Physics

Kukula kwa mphamvu ya net torque - mavuto ndi mayankho

1. Mphamvu P imagwiritsidwa ntchito kumapeto kwa mtanda wokhala ndi kutalika kwa mamita awiri. Kodi kukula kwa mphamvu ndi kotani ? Mzere wozungulira pa mfundo A.

Kukula kwa mphamvu ya net torque - mavuto ndi mayankho 1 Zodziwika:

Mphamvu (F) = 10 N

Kutalika kwa AB (r _AB) = 2 m

Mphamvu F ndi yolunjika pa mtanda.

Mkono wa lever (l ) = r _ABsin 90 ^o = (2 m)(1) = 2 m

Kufunidwa: Mphamvu yozungulira mzere wozungulira

Yankho:

Mphamvu ya mphamvu:

τ = F l = (10 N)(2 m) = 20 N m

Chizindikiro chowonjezera chifukwa chakuti mtandawo umazungulira mozungulira mozungulira wotsatira wotchi.

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2. Kutalika kwa beam AB ndi 2 m ndipo kukula kwa mphamvu F ndi 10 N. Kodi kukula kwa torque ndi kotani? Mzere wozungulira pa mfundo A.

Kukula kwa mphamvu ya net torque - mavuto ndi mayankho 2 Zodziwika:

Mphamvu (F) = 10 N

Kutalika kwa AB (r _AB) = 2 m

Mkono wa lever (l ) = r _ABsin 60 ^o = (2 m)(0.5 √3 ) = √3 m

Kufunidwa: Mphamvu yozungulira mzere wozungulira

Yankho:

Mphamvu ya mphamvu:

τ = F l = (10 N)( √3 m) = 10 √3 N m

Chizindikiro chowonjezera chifukwa mphamvu F imapangitsa kuti mtandawo uzizungulira mozungulira motsutsa wotchi.

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3. Kutalika kwa mtanda ndi mamita awiri. Kukula kwa F ₁ ndi 10 N ndipo kukula kwa F ₂ ndi 15 N. Dziwani mphamvu ya ukonde pakati pa mtanda.

Mzere wozungulira pakati pa mtanda.

Kukula kwa mphamvu ya net torque - mavuto ndi mayankho 3 Zodziwika:

Mphamvu 1 (F ₁) = 10 N

Mtunda pakati pa F ₁ ndi pakati pa mtanda (r ₁ ) = 1 m

Mkono wa lever 1 (l ₁ ) = r ₁ sin 90 ^o = (1 m)(1) = 1 m

Mphamvu F ₁ndi yolunjika ku mtengo.

Mphamvu 2 (F ₂) = 15 N

Mtunda pakati pa F ₂ ndi pakati pa mtanda (r ₂) = 1 m

Mphamvu F ₂ndi yolunjika ku mtengo.

Mkono wa lever 2 (l ₂) = r ₁ sin 90 ^o = (1 m)(1) = 1 m

Kufunidwa: Mphamvu yozungulira kuzungulira mzere wozungulira

Yankho:

Mphamvu ya 1:

τ ₁ = F ₁ l ₁ = (10 N)( 1 m) = 10 N m

Chizindikiro chowonjezera chifukwa mphamvu ya F ₁ imapangitsa kuti kuwala kuzungulire mozungulira mozungulira.

Mphamvu ya 2:

τ ₂ = F ₂l ₂= (15 N) ( 1 m) = -15 N

Chizindikiro cha minus chifukwa mphamvu F ₂ imapangitsa kuti mtanda uzungulire mozungulira wotchi.

Mphamvu ya ukonde:

Σ τ = ₁ – τ ₂ = 10 – 15 = – 5 N m

Chizindikiro cha minus ndi chakuti kuwalako kumazungulira mozungulira wotchi.

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4. Kutalika kwa beam AB ndi 2 m, kukula kwa F ₁ ndi 10 N ndipo kukula kwa F ₂ ndi 10 N. Dziwani mphamvu ya neti pakati pa beam.

Mzere wozungulira pakati pa mtanda.

Zodziwika:

Mphamvu 1 (F ₁ ) = 10 Nn

Mtunda pakati pa F ₁ ndi pakati pa mtanda (r ₁ ) = 1 m

Mkono wa lever 1 (l ₁ ) = r ₁ sin 60 ^o = (1 m)(0.5 √3 ) = 0.5 √3 m

Mphamvu 2 (F ₂ ) = 10 N

Mtunda pakati pa F ₂ ndi pakati pa mtanda (r ₂ ) = 1 m

Mphamvu F ₂ ndi yolunjika ku mtengo.

Mkono wa lever 2 (l ₂ ) = r ₂ sin 90 ^o = (1 m)(1) = 1 m

Kufunidwa: Mphamvu yozungulira kuzungulira mzere wozungulira

Yankho:

Mphamvu ya 1:

τ ₁ = F ₁ l ₁ = (10 N)( 0.5 √3 m) = 5 √3 = 8.7 Nm

Chizindikiro chowonjezera chifukwa mphamvu F ₁ imapangitsa kuti mtandawo uzizungulira mozungulira wotchi.

Mphamvu ya 2:

τ ₂ = F ₂ l ₂ = (10 N)( 1 m) = -10 N m

Chizindikiro cha minus chifukwa mphamvu F ₂ imapangitsa kuti mtanda uzungulire mozungulira wotchi.

Mphamvu ya ukonde:

Σ τ = ₁ – τ ₂ = 8.7 – 10 = – 1.3 N m

Chizindikiro cha minus chifukwa mphamvu ya ukonde imapangitsa kuti kuwala kuzungulire mozungulira wotchi.

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5. Kutalika kwa mtanda ndi 10 m, kukula kwa F ₁ ndi 10 N, kukula kwa F ₂ ndi 10 N ndipo kukula kwa F ₃ ndi 15 N. Mtunda pakati pa mfundo A ndi mfundo C ndi 7.5 m. Mphamvu F ₂ ili pakati pa mtanda. Dziwani mphamvu yozungulira mfundo C yomwe ili pa 2.5 m kuchokera pa mfundo B.

Mzere wozungulira uli pamalo C

Kukula kwa mphamvu ya net torque - mavuto ndi mayankho 5 Zodziwika:

Mphamvu 1 (F ₁) = 10 N

Mtunda pakati pa F ₁ ndi mfundo C (r ₁ ) = 2.5 m

Mphamvu F ₁ndi yolunjika ku mtengo.

Mkono wa lever 1 (l ₁) = r ₁sin 90 ^o = ( 2.5 m)( 1 ) = 2.5 m

Mphamvu 2 (F ₂) = 10 N

Mtunda pakati pa F ₂ndi mfundo C (r ₂) = 2.5 m

Mphamvu F2 _ndiyolunjika ku mtanda.

Mkono wa lever 2 (l ₂) = r ₂sin 90 ^o = ( 2.5 m)(1) = 2.5 m

Mphamvu 3 (F ₃) = 15 N

Mtunda pakati pa F ₃ ndi mfundo C (r ₃) = 7.5 m

Mphamvu F3 _ndiyolunjika ku mtanda.

Mkono wa lever 3 (l ₃) = r ₃sin 90 ^o = (7.5 m)(1) = 7.5 m

Kufunidwa: Mphamvu yozungulira kuzungulira mzere wozungulira

Yankho:

Mphamvu ya 1:

τ ₁= F ₁l ₁= (10 N)( 2.5 m) = 25 N m

Chizindikiro chowonjezera chifukwa mphamvu F ₁ imapangitsa kuti mtandawo uzizungulira mozungulira wotchi.

Mphamvu ya 2:

τ ₂= F ₂l ₂= (10 N)( 2.5 m) = 25 N m

Chizindikiro cha kuphatikiza chifukwa mphamvu F2 _imapangitsakuti kuwala kuzungulire mozungulira wotchi.

Mphamvu ya 3:

τ ₃= F ₃l ₃= (15 N)( 7.5 m) = -112..5 N m

Chizindikiro cha minus chifukwa mphamvu F ₃ imapangitsa kuti mtanda uzungulire mozungulira wotchi.

Mphamvu ya ukonde:

Σ τ = τ ₁+ τ ₂– τ ₃= 25 + 25 – 112.5 = – 62.5 N m

Chizindikiro cha minus chifukwa mphamvu ya ukonde imapangitsa kuti kuwala kuzungulire mozungulira wotchi.

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6. Kutalika kwa mtanda ndi 10 m, kukula kwake ndi F₁ ndi 10 N, kukula kwa F₂ ndi 10 N ndipo kukula kwa F₃ ndi 10 N. Dziwani mphamvu ya ukonde pafupi ndi mfundo A, yomwe ili pamtunda wa mamita 5 kuchokera ku poi Kukula kwa mphamvu ya net torque - mavuto ndi mayankho 6 kugwiritsa ntchito mphamvu F₁.

Mzere wozungulira pa mfundo A.

Zodziwika:

Mphamvu 1 (F ₁ ) = 10 N

Mtunda pakati pa F ₁ndi mfundo A (r ₁) = 5 m

Mkono wa lever 1 (l ₁) = r ₁ sin 60 ^o = (5 m)(0.5 √3 ) = 2.5 √3 m

Mphamvu 2 (F ₂) = 10 N

Mtunda pakati pa F ₂ndi mfundo A (r ₂) = 0

Mphamvu F2 _ndi yolunjika ku mtanda.

Mkono wa lever 2 (l ₂) = r ₂ sin 90 ^o = (0)(1) = 0

Mphamvu 3 (F ₃) = 10 N

Mtunda pakati pa F ₃ndi mfundo A (r ₃) = 10 m

Mkono wa lever 3 (l ₃) = r ₃sin 30 ^o = (10 m)(0.5) = 5 m

Kufunidwa: mphamvu yozungulira kuzungulira mzere wozungulira

Yankho:

Mphamvu ya 1:

τ ₁= F ₁l ₁= (10 N)( 2.5 √3 m ) = 25√3 = 43.3 N m

Chizindikiro chowonjezera chifukwa mphamvu F ₁imapangitsa kuti mtandawo uzizungulira mozungulira wotchi.

Mphamvu ya 2:

τ ₂= F ₂l ₂= (10 N) (0) = 0

Mphamvu ya 3:

τ ₃= F ₃l ₃= (10 N)( 5 m) = -50 N m

Chizindikiro cha minus chifukwa mphamvu F ₃ imapangitsa kuti mtanda uzungulire mozungulira wotchi.

Mphamvu ya ukonde:

Σ τ = τ ₁+ τ ₂– τ ₃= 43.3 + 0 – 50 = – 6.7 N m

Chizindikiro cha minus chifukwa mphamvu ya ukonde imapangitsa kuti kuwala kuzungulire mozungulira wotchi.

Werengani zambiri

Kugundana pang'ono kwa gawo limodzi - mavuto ndi mayankho

1. Chinthu cha magalamu 500 , A, chikuyenda pa 10 m/s ndi chinthu cha magalamu 200, B, chikuyenda pa 12 m/s. Zinthuzo zimayandikirana ndipo zimagundana. Ngati liwiro la chinthu A pambuyo pa kugundana ndi 6 m/s, kodi liwiro la chinthu B pambuyo pa kugundana ndi lotani?

Zodziwika:

Kulemera kwa chinthu 1 (m ₁) = magalamu 500 = 0.5 kg

Kulemera kwa chinthu 2 (m ₂) = magalamu 200 = 0.2 kg

Liwiro loyambirira la chinthu 1 (v ₁) = -10 m/s

Liwiro loyambirira la chinthu 2 (v ₂) = 12 m/s

Liwiro lomaliza la chinthu 1 (v ₁') = 6 m/s

Zizindikiro za kuphatikiza ndi kuchotsera zimasonyeza kuti zinthuzo zimayenda mosiyana.

Kufunidwa : liwiro lomaliza la chinthu 2 (v ₂')

Yankho:

m₁ v₁ +m₂ v₂ = m₁ v₁' + m₂ v₂'

(0.5)(-10) + (0.2)(12) = (0.5)(6) + (0.2)(v ₂')

-5 + 2.4 = 3 + 0.2 v ₂'

-2.6 = 3 + 0.2 v ₂'

-2.6 – 3 = 0.2 v ₂'

-5.6 = 0.2 v ₂'

v ₂' = -5.6 / 0.2

v ₂' = -28 m/s

Liwiro la chinthu 2 pambuyo pa kugundana ndi 28 m/s.

Zizindikiro za kuphatikiza ndi kuchotsera zimasonyeza kuti zinthuzo zimayenda mosiyana.

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2. Zinthu ziwiri zofanana zimayandikirana ndipo zimagundana. Liwiro la chinthu 1 ndi 6 m/s ndipo liwiro la chinthu 2 ndi 8 m/s. Pambuyo pa kugundana, chinthu 2 chimasuntha kumanzere ndi liwiro la 5 m/s. Kodi kukula ndi komwe kuli liwiro la chinthu 1 pambuyo pa kugundana ndi kotani?

Dziwani:

Kulemera kwa chinthu 1 (m ₁) = m

Kulemera kwa chinthu 2 (m2 ₎= m

Liwiro loyambirira la chinthu 1 (v ₁) = -6 m/s

liwiro loyambirira la chinthu 2 (v ₂) = 8 m/s

Liwiro lomaliza la chinthu 2 (v ₂') = -5 m/s

Kufunidwa : kukula ndi komwe chinthu 1 chikupita pambuyo pa kugundana

Yankho:

Njira yosungira mphamvu yolunjika :

m₁ v₁ +m₂ v₂ = m₁ v₁' + m₂ v₂'

mv ₁+ m v ₂= mv 1 _'+ m v ₂'

m (v ₁+ v ₂) = m (v ₁' + v ₂')

v ₁+ v ₂= v ₁' + v ₂'

-6 + 8 = v ₁' – 5

2 = v ₁' – 5

2 + 5 = v ₁'

v ₁' = 7 m/s

Liwiro la chinthu 1 pambuyo pa kugundana (v ₁') ndi 3 m/s.

Zizindikiro za kuphatikiza ndi kuchotsera zimasonyeza kuti zinthuzo zimayenda mosiyana.

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3. Mpira wa 1-kg, mpira wa 1 ndi 2-kg, uli ndi mbali imodzi ndipo umagundana mopanda kusinthasintha. Mpira woyamba usanagundane, umayenda ndi liwiro la 10 m/s ndipo mpira wa 2 umayenda ndi liwiro la 5 m/s. Liwiro la mpira wa 2 pambuyo pa kugundana ndi 4 m/s. Dziwani liwiro la mpira woyamba pambuyo pa kugundana.

Zodziwika:

Mpira wolemera 1 (m1 ₎= 1 kg

Mpira wolemera 2 (m2 ₎= 2 kg

Liwiro la mpira 1 (v ₁) = 10 m/s

Liwiro la mpira 2 (v ₂) = 5 m/s

Liwiro lomaliza la mpira 2 (v ₂') = 4 m/s

Chizindikiro chowonjezera cha liwiro chimasonyeza kuti mipira ili ndi mbali imodzi.

Kufunidwa : liwiro lomaliza la mpira 1 (v ₁')

Yankho:

m₁ v₁ +m₂ v₂ = m₁ v₁' + m₂ v₂'

(1) (10) + (2) (5) = (1) (v ₁') + (2) (4)

10 + 10 = v ₁' + 8

20 – 8 = v ₁'

v ₁' = 12 m/s

Liwiro la mpira 1 pambuyo pa kugundana ndi 12 m/s.

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Werengani zambiri

Kugundana kwa inelastic mu gawo limodzi - mavuto ndi mayankho

1. Chipolopolo cha magalamu 30 chomwe chikuyenda pa liwiro la 30 m/s chagundana ndi chipika cha 1-kg pamene chapumula. Dziwani liwiro la chipikacho ngati chipolopolocho ndi chipikacho zalumikizana pamodzi chifukwa cha kugundanako.

Zodziwika:

Kulemera kwa chipolopolo (m ₁) = magalamu 30 = 0.03 kg

Kulemera kwa chipika (m2 ₎= 1 kg

Liwiro loyamba la chipolopolo ( v ₁) = 30 m/s

liwiro loyambirira la chipika (v ₂) = 0 ( chipika chili pamalo opumulira )

Kufunidwa : liwiro la chipolopolo ndi chipika pambuyo pa kugundana (v')

Yankho:

m ₁v ₁+ m ₂v ₂= (m ₁+ m ₂) v'

(0.03)(30) + (1)(0) = (0.03 + 1) v'

0.9 + 0 = 1.03 v'

0.9 = 1,03 v'

v' = 0.9 / 1,03

v' = 0.87 m/s

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2. Mpira wa biliyadi A wolemera makilogalamu 2 ukuyenda ndi liwiro v _A= 6 ms ⁻¹ umagundana ndi mpira B wolemera wofanana. Ngati kugundana kuli kosalala bwino, kodi liwiro la mipira iwiriyo ndi lotani pambuyo pa kugundana?

Zodziwika:

Kulemera A (m _A) = 2 kg

Kulemera B (m _B) = 2 kg

Liwiro loyamba la mpira A (v _A) = -6 m/s

Liwiro loyamba la mpira B (v _B) = 4 m/s

Zizindikiro za kuphatikiza ndi kuchotsera zimasonyeza kuti zinthuzo zimayenda mosiyana.

Ankafuna : liwiro la mipira iwiriyo pambuyo pa kugundana. (v')

Yankho:

m _Av _A+ m _Bv _B= (m _A' + m _B) v'

(2)(-6) + (2)(4) = (2 + 2) v'

-12 + 8 = 4 v'

-4 = 4 v'

v' = -4 / 4

v' = -1 m/s

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3. m₁ = makilogalamu 3 ndi m₂ = makilogalamu 4 yandikirana wina ndi mnzake mbali yosiyana ndi liwiro la v₁ = 10 m/s ndi v₂ = 12 m/s. Ngati kugundana kuli kosalala bwino, kodi liwiro la mipira iwiriyo pambuyo pa kugundana ndi lotani?

Zodziwika:

Chinthu cholemera 1 (m1 ₎= 3 kg

Chinthu cholemera 2 (m2 ₎= 4 kg

Liwiro la chinthu 1 (v ₁) = -10 m/s

Liwiro la chinthu 2 (v ₂) = 12 m/s

Kufunidwa : liwiro pambuyo pa kugundana (v')

Yankho:

m ₁v ₁+ m ₂v ₂= (m ₁' + m ₂) v'

(3)(-10) + (4)(12) = (3 + 4) v'

-30 + 48 = 7 v'

18 = 7 v'

v' = 18 / 7

v' = 2.6 m/s

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Werengani zambiri

Kugundana kolimba bwino mu gawo limodzi - mavuto ndi mayankho

1. Mpira wa magalamu 200, A, womwe ukuyenda pa liwiro la 10 m/s, umagunda mpira wa magalamu 200, B, pamene ukupuma. Kodi liwiro la mpira A ndi mpira B ndi lotani pambuyo pa kugundana?

Zodziwika:

Kulemera kwa mpira A (m _A) = magalamu 200 = 0.2 kg

Kulemera kwa mpira B (m _B) = magalamu 200 = 0.2 kg

Liwiro la mpira A musanagunde (v _A) = 10 m/s

Liwiro la mpira B musanagunde (v _B) = 0

Kufunidwa: liwiro la mpira A (v _A') ndi liwiro la mpira B (v _B') pambuyo pa kugundana

Yankho:

v _A' = v _B= 0

v _B' = v _A= 10 m/s

[irp]

2. Zinthu ziwiri zofanana zimayandikirana, zimagundana kenako zimadumphadumpha. Liwiro la kulemera kwa A musanagundane ndi 8 m/s ndipo liwiro la kulemera kwa B musanagundane ndi 12 m/s. Kodi kukula ndi njira ya liwiro la kulemera kwa A ndi kulemera kwa B pambuyo pa kugundana ndi kotani?

Zodziwika:

Uzito A (m _A) = m

Uzito B (m _B) = m

Liwiro la kulemera A musanagunde (v _A) = -8 m/s

Liwiro la kulemera kwa B musanagunde (v _B) = 12 m/s

Zizindikiro za kuphatikiza ndi kuchotsera zimasonyeza kuti zinthuzo zimayenda mosiyana.

Kufunidwa: kukula ndi malangizo a liwiro la kulemera A (v _A') ndi kulemera B (v _B') pambuyo pa kugundana

Yankho:

Mu kugundana kosalala bwino, ngati zinthu zofanana ndi kulemera, ndiye kuti liwiro la A pambuyo pa kugundana (v _A') = liwiro la B isanafike kugundana (v _B) ndi liwiro la B pambuyo pa kugundana (v _B') = liwiro la A isanafike kugundana (v _A).

Ngati A isanagunde, ipita kumanja ndipo B ipita kumanzere, ndiye kuti, ikagunda, A ipita kumanzere ndipo B ipita kumanja.

Zinthuzo zili ndi kulemera kofanana ndipo kugundana kwake kumakhala kosalala bwino kotero zinthu zonse ziwiri zimasinthasintha liwiro.

v _A' = -v _B= -12 m/s

v _B' = v _A= 8 m/s

Zizindikiro za kuphatikiza ndi kuchotsera zimasonyeza kuti zinthuzo zimayenda mosiyana.

[irp]

3. Chinthu cha 2-kg, A, chomwe chikuyenda pa liwiro la 10 m/s chikugunda mpira wa 4-kg, B, chikuyenda pa liwiro la 20 m/s. Ngati kugundana kuli kotambasuka bwino, kodi liwiro la chinthu A ndi chinthu B ndi lotani pambuyo pa kugundana?

Zodziwika:

Kulemera A (m _A) = 2 kg

Kulemera B (m _B) = 4 kg

Liwiro la chinthu A musanagunde (v _A) = 10 m/s

Liwiro la chinthu B musanagunde (v _B) = 20 m/s

Kufunidwa : liwiro la chinthu A (v _A') ndi liwiro la chinthu B (v _B') pambuyo pa kugundana

Yankho :

Mu kugundana kosalala bwino , ngati zinthuzo zili ndi kulemera kofanana ndipo zikuyandikirana, liwiro la chinthucho pambuyo pa kugundana limawerengedwa pogwiritsa ntchito njira iyi:

Kugundana kolimba bwino mu gawo limodzi - mavuto ndi mayankho 1

Liwiro la chinthu A pambuyo pa kugundana:

Kugundana kolimba bwino mu gawo limodzi - mavuto ndi mayankho 2

[irp]

4. Kuyenda kwa magalamu 100 pa liwiro la 20 m/s kumagunda khoma lomwe limagundana bwino kwambiri. Kodi kukula ndi komwe limayenda ndi liwiro la chinthu pambuyo pa kugundana ndi chiyani?

Zodziwika:

Kulemera (m _A) = magalamu 100 = 0.1 kg

Kulemera kwa khoma (m _B) = kosatha

Liwiro la kulemera musanagunde (v _A) = 20 m/s

Liwiro la kulemera pambuyo pa kugundana (v _B) = 0

Kufunidwa : kukula ndi komwe liwiro la kugundana likupita

Yankho:

Ngati v _B= 0, m _Ayaying'ono kwambiri ndipo m ₂yayikulu kwambiri ndiye v _A' = -v _Andi v ₂' = 0.

Zizindikiro za kuphatikiza ndi kuchotsera zimasonyeza kuti zinthuzo zimayenda mosiyana.

5. Mipira iwiri, A yokhala ndi kulemera kwa 2-kg ndi mpira B yokhala ndi kulemera kwa 5-kg, isanayambe komanso itatha kugundana ikuwonetsedwa pachithunzi chili pansipa. Ngati kugundanako kuli kotambasuka bwino, kodi liwiro la mpira A limakhala lotani isanafike kugundana?

Zodziwika:

Unyinji wa mpira A (m_A) = 2 kg Kugundana kosalala bwino - mavuto ndi mayankho 1

Kulemera kwa mpira B (m _B) = 5 kg

Liwiro la mpira B musanagunde (v _B) = 2 m/s

Liwiro la mpira A pambuyo pa kugundana (v _A') = 5 m/s

Liwiro la mpira B pambuyo pa kugundana (v _B') = 4 m/s

Mipira yonse ikupita kumanja kotero liwiro lawo lasainidwa kuti ndi labwino.

Kufunidwa: Liwiro la mpira A musanagunde (v _A)

Yankho:

m_A v_A +m_B v_B = m_A v_A' + m_B v_B'

2 (v _A) + (5) (2) = (2) (5) + (5) (4)

2(v _A) + 10 = 10 + 20

2(v _A) + 10 = 30

2(v _A) = 30 – 10

2(v _A) = 20

v _A= 20/2

v _A = 10 m/s

[irp]

6. Zinthu A ndi B zimayenda mopingasa, monga momwe chithunzi chili pansipa chikusonyezera. Ngati kugundana kuli kosalala bwino ndipo liwiro la chinthu B pambuyo pa kugundana ndi 15 m/s ¹ , kodi liwiro la chinthu A pambuyo pa kugundana ndi lotani?

Zodziwika:

Unyinji wa chinthu A (m_A) = 5 kg Kugundana kosalala bwino - mavuto ndi mayankho 2

Kulemera kwa chinthu B (m _B) = 2 kg

Liwiro la chinthu A musanagunde (v _A) = 12 m/s

Liwiro la chinthu B musanagunde (v _B) = 10 m/s

Liwiro la chinthu B pambuyo pa kugundana (v _B') = 15 m/s

Zinthu zonse ziwiri, zisanachitike komanso zitachitika, zimapita kumanja kotero kuti liwiro lawo likhala ndi chizindikiro chabwino.

Kufunidwa: Liwiro la chinthu A pambuyo pa kugundana (v _A')

Yankho:

m_A v_A +m_B v_B = m_A v_A' + m_B v_B'

(5) (12) + (2) (10) = (5)v _A' + (2) (15)

60 + 20 = (5)v _A' + 30

80 = (5)v _A' + 30

80 – 30 = (5)v _A'

50 = (5)v _A'

v _A' = 50/5

v _A' = 10 m/s

[wpdm_package id='1156′]

Werengani zambiri

Mphamvu ndi chikhumbo - mavuto ndi mayankho

1. Mpira waung'ono umaponyedwa mopingasa ndi liwiro losasintha la 10 m/s. Mpirawo umagunda khoma ndipo umawalanso ndi liwiro lomwelo. Kodi kusintha kwa mphamvu ya mpira ndi kotani?

Zodziwika:

Kulemera (m) = 0.2 kg

Liwiro loyambirira (v _o ) = -10 m/s

Liwiro lomaliza (v _t ) = 10 m/s

Zizindikiro za kuphatikiza ndi kuchotsera zimasonyeza kuti zinthuzo zimayenda mosiyana.

Kufunidwa : kusintha kwa mphamvu yolunjika (Δp)

Yankho:

Fomula ya kusintha kwa momentum yolunjika :

Δp = mv _t – mv _o = m (v _t – v _o )

Kusintha kwa mphamvu yolunjika:

Δp = 0.2 (10 – (-10)) = 0.2 (10 + 10)

Δp = 0.2 (20)

Δp = 4 kg m/s

[irp]

2. Mpira wa magalamu 10 umagwa momasuka kuchokera kutalika, umagunda pansi pa 15 m/s, kenako umabwerera mmwamba pa 10 m/s. Dziwani mphamvu!

Zodziwika:

Kulemera (m) = magalamu 10 = 0.01 kg

Liwiro loyambirira (v _o ) = -15 m/s

Liwiro lomaliza (v _t ) = 10 m/s

Wanted: Impulse (I)

Yankho:

Chikoka (I) chimafanana ndi kusintha kwa mphamvu (Δp)

I = mv _t – mv _o = m (v _t – v _o )

Chikhumbo:

Ine = 0.01 (10 – (-15)) = 0.01 (10 + 15)

Ine = 0.01 (25)

I = 0.25 kg m/s

[irp]

3. Mpira wa magalamu 200 unaponyedwa mopingasa ndi liwiro la 4 m/s, kenako mpirawo unamenyedwa mbali yomweyo. Kutalika kwa mpirawo ukakhudzana ndi mtolo ndi masekondi 2 mil ndipo liwiro la mpirawo likatuluka mtolo ndi 12 m/s. Mphamvu yomwe womenya mpirayo amagwiritsa ntchito pa mpira ndi …

Zodziwika:

Kulemera (m) = magalamu 200 = 0.2 kg

Liwiro loyambirira (v _o ) = 4 m/s

Liwiro lomaliza (v _t ) = 12 m/s

Nthawi yopuma (t) = 2 milliseconds = (2/1000) masekondi = 0.002 masekondi

Kufunidwa : Kukula kwa mphamvu (F)

Yankho:

Fomula ya chikoka:

Ine = F t

Fomula ya kusintha kwa mphamvu:

mv _t – mv _o = m (v _t – v _o )

Chikoka (I) chimafanana ndi kusintha kwa mphamvu (Δp)

I = Δp

F t = m (v _t – vo _o )

F (0.002) = (0.2)(12 - 4)

F (0.002) = (0.2)(8)

F (0.002) = 1.6

F = 1.6 / 0.002

F = 800 Newton

[wpdm_package id='1155′]

Werengani zambiri

Kuthamanga kwa Linear - Mavuto ndi Mayankho

1. Chinthu chimayenda pa liwiro losasintha la 10 m/s. Werengani mphamvu ya chinthucho.

Zodziwika :

Kulemera (m) = 1 kg

Liwiro (v) = 10 m/s

Kufunidwa: linear momentum (p)

Yankho:

Fomula ya momentum yolunjika:

p = mv

p = mzere wolunjika, m = kulemera, v = liwiro

Mphamvu yolunjika:

p = mv = (1)(10) = 10 kg m/s ²

[irp]

2. Chipolopolo cha makilogalamu awiri ndi chipolopolo cha makilogalamu anayi chimayenda pa liwiro losasintha la 20 m/s. Kodi mphamvu ya mabuloko ndi yotani?

Zodziwika:

Kulemera kwa chipika A (m _A) = 2 kg

Kulemera kwa chipika B (m _B) = 4 kg

Liwiro la chipika A (v _A) = 20 m/s

Liwiro la chipika B (v _B) = 20 m/s

Kufunidwa: Linear momentum ya block A (p _A) ndi linear momentum ya block B (p _B)

Yankho:

Mphamvu yolunjika ya block A :

p _A= m _Av _A= (2) (20) = 40 kg m/s

Mphamvu yolunjika ya block B :

p _B= m _Bv _B= (4)(20) = 80 kg m/s

[irp]

3. Buloko la makilogalamu awiri limayenda pa liwiro losasintha la 2 m/s ndipo buloko la makilogalamu awiri limayenda pa liwiro losasintha la 4 m/s. Dziwani momwe mabaloko alili.

Zodziwika:

Kulemera kwa chipika A (m _A) = 2 kg

Kulemera kwa chipika B (m _B) = 2 kg

Liwiro la chipika A (v _A) = 2 m/s

Liwiro la chipika B (v _B) = 4 m/s

Kufunidwa: mphamvu yolunjika ya mabuloko

Yankho:

Mphamvu yolunjika ya block A :

p _A= m _Av _A= (2) (2) = 4 kg m/s

Mphamvu yolunjika ya block B:

p _B= m _Bv _B= (2)(4) = 8 kg m/s

[irp]

4. Chinthu cholemera makilogalamu 5 chili pamalo opumulira. Kodi mphamvu yolunjika ya mphamvuyo ndi yotani?

Zodziwika:

Kulemera (m) = 5 kg

Liwiro la chinthu (v) = 0

Kufunidwa : mphamvu yolunjika (p)

Yankho:

p = mv = (5)(0) = 0

[wpdm_package id='1155′]

Werengani zambiri

Mphamvu - mavuto ndi mayankho

Mphamvu ndi liwiro limene ntchito imagwiridwa mu nthawi inayake. Mwa masamu, mphamvu ndi chiŵerengero cha ntchito/nthawi.

P = W/t

Kufotokozera: P = mphamvu (Joule/sekondi = Watt), W = ntchito (Joule), t = nthawi yopuma (sekondi)

Kutengera ndi equation iyi, tinganene kuti kuchuluka kwa ntchito, mphamvu zimakhala zazikulu. Kumbali ina, kuchepa kwa ntchito, mphamvu zimakhala zochepa. Kuchuluka kwa ntchito kumatanthauza kuchuluka kwa ntchito.

[irp]

Mphamvu ndi scalar. Gawo la SI la mphamvu ndi Joule/lachiwiri. Joule/lachiwiri = Watt (yofupikitsidwa ngati W), yomwe imatchedwa choncho polemekeza James Watt. Gawo la ufumu wa Britain la mphamvu ndi foot-pounds pa sekondi.

Chipangizochi ndi chaching'ono kwambiri kuti chigwiritsidwe ntchito, kotero chimagwiritsidwa ntchito mphamvu yayikulu ya horsepower (yofupikitsidwa ngati hp). Mphamvu imodzi ya horsepower = 550 foot-pounds pa sekondi = 764 Watts = ¾ kilowatt.

Kuchuluka kwa ntchito kungawonetsedwenso mu mayunitsi amphamvu x nthawi, mwachitsanzo, kilowatt-hours kapena kWh. KWh imodzi imatanthauza ntchito yochitidwa pamlingo wosasintha wa 1 kiloWatt kwa ola limodzi.

1. Munthu wolemera makilogalamu 50 amathamanga kukwera masitepe otalika mamita 10 m'mphindi ziwiri. Kuthamanga chifukwa cha mphamvu yokoka (g) ndi 10 m/ s . ^2. Dziwani mphamvu.

Zodziwika:

Kulemera (m) = 50 kg

Kutalika (h) = mamita 10

Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s ²

Nthawi yopuma (t) = mphindi ziwiri = 2 (60) = masekondi 120

Akufuna : Mphamvu (P)

Yankho:

Fomula ya mphamvu:

P = W / t

P = mphamvu , W = ntchito , t = nthawi

Fomula ya Ntchito:

W = F s = wh = mgh

W = ntchito , F = mphamvu , w = kulemera , d = kusamuka , h = kutalika , m = kulemera, g = kuthamanga chifukwa cha mphamvu yokoka

W = mgh = (50)(10)(10) = 5000 Joules.

P = W / t = 5000 / 120 = 41.7 Joules/se c on d.

[irp]

2. Werengani mphamvu yofunikira kwa munthu wolemera makilogalamu 60 amene akukwera mtengo wautali mamita 5 m'masekondi 10. Kuthamanga chifukwa cha mphamvu yokoka ndi 10 m/s ².

Zodziwika:

Kulemera (m) = 60 kg

Kutalika (h) = mamita awiri s

Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s ²

Nthawi yopuma (t) = masekondi 10

Akufuna : Mphamvu

Yankho:

Ntchito:

W = mgh = (60)(10)(5) = 3000 Joules

Mphamvu:

P = W / t = 3000 / 10 = 300 Joules/se cond.

3. Sewero loseketsa lozungulira lokhala ndi mphamvu ya ma watts 300 ndi mphindi 5 lozungulira ma raundi 5. Mphamvu yomwe imagwiritsa ntchito ndi….

A. 15 kJ

B. 75 kJ

C. 90 kJ

D. 450 kJ

Zodziwika:

Mphamvu (P) = 300 Watts = 300 Joules/sekondi

Nthawi (T) = mphindi 5 = 5 (masekondi 60) = masekondi 300

Chiwerengero cha maulendo = 5

Kufunidwa: Mphamvu zomwe zimagwiritsidwa ntchito ndi sewero loseketsa

Yankho:

Mphamvu - mavuto ndi mayankho

Yankho lolondola ndi D.

[wpdm_package id='1190′]

Werengani zambiri

Kugwiritsa ntchito mphamvu yamakina yosungira kuti iyende bwino - mavuto ndi mayankho

1. Chipika chimatsika pansi pa malo otsetsereka bwino popanda kukangana . Kodi liwiro la chipikacho ndi chiyani chikagunda pansi? Kuthamanga chifukwa cha mphamvu yokoka ndi 10 m/s ²

Kugwiritsa ntchito mphamvu ya makina yosungira kuti munthu ayende panjira yolunjika 1 Zodziwika:

Kutalika (h) = 8 m

Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s ²

Kufunidwa : liwiro (v)

Yankho :

Mphamvu yoyambirira yamakina (ME _o) = mphamvu yokoka (PE)

ME _o= PE = mgh = m (10)(8) = 80 m

Mphamvu yomaliza yamakina (ME _t ) = mphamvu ya kinetic (KE)

ME _t= KE = ½ mv ²

Mfundo yosungira mphamvu ya makina imati mphamvu yoyamba ya makina = mphamvu yomaliza ya makina:

INE _o= INE _t

80 m = ½ mv ²

80 = ½ v ²

160 = v ²

v = √160 = √(16)(10) = 4√10 m/s

[irp]

2. Chinthu cholemera makilogalamu 1 chimatsika pansi pa mamita 8. Dziwani mphamvu ya kinetic chinthucho chikayenda pa mamita 5… Kuthamanga chifukwa cha mphamvu yokoka g = 10 m/s ²

Kugwiritsa ntchito mphamvu ya makina yosungira kuti munthu ayende panjira yolunjika 2 Zodziwika:

Kulemera (m) = 0.2 kg

d = mamita 5

Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s ²

Kufunidwa : mphamvu ya kinetic (KE)

Yankho:

uchimo 30 ^o = h / d

0.5 = maola / 5

h = (0.5)(5) = mamita 2.5

Kusintha kwa kutalika kwa chinthucho ndi mamita 2.5.

Mphamvu yoyambirira ya makina (ME _o ) = mphamvu yokoka (PE)

ME _o= PE = mgh = (1)(10)(2.5) = 25 Joules

Mphamvu yomaliza yamakina (ME _t ) = mphamvu ya kinetic (KE)

ME _t = KE

Mfundo yosungira mphamvu ya makina imati mphamvu yoyamba ya makina = mphamvu yomaliza ya makina:

INE _o= INE _t

25 = KE

Mphamvu ya kinetic = 25 Joules.

[wpdm_package id='1170′]

Werengani zambiri

Kugwiritsa ntchito mphamvu yamakina yosungira kuti iyende pamalo okhota - mavuto ndi mayankho

1. Chipika cha 1 kg chimatsikira pansi pamwamba posalala. Dziwani mphamvu ya kayendedwe kake ndi liwiro la chipikacho pamalo otsika kwambiri. Kuthamanga chifukwa cha mphamvu yokoka ndi 10 m/s ².

Kugwiritsa ntchito mphamvu ya makina yosungira kuti iyende pamwamba pa curve 1 Zodziwika:

Kulemera (m) = 1 kg

Kusintha kwa kutalika (h) = 5 m

Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s ²

Kufunidwa: Mphamvu ya Kinetic (KE) ndi liwiro la chipikacho.

Yankho:

(a) Mphamvu ya kinetic

Mphamvu yoyambirira ya makina = mphamvu yokoka

ME _o= PE = mgh = (1)(10)(5) = 50 Joules

Mphamvu yomaliza yamakina = mphamvu ya kinetic

ME _t= KE = ½ mv _t²

Mfundo yosungira mphamvu ya makina imati mphamvu yoyamba ya makina = mphamvu yomaliza ya makina:

INE _o= INE _t

PE = KE

50 = KE

Mphamvu ya kinetic (KE) = 50 Joules.

(b) Liwiro la Block

Mfundo yosungira mphamvu zamakanika:

Mphamvu yoyambirira yamakina (ME _o) = mphamvu yomaliza yamakina (ME _t)

Mphamvu yokoka (PE) = mphamvu ya kinetic (KE)

50 = ½ mv ²

2(50) / m = v ²

100 / 1 = v ²

100 = v ²

v = √100

v = 10 m/s

[irp]

2. Chinthu cholemera makilogalamu awiri chimatsika pansi popanda kukangana. Kodi mphamvu ya kinetic ndi liwiro la chinthucho mamita awiri kuchokera pansi ndi chiyani? Kuthamanga chifukwa cha mphamvu yokoka ndi 10 m/s ²

Kugwiritsa ntchito mphamvu ya makina yosungira kuti iyende pamwamba pa curve 2 Zodziwika:

Kulemera (m) = 2 kg

Kusintha kwa kutalika (h) = 10 – 2 = 8 m

Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s ²

Kufunidwa : mphamvu ya kinetic (KE) ndi liwiro (v) pa mamita awiri pamwamba pa nthaka.

Yankho:

(a) Mphamvu ya kinetic pamtunda wa mamita awiri kuchokera pansi

Mphamvu yoyambirira ya makina = mphamvu yokoka

ME _o= PE = mgh = (2)(10)(8) = 160 Joules

Mphamvu yomaliza yamakina = mphamvu ya kinetic

ME _t= KE = ½ mv _t²

Mfundo yosungira mphamvu ya makina imati mphamvu yoyamba ya makina = mphamvu yomaliza ya makina:

INE _o= INE _t

PE = KE

160 = KE

Mphamvu ya kinetic (KE) pa mamita awiri pamwamba pa nthaka ndi 160 Joules.

(b) Liwiro la chinthu pamalo otsika kwambiri

Mfundo yosungira mphamvu zamakanika:

Mphamvu yoyambirira yamakina (ME _o) = mphamvu yomaliza yamakina (EM _t)

Mphamvu yokoka (PE) = mphamvu ya kinetic (KE)

160 = ½ mv ²

160 = ½ (2) v ²

160 = v ²

v = √160 = √(16)(10) = 4√10 m/s

[wpdm_package id='1167′]

Werengani zambiri

Kugwiritsa ntchito mphamvu yamakina yosungira kayendedwe ka zombo - mavuto ndi mayankho

1. Mpira wokankha umachoka pansi pa ngodya θ = 30 ^o ndi liwiro loyambirira la 10 m/s. Kulemera kwa mpira = 0.1 kg. Kuthamanga chifukwa cha mphamvu yokoka ndi 1 0 m/s ² . Dziwani (a) Mphamvu yokoka pamalo okwera kwambiri (b) Malo okwera kwambiri kapena kutalika kwakukulu

Zodziwika:

Kulemera (m) = 0.1 kg

Liwiro loyambirira (v _o) = 10 m/s

Ngodya = 30 ^o

Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s ²

Yankho:

(a) Mphamvu yokoka

Kugwiritsa ntchito mphamvu ya makina yosungira kayendedwe ka zombo - mavuto ndi mayankho 1

Werengerani gawo lopingasa (v _ox) ndi gawo loyima (v _oy) la liwiro loyambirira.

Kugwiritsa ntchito mphamvu ya makina yosungira kayendedwe ka zombo - mavuto ndi mayankho 2 v_ox=v_o cos θ = (10)(cos 30^o) = (10)(0.5√3) = 5√3 m/s

v _oy= v _o tchimo θ = (10)(tchimo 30 ^o ) = (10)( 0.5) = 5 m/s

Mphamvu yoyambirira yamakina

Mphamvu yoyambirira yamakina (ME _o) = mphamvu ya kinetic (KE)

ME _o= KE = ½ mv _o² = ½ (0.1) (10) ² = ½ (0.1) (100) = ½ (10) = 5 Joules

Mphamvu yomaliza yamakina

Mphamvu ya kinetic pamalo okwera kwambiri:

KE = ½ mv _ox² = ½ (0.1) (5√3) ² = ½ (0.1) ((25) (3)) = ½ (0.1) (75) = 3.75 Joules

Mfundo yosungira mphamvu zamakanika

Mphamvu yoyambirira yamakina (ME _o) = mphamvu yomaliza yamakina (ME _t)

KE = PE + KE

5 = EP + 3.75

PE = 5 – 3.75 = 1.25 Joule

Mphamvu yokoka yomwe imapezeka pamalo okwera kwambiri ndi 1.25 Joules.

(b) Malo okwera kwambiri kapena kutalika kwakukulu

PE = mgh

1.25 = (0.1)(10) h

1.25 = ola

Kutalika kwakukulu ndi mamita 1.25.

[irp]

2. Mpira wa 0.1-kg umayendetsedwa mopingasa ndi liwiro loyambirira v _o= 10 m/s kuchokera ku nyumba yokwera mamita 10. Kuthamanga chifukwa cha mphamvu yokoka ndi 10 m/s ^2. Dziwani mphamvu ya kinetic ya mpirawo ukagunda pansi.

Zodziwika:

Kulemera (m) = 0.1 kg

Liwiro loyambirira (v _o) = 10 m/s

Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s ²

Kusintha kwa kutalika (h) = 10 – 2 = 8 m

Kufunidwa: mphamvu ya kinetic pa mamita awiri pamwamba pa nthaka

Yankho:

Mphamvu yokoka (PE) = mgh = (0.1)(10)(10) = 10 Joules

Mphamvu yoyambirira ya kinetic (KE) = ½ mv _o² = ½ (0.1)(10) ² = ½ (0.1)(100) = ½ (10) = 5 Joules

Mphamvu yomaliza ya kinetic = mphamvu yoyamba yokoka + mphamvu yoyambirira ya kinetic = 10 + 5 = 15 Joules

[wpdm_package id='1173′]

Werengani zambiri