūwāhi P

He pai te utunga A, nō reira kei tawhiti atu te ahunga o ngā pūwāhi o te mara hiko i te utunga A (ki te taha matau).

Te rahi o te āpure hiko i whakaputaina e te utu B i te pūwāhi P:

He pai te utunga B, nō reira kei tawhiti atu te ahunga o ngā pūwāhi o te mara hiko i te utunga B (ki te taha mauī).

Ko te papa hiko katoa i te pūwāhi P = 0:

Ka whakamahia e mātou te tātai tapawhā hei whakatau i te a.

Kore te rahi o te āpure hiko kei te 8 cm mai i te utunga A, 12 cm rānei mai i te utunga B.

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5. I runga i te ahua i raro nei, ko tēhea te pūwāhi P kia kore ai te papa hiko i te pūwāhi P? (k = 9 x 10 ⁹ Nm ² C ⁻² , 1 μC = 10 ⁻⁶ C)

otinga

Ttātaihia te kaha o te papa hiko i te pūwāhi P, me te whakaaro kei te pūwāhi P he utu whakamātautau pai. Q₁ he pai, ā, ko Q₂ he tōraro, nō reira me noho te pūwāhi P ki te taha matau o Q₂ ki te taha maui rānei o Q₁. Mena kei te taha maui o Q te pūwāhi P₁; te papa hiko i hangaia e Q₁ kei te pūwāhi P kei te taha maui (kei tawhiti atu i a Q₁) me te papa hiko i hangaia e Q₂ i te pūwāhi P ki te taha matau (ki te taha Q₁). He rerekē te ahunga o te papa hiko, ā, ka whakakorea ngā papa hiko e rua tetahi i tetahi, ā, ka kore te kaha o te papa hiko i te pūwāhi P.

Mōhiotia:

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

Te tawhiti i waenganui i te utu 1 me te utu 2 = 3 cm

Te tawhiti i waenganui i a Q ₁ me te pūwāhi P (r _1P ) = a

Te tawhiti i waenganui i a Q ₂ me te pūwāhi P (r _2P ) = 3 + a

E hiahiatia ana: te taunga o te pūwāhi P kia kore ai te papa hiko i te pūwāhi P

Rongoā:

Kei te taha maui o Q 1 _te Pūwāhi P.

Ko te mara hiko i hangaia e Q ₁ i te pūwāhi P:

He pai te utu whakamātautau, ā, he pai hoki a Q ₁ , nō reira ko te ahunga o te āpure hiko kei te taha mauī.

Ko te mara hiko i hangaia e Q ₂ i te pūwāhi P:

He pai te utu whakamātautau, ā, he kino te Q ₂ , nō reira kei te taha matau te ahunga o te āpure hiko.

Te mara hiko kupenga i te pūwāhi A:

Whakamahia te tātai tapawhā hei whakatau i te:

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

Te tawhiti i waenganui i a Q ₂ me te pūwāhi P (r _2P ) = 3 + a = 3 – 1.8 = 1.2 cm.

Kei te 1.2 cm te tawhiti o te pūwāhi P ki te taha matau o _Q1.

[irp]

Pānuitia atu

1. E rua ngā utunga pūwāhi, Q_A = +8 μC me te Q_B = -5 μC, e wehea ana e te tawhiti r = 10 cm. He aha te rahi o te te kaha hiko. Ko te pūmau k = 8.988 x 10⁹ Nm²C^-2 = 9x10⁹ Nm²C^-2.

Mōhiotia:

Utu A (q _A ) = +8 μC = +8 x 10 ^-6 C

Utu B (q _B ) = -5 μC = -5 x 10 ^-6 C

k = 9 x 10 ⁹ Nm ² C ⁻²

Ko te tawhiti i waenganui i ngā utu A me B (r _AB ) = 10 cm = 0.1 m

E hiahiatia ana : Te rahi o te kaha hiko

Rongoā:

Te tauira o te ture a Coulomb :

Te rahi o te kaha hiko:

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2. E rua ngā matūriki kua utua, e whakaaturia ana i te pikitia i raro nei. Ko Q _P = +10 μC me Q _q = +20 μC e wehea ana e te tawhiti r = 10 cm. He aha te rahi o te kaha hiko-pūmau?

Mōhiotia:

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

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

k = 9 x 10 ⁹ Nm ² C ⁻²

Ko te tawhiti i waenganui i ngā utu P me Q (r _PQ ) = 12 cm = 0.12 m = 12 x 10 ^-2 m

E hiahiatia ana: Te rahi o te kaha hiko

Rongoā:

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3. E toru ngā matūriki kua whakarārangihia kia rite ki te pikitia i raro nei. Utu A = -5 μC, utu B = +10 μC me utu C = -12 μC. Tātaihia te kaha hiko pūmau ki runga i te matūriki B nā ngā utu e rua e toe ana.

Mōhiotia:

Utu A (q _A ) = -5 μC = -5 x 10 ^-6 C

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

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

k = 9 x 10 ⁹ Nm ² C ⁻²

Ko te tawhiti i waenganui i ngā matūriki A me B (r _AB ) = 6 cm = 0.06 m = 6 x 10 ^-2 m

Ko te tawhiti i waenganui i ngā matūriki B me C (r _BC ) = 4 cm = 0.04 m = 4 x 10 ^-2 m

E hiahiatia ana: Te rahi me te ahunga o te kaha hikohiko kupenga i runga i te matūriki B

Rongoā:

Ko te kaha kupenga i runga i te matūriki B ko te tapeke whārite o te kaha F _BA i pā ki te matūriki B e te matūriki A me te kaha F _BC i pā ki te matūriki B e te matūriki C.

Ko te kaha F _BA i pā ki te matūriki B e te matūriki A:

 

Ko te ahunga o te kaha hikohiko e tohu ana ki te matūriki A (e tohu ana ki te maui).

Ko te kaha F _BC i pā ki te matūriki B e te matūriki A:

 

Ko te ahunga o te kaha hikohiko e tohu ana ki te matūriki C (tohu ki te taha matau).

Ko te kaha hiko pūmau kupenga i runga i te matūriki B :

F _B = F _AB – F _BC = 675 N – 125 N = 550 Ngā Newton.

Ko te ahunga o te kaha hiko pūmau i runga i te matūriki B e tohu ana ki te matūriki C (e tohu ana ki te taha matau).

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4. Kua wehea a +Q ₁ = 10 μC, +Q ₂ = 50 μC me Q ₃ e ai ki te pikitia i raro nei. He aha te utu hiko pūmau i runga i te matūriki 3 mēnā he kore te kaha hiko pūmau kupenga i runga i te matūriki 2.

Mōhiotia:

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

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

Ko te tawhiti i waenganui i ngā utu 1 me te 2 (r ₁₂ ) = 2 cm = 0.02 m = 2 x 10 ^-2 m

Ko te tawhiti i waenganui i te utu 2 me te utu 3 (r ₂₃ ) = 6 cm = 0.06 m = 6 x 10 ^-2 m

Ko te kaha hiko pūmau kupenga i runga i te matūriki 2 (F ₂ ) = 0

E hiahiatia ana : utu 3 (q ₃ )

Rongoā:

Ko te kaha kupenga i runga i te matūriki 2 ko te tapeke whārite o te kaha F ₂₁ i pā ki te matūriki 2 e te matūriki 1 me te kaha F ₂₃ i pā ki te matūriki 2 e te matūriki 3.

Ko te kaha F ₂₁ i pā ki te matūriki 2 e te matūriki 1:

Ko te ahunga o te kaha hikohiko e tohu ana ki te matūriki 3 (tohu ki te taha matau).

Te kaha F₂₃ i pāngia e te matūriki 3 ki te matūriki 2: 

Ko te ahunga o te kaha hikohiko e tohu ana ki te matūriki 1 (tohu ki te maui).

Ko te kaha hiko pūmau kupenga i runga i te matūriki 2 = 0:

Pānuitia atu

1. Ka ^huri te mea he 2 kg m² tōna tere ā-pūmau i te 1 rad/s. He aha te tere koki o te mea?

Mōhiotia:

^{Te wā} o te korenga o te kaha (I) = 2 kg m²

Tere koki ( ω ) = 1 rad/s

E hiahiatia ana: Te nekehanga koki (L)

Rongoā:

Tātai o te nekehanga koki:

L = I ω

L = te nekehanga koki (kg m ² /s), I = te nekehanga o te korekore (kg m ² ), ω = te tere koki (rad/s)

Te nekehanga koki:

L = I ω = (2)(1) = 2 kg m ² /s

[irp]

2. E hurihuri ana tētahi porotaka rango 2- kg te taumaha, ko tōna radius he 0.1 m te roa , i te tere koki pumau o te 2 rad/s. He aha te nekehanga koki o te porotaka?

Mōhiotia:

Te taumaha o te pūreirei (m) = 2 kg karamu

Te whānui o te pūrakau (r) = 0.1 m

Tere koki (ω) = 2 r ad/s

E hiahiatia ana: Te nekehanga koki

Rongoā:

Te tātai o te wā o te korehau mō te rango totoka:

I = 1/2 mr ²

I = te tere o te korenga o te kaha (kg m ² ), m = te papatipu (kg), r = te pūtoro (m)

Te wā o te korekore:

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

Te tere koki:

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

[irp]

3. E huri ana tētahi porowhita ōrite 2-kg te taumaha, ko tōna radius he 0.2 m te hurihanga i te 4 rad/s. He aha te nekehanga koki o te pōro?

Mōhiotia:

Taumaha o te pōro (m) = 2 kg

Te whānui o te pōro (r) = 0.2 m

Tere koki (ω) = 4 ra d/s

E hiahiatia ana: Te nekehanga koki

Rongoā:

Te tātai o te nekehanga o te korehau mō te porowhita ōrite:

I = (2/5) mr ²

I = te nekehanga t o te korekore (kg m ² ), m = te papatipu (kg), r = te pūtoro (m)

Te wā o te korehau mō te porowhita ōrite:

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

Te nekehanga koki o te porowhita:

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

[irp]

4. Ka huri te matūriki 1-kg i te tere koki pumau o te 2 rad/s. He aha te tere koki mēnā he 10 cm te radius o te porowhita?

Mōhiotia:

Papatipu o te mea (m) = 1 kg karamu

Ko te pūtoro o te porowhita (r) = 10 cm = 10/100 = 0.1 m

Ko te tere koki (ω) = 2 rad/ s

E hiahiatia ana: Te nekehanga koki

Rongoā:

Te tātai o te wā o te korehau mō ngā matūriki:

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

Te nekehanga koki:

L = I ω = (0.01)(2) = 0.02 kg m ² /s

Pānuitia atu

1. Ko te tere o te inertia o tētahi mea he 1 kg m² ^{, ā} , ka huri ia i te tere koki pumau o te 2 rad/s. He aha te pūngao nekeneke hurihuri o te mea?

Mōhiotia:

Ko te wā o te korenga o te kaha ⁽ I) = 1 kg m²

Ko te tere koki ( ω) = 2 rad/s

E hiahiatia ana: Te pūngao nekeneke hurihuri (K E )

Rongoā:

Ko te tātai o te pūngao nekeneke hurihuri:

KE = 1/2 I ω ²

KE = te pūngao nekeneke hurihuri (kg m²/s²), ahau = te wā o te korekore (kg m²), ω = te tere koki (rad/s)

Te pūngao nekeneke hurihuri:

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

[irp]

2. He porotaka rango 20-kg te taumaha , he 0.2 m te whānui, e hurihuri ana i te tere koki pumau o te 4 rad/s. He aha te kaha nekeneke hurihuri o te porotaka?

Mōhiotia:

Te taumaha o te pūrakau rango (m) = 20 kg karamu

Ko te pūtoro o te rango (r) = 0.2 m

Ko te tere koki (ω) = 4 ra d/s

E hiahiatia ana: He aha te pūngao nekeneke hurihuri?

Otinga;

Te tātai o te wā o te korekore o te rango:

I = 1/2 mr ²

I = te wā o te korekore ( kg m ² ), m = papatipu (kg), r = te pūtoro (mita)

Te wā o te korekore o te pūrakau rango:

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

Te pūngao nekeneke hurihuri o te pūrakau:

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

[irp]

3. He pōro 10 kg te taumaha, ko te radius he 0.1 m te hurihanga i te pūmau o te 10 rad/s. He aha te pūngao nekeneke o te pōro?

Mōhiotia:

Taumaha o te pōro (m) = 10 kg

Te whānui o te pōro (r) = 0.1 m

Tere koki (ω) = 10 r ad/s

E hiahiatia ana: Te pūngao nekeneke hurihuri

Rongoā:

Te tātai o te wā o te korekore:

I = (2/5) mr ²

I = te tere o te korenga o te kaha (kg m ² ), m = te papatipu (kg), r = te pūtoro (m)

Te wā o te korekore o te pōro:

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

Te pūngao nekeneke hurihuri o te pōro:

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

[irp]

4. Ka huri tetahi matūriki 0.5- kg te taumaha i te tere koki pumau o te 2 rad/s. He aha te pūngao nekeneke hurihuri o te matūriki mēnā he 10 cm te radius o te porowhita?

Mōhiotia:

Papatipu o te matūriki (m) = 0.5 kg g

Ko te pūtoro o te pōro (r) = 10 cm = 10/100 = 0.1 m

Ko te tere koki (ω) = 2 rad/ s

E hiahiatia ana: Te pūngao nekeneke hurihuri

Rongoā:

Te wā o te korekore mō ngā matūriki:

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

Te pūngao nekeneke hurihuri:

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

Pānuitia atu

1. Ka pāngia tētahi kaha F ki tētahi taura e takai ana i tētahi pūreirei rango. Ko te taipana he 2 N m, ā, ko te wā o te korehau he 1 kg m ² , he aha te whakaterenga koki o te rango.

Mōhiotia:

Taipana ( τ ) = 2 N m

Ko te wā o te korenga o te kaha (I) = 1 kg ^m²

E hiahiatia ana: Te whakaterenga koki o te rango

Rongoā:

Στ = I α

Στ = taipana kupenga, I = momeniti inertia, α = whakatere koki

Te whakaterenga koki o te rango:

α = Στ / I = 2 / 1 = 2 rad/s ²

[irp]

2. Ka pāngia tētahi kaha F ki tētahi taura e takai ana i tētahi pūreirei rango. Ko te rahi o te kaha he 10 N, ko te radius o te rango he 0.2 m, ā, ko te nekehanga o te inertia he 1 kg m² . He aha te whakaterenga koki o te rango?

Mōhiotia:

Te kaha (F) = 10 N

Te whānui o te rango (R) = 0.2 m

Ko te wā o te korenga o te kaha (I) = 1 kg ^m²

E hiahiatia ana: Te whakaterenga koki o te rango.

Rongoā:

τ = FR

τ = taipana, F = kaha, R = pūtoro o te rango

Taipana:

τ = FR = (1 0 N)(0.2 m) = 2 N m

Στ = I α

Στ = taipana kupenga, I = momeniti inertia, α = whakatere koki

Te whakaterenga koki o te rango:

α = Στ / I = 2 / 1 = 2 rad/s ²

[irp]

3. Ka pāngia tētahi kaha F ki tētahi taura e takai ana i tētahi pūreirei rango. Ko te rahi o te kaha he 10 N, ko te radius o te rango he 0.2 m, ā, ko te papatipu o te rango he 20 kg m² ^. He aha te whakaterenga koki o te rango?

Mōhiotia:

Te kaha (F) = 10 N

Te whānui o te rango (R) = 0.2 m

Taumaha o te rango (M) = 20 kg

E hiahiatia ana: Te whakaterenga koki o te rango

Rongoā:

τ = FR = (1 0 N)(0.2 m) = 2 N m

Te wā o te korekore:

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

Te whakaterenga koki o te rango:

α = Στ / I = 2 / 0.4 = 5 rad/s ²

[irp]

4. He poraka 1-kg e iri ana i tētahi taura e takai ana i tētahi porotaka rango. Ko te tere o te inertia o te porotaka he 1 kg m² ^, ā, ko te radius o te porotaka he 0.2 m. He aha te whakaterenga koki o te porotaka? Ko te whakaterenga nā te kaha ā-papatipu he 10 m/ ^s².

Mōhiotia:

Te kaha o te korenga o te pūrakau (I) = 1 kg ^m²

Taumaha o te poraka (m) = 1 kg

Te whakaterenga nā te kaha ā-papa (g) = 10 m/s ²

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

Te whānui o te pūrakau (R) = 0.2 m

E hiahiatia ana: Te whakaterenga koki

Rongoā:

Taipana:

τ = FR = w R = (1 0 N)(0.2 m) = 2 N m

Te wā o te korekore:

I = 1 kg ^m²

Whakaterenga koki:

α = Στ / I = 2 / 1 = 2 rad/s ²

[irp]

5. He poraka 1-kg e iri ana i tētahi taura e takai ana i tētahi pōro rango. Ko te taumaha o te pōro he 20 kg , ā, ko te radius o te pōro he 0,2 m. He aha te whakaterenga koki o te pōro me te whakaterenga taka noa o te poraka? Ko te whakaterenga nā te kaha ā-papatipu he 10 m/ ^s2.

Mōhiotia:

Te taumaha o te pūrakau (M) = 20 kg

Te whānui o te pūrakau (R) = 0,2 m

Taumaha o te poraka (m) = 1 kg

Te whakaterenga nā te kaha ā-papa (g) = 10 m/s ²

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

E hiahiatia ana: te whakaterenga koki o te pūrakau me te whakaterenga taka noa o te poraka.

Rongoā:

Te taipana:

τ = FR = w R = (1 0 N)(0.2 m) = 2 N m

Te wā o te korekore o te pūrakau rango:

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

Te whakaterenga koki o te pūrakau:

α = Στ / I = 2 / 0.4 = 5 rad/s ²

Ko te whakaterenga taka noa o te poraka:

a = R α = (0.2)(5) = 1 m/s ²

Pānuitia atu

Te wā o te korekore o te matūriki

1. He pōro 100-karamu e hono ana ki tētahi pito o te taura, he 30 cm te roa. He aha te tere o te inertia o te pōro ki te tuaka hurihuri AB? Kaua e aro ki te taumaha o te taura.

Mōhiotia:

Te tuaka hurihuri i AB

Papatipu pōro (m) = 100 karamu = 100/1000 = 0.1 kg

Ko te tawhiti i waenganui i te pōro me te tuaka hurihuri (r) = 30 cm = 0.3 m

E hiahiatia ana: Te wā o te korenga o te pōro (I)

Rongoā:

I = mr ² = (0.1 kg)(0.3 m) ²

I = (0.1 kg)(0.09 ^m² )

I = 0.009 kg ^m²

[irp]

2. He pōro 100-karamu, m1 _, me te pōro 200-karamu, m2 , e honoa ana e te tokotoko he 60 cm te roa. Kāore e arohia _te papatipu o te tokotoko. Kei waenganui o te tokotoko te tuaka hurihuri. He aha te tere o te inertia o te pōro ki te tuaka hurihuri?

Mōhiotia:

Taumaha o te pōro 1 (m1 ₎ = 100 karamu = 100/1000 = 0.1 kg

Ko te tawhiti o te pōro 1 me te tuaka hurihuri (r ₁ ) = 30 cm = 30/100 = 0.3 m

Taumaha o te pōro (m² ₎ = 200 karamu = 200/1000 = 0.2 kg

Ko te tawhiti o te pōro 2 me te tuaka hurihuri (r ₂ ) = 30 cm = 30/100 = 0.3 m

E hiahiatia ana: te wā o te korekore o ngā pōro

Whakautu:

I = 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 ^m² + 0.018 kg ^m²

I = 0.027 kg ^m²

[irp]

3. He pōro 200-karamu, m1 me te pōro 100-karamu, m2 _{, e honoa ana e te tokotoko he 60 cm te roa. Kaua e aro ki te taumaha o te} tokotoko. Kei te pōro m2 te tuaka hurihuri . He aha te tere o te inertia o ngā pōro? Kaua e aro ki te taumaha o te tokotoko_.

Mōhiotia:

Taumaha o te pōro 1 (m1 ₎ = 2 00 karamu = 200/1000 = 0.2 kg

Ko te tawhiti i waenganui i te pōro 1 me te tuaka hurihuri (r ₁ ) = 60 cm = 60/100 = 0.6 m

Taumaha o te pōro 2 (m2 ₎ = 100 karamu = 100/1000 = 0.1 kg

Ko te tawhiti i waenganui i te pōro 2 me te tuaka hurihuri (r ₂ ) = 0 m

E hiahiatia ana: Te wā o te korekore o ngā pōro

Rongoā:

I = 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 ^m²

[irp]

4. Ko te taumaha o ia pōro he 100 karamu, he taura hono. Ko te roa o te taura he 60 henimita, ā, ko te whānui o te taura he 30 henimita. He aha te tere o te inertia o te pōro ki te tuaka hurihuri? Kaua e aro ki te taumaha o te taura.

Mōhiotia:

Papatipu o te pōro = m1 ₌ m2 ₌ m3 ₌ m4 ₌ 1 00 karamu = 100/1000 = 0.1 kg

Ko te tawhiti i waenganui i te pōro me te tuaka hurihuri (r ₁ ) = 30 cm = 30/100 = 0.3 m

Ko te tawhiti i waenganui i te pōro 2 me te tuaka hurihuri (r ₂ ) = 30 cm = 30/100 = 0.3 m

Ko te tawhiti i waenganui i te pōro 3 me te tuaka hurihuri (r ₃ ) = 30 cm = 30/100 = 0.3 m

Ko te tawhiti i waenganui i te pōro 4 me te tuaka hurihuri (r ₄ ) = 30 cm = 30/100 = 0.3 m

Mōhiotia: Te wā o te korekore

Rongoā:

I = 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

[irp]

Te wā o te korekore o tētahi mea pakari

5. He aha te tere o te inertia o tētahi tokotoko 2-kg te roa, he rite tonu ki te 2 m te roa? Kei waenganui o te tokotoko te tuaka hurihuri.

Mōhiotia:

Taumaha o te tokotoko (M) = 2 kg

Te roa o te tokotoko (L) = 2 m

E hiahiatia ana: Te wā o te korekore

Rongoā:

Ko te tātai o te wā o te korekore ina kei waenganui o te tokotoko roa ōrite te tuaka hurihuri:

I = (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 ^m²

I = 2/3 kg ^m²

[irp]

6. He aha te tere o te inertia o tētahi tokotoko 2-kg te roa, ā, he 2 m te roa? Kei tētahi pito o te tokotoko te tuaka hurihuri.

Mōhiotia:

Taumaha o te tokotoko (M) = 2 kg

Ko te roa o te tokotoko mārō (L) = 2 m

E hiahiatia ana: Te wā o te korekore

Rongoā:

Ko te tātai mō te wā o te korekore ina kei te pito kotahi o te tokotoko te tuaka hurihuri:

I = (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 ^m²

[irp]

7. He rango totoka 10-kg te taumaha, ko te radius he 0.1 m. Kei waenganui o te rango totoka te tuaka hurihuri, e whakaaturia ana i te ahua i raro nei. He aha te tere o te inertia o te rango?

Mōhiotia:

Taumaha o te rango totoka (M) = 10 kg

Te whānui o te rango (L) = 0.1 m

E hiahiatia ana: Te wā o te korekore

E hiahiatia ana: Te wā o te korekore

Rongoā:

Ko te tātai o te wā o te korekore ina kei waenganui o te rango te tuaka hurihuri:

I = (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 ^m²

8. He porowhita ōrite 20-kg te taumaha, ko te roa he 0.1 m. Kei waenganui o te porowhita te tuaka hurihuri e whakaaturia ana i te ahua i raro nei.

Mōhiotia:

Papatipu o te porowhita (M) = 20 kg

Ko te pūtoro o te porowhita (L) = 0.1 m

E hiahiatia ana: he wā o te korekore

Rongoā:

Ko te tātai o te wā o te korekore ina kei waenganui o te porowhita te tuaka hurihuri:

I = (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 ^m²

I = 0.08 kg ^m²

[irp]

9. He pereti angiangi tapawhā rite ki te 2-kg te taumaha, he 0.5 m te roa, he 0.2 m te whānui. Kei waenganui o te pereti tapawhā rite te tuaka hurihuri e whakaaturia ana i te ahua i raro nei. He aha te tere o te inertia o te tapawhā rite?

Mōhiotia:

Taumaha o te pereti tapawhā (M) = 2 kg

Te roa o te pereti (a) = 0.5 m

Ko te whānui o te pereti (b) = 0.2 m

E hiahiatia ana: Te Wā o te Āhuakore

Rongoā:

Te tātai o te wā o te korekore ina kei waenganui o te pereti te tuaka hurihuri:

I = (1/12 ) M (a ² + b ² )

I = (1/12)(2)(0.5 ² + 0.2 ² )

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

I = (1/6)(0.29)

I = 0.29/6 kg ^m²

Pānuitia atu