Mafunso a Chitsanzo cha Mphamvu Yozungulira

Zitsanzo 11 za Mafunso Okhudza Kusinthasintha kwa Mayendedwe

Nthawi ya Kalembedwe

1. Ndodo yopepuka kwambiri, yotalika masentimita 140. Mphamvu zitatu zimagwira ntchito pa ndodo, F1 ₌ 20 Newton, _F2 = 10 N, ndi F3 ₌ 40 N, iliyonse ili ndi malangizo ndi malo monga momwe zasonyezedwera pachithunzichi. Kukula kwa mphamvu yomwe imapangitsa ndodo kuzungulira pakati pa kulemera kwake ndi...

A. 40 Nm

B. 39 Nm

C. 28 Nm

D. 14 Nm

E. 3 Nm

Zokambirana

Amadziwika kuti:

Pakati pa kulemera kwa ndodoyo pali pakati pa ndodoyo.

Kutalika kwa ndodo (l) = 140 cm = 1,4 mamita

Mphamvu 1 (F ₁ ) = 20 N, mkono wa mphamvu 1 (l ₁ ) = 70 cm = 0,7 mamita

Mphamvu 2 (F ₂ ) = 10 N, mkono wa mphamvu 2 (l ₂ ) = 100 cm – 70 cm = 30 cm = 0,3 mamita

Mphamvu 3 (F ₃ ) = 40 N, mkono wa mphamvu 3 (l ₃ ) = 70 cm = 0,7 mamita

Funso: Kukula kwa mphamvu ya ndodo yomwe imapangitsa kuti ndodoyo izizungulira pakati pa kulemera kwake

Yankho:

Mphamvu ya mphindi 1 imapangitsa kuti ndodo izungulire mozungulira wotchi. Chifukwa chake, mphamvu ya mphindi 1 ndi yoipa.

τ ₁ = F ₁ l ₁ = (20 N)(0,7 m) = -14 N m

Mphamvu ya mphindi 2 imapangitsa kuti ndodo izungulire mozungulira wotchi. Chifukwa chake, mphamvu ya mphindi 2 ndi yabwino.

τ ₂ = F ₂ l ₂ = (10 N)(0,3 m) = 3 N m

Mphamvu ya mphindi 3 imapangitsa kuti ndodo izungulire mozungulira wotchi. Chifukwa chake, mphamvu ya mphindi 3 ndi yoipa.

τ ₃ = F ₃ l ₃ = (40 N)(0,7 m) = -28 N m

Mphamvu yotsatira:

Στ = -14 Nm + 3 Nm – 28 Nm = – 42 Nm + 3 Nm = -39 Nm

Kukula kwa mphamvu ya mphindi ndi mamita 39 a Newton. Chizindikiro chotsutsa chimatanthauza kuti ndodoyo imazungulira motsutsa wotchi.

Yankho lolondola ndi B.

2. Ndodo AB, yomwe kulemera kwake sikunyalanyazidwa, imayikidwa mopingasa ndipo imagwira ntchito ndi mphamvu zitatu monga momwe zasonyezedwera pachithunzichi. Mphamvu yomwe imachokera pa ndodo ikazunguliridwa pa mzere wa D ndi… (sin 53 ^o = 0,8)

A. 2,4 N m

B. 2,6 N m

C. 3,0 N m

D. 3,2 N m

E. 3,4 N m

Zokambirana

Amadziwika kuti :

Mzere wozungulira kapena pivot uli pamalo a D.

F ₁ = 10 N ndi l ₁ = r ₁ tchimo θ = (40 cm) (tchimo 53 ^o ) = (0,4 m) (0,8) = mita 0,32

F ₂ = 10√2 N ndi l ₂ = r ₂ tchimo θ = (20 cm)(tchimo 45 ^o ) = (0,2 m)(0,5√2) = 0,1√2 mamita

F ₃ = 20 N ndi l ₃ = r ₁ tchimo θ = (10 cm) (tchimo 90 ^o ) = (0,1 m) (1) = mita 0,1

Anafunsa : Nthawi yogwira ntchito ya mphamvu

Yankho :

τ ₁ = F ₁ l ₁ = (10 N) (0,32 m) = 3,2 Nm

(zabwino chifukwa mphindi iyi ya mphamvu imapangitsa kuti chipikacho chizungulire motsutsa wotchi)

τ ₁ = F ₂ l ₂ = (10√2 N)( 0,1√2 m) = -2 Nm

(zoipa chifukwa mphindi iyi ya mphamvu imapangitsa kuti chipikacho chizizungulira mozungulira wotchi)

τ ₁ = F ₂ l ₂ = (20 N) (0,1 m) = 2 Nm

(zabwino chifukwa mphindi iyi ya mphamvu imapangitsa kuti chipikacho chizungulire motsutsa wotchi)

Mphamvu yotsatira:

Στ = τ ₁ – τ ₁ + τ ₃

Στ = 3,2 Nm – 2 Nm + 2 Nm

Στ = 3,2 Nm

Yankho lolondola ndi D.

3. Ndodo AB, yomwe kulemera kwake sikunyalanyazidwa, imayikidwa mopingasa ndipo imagwira ntchito ndi mphamvu zitatu monga momwe zasonyezedwera pachithunzichi. Mphamvu yomwe imachokera pa ndodo ikazunguliridwa pa mzere wa D ndi… (sin 53 ^o = 0,8)

A. 2,4 Nm

B. 2,6 Nm

C. 3,0 Nm

D. 3,2 Nm

E. 3,4 Nm

Zokambirana

Amadziwika kuti :

Mzere wozungulira uli pa D.

Mtunda pakati pa F ₁ ndi mzere wozungulira (r _AD ) = 40 cm = 0,4 m

Mtunda pakati pa F2 _ndi mzere wozungulira (r _BD ) = 20 cm = 0,2 m

Mtunda pakati pa F ₃ ndi mzere wozungulira (r _CD ) = 10 cm = 0,1 m

F1 = 10 _Newtons

F ₂ = 10√2 Newton

F3 = 20 _Newtons

Tchimo 53 ^o = 0,8

Funso : Mphamvu yochokerapo ngati ndodoyo yazunguliridwa pa mzere wa D

Yankho :

Werengerani nthawi ya mphamvu yopangidwa ndi mphamvu iliyonse.

Nthawi ya mphamvu 1

Στ ₁ = (F ₁ )(r _AD tchimo 53 ^o ) = (10 N)(0,4 m)(0,8) = 3,2 Nm

Mphamvu ya 1 ndi yabwino chifukwa njira yozungulira ndodo yomwe imachitika chifukwa cha mphamvu ya 1 imayenda mozungulira wotchi.

Nthawi ya mphamvu 2

Στ ₂ = (F ₂ )(r _BD tchimo 45 ^o ) = (10√2 N)(0,2 m)(0,5√2) = -2 Nm

Mphamvu ya mphindi 2 ndi yoipa chifukwa njira yozungulira ndodo yomwe imachitika chifukwa cha mphamvu ya mphindi 2 ili mbali imodzi ndi momwe manja a wotchi amazungulira.

Nthawi ya mphamvu 3

Στ ₃ = (F ₃ )(r _CD sin 90 ^o ) = (20 N)(0,1 m)(1) = 2 Nm

Mphamvu ya 3 ndi yabwino chifukwa njira yozungulira ndodo yomwe imachitika chifukwa cha mphamvu ya 3 imayenda mozungulira wotchi.

Mphamvu yochokerapo

Στ = Στ ₁ + Στ ₂ + Στ ₃

Στ = 3,2 – 2 + 2

Στ = 3,2 Newton mita

Yankho lolondola ndi D.

Nthawi ya Inertia

4. Taganizirani chithunzi cha mipira iwiri yolumikizidwa ndi waya. Kutalika kwa waya = 12 m, l ₁ = 4 m ndi kulemera kwa waya sikunyalanyazidwa, kotero kukula kwa mphindi ya inertia ya dongosolo ndi…

A. 52,6 kg m²

B. 41,6 kg m ²

C. 34,6 kg m ²

D. 22,4 kg m ²

E. 20,4 kg m ²

Zokambirana

Amadziwika kuti :

Kulemera kwa mpira A (m _A ) = 0,2 kg

Kulemera kwa mpira B (m _B ) = 0,6 kg

Mtunda pakati pa mpira A ndi mzere wozungulira (r _A ) = mamita 4

Mtunda pakati pa mpira B ndi mzere wozungulira (r _B ) = 12 – 4 = mamita 8

Funso : Nthawi ya kusakhazikika (I) kwa dongosololi

Yankho :

Nthawi ya kutopa kwa mpira A

I _A = (m _A )(r _A ² ) = (0,2)(4) ² = (0,2)(16) = 3,2kg m ²

Nthawi ya kutopa kwa mpira B

I _B = (m _B )(r _B ² ) = (0,6)(8) ² = (0,6)(64) = 38,4 kg m ²

Nthawi ya kusagwira ntchito kwa dongosolo la tinthu tating'onoting'ono :

Ine = I _A + I _B = 3,2 + 38,4 = 41,6 kg m ²

Yankho lolondola ndi B.

Lamulo Lachiwiri la Newton la Kuyenda Kozungulira

5. Yang'anani chithunzi cha gudumu lolimba lofanana mbali imodzi. Chingwe chimakulungidwa m'mphepete mwa gudumu kenako kumapeto kwa chingwecho kumakokedwa ndi mphamvu F ya 6 N. Ngati kulemera kwa gudumu ndi 5 kg ndipo utali wake ndi 20 cm, kuthamanga kwa gudumu ndi…

A. 0,12 rad s^-2

B. 1,2 rad s ^–2

C. 3,0 rad s ^–2

D. 6,0 rad s ^–2

E. 12,0 rad s ^–2

Zokambirana

Amadziwika kuti:

Mphamvu yokoka (F) = 6 Newton

Kulemera kwa mawilo (M) = 5 kg

Utali wa mawilo (R) = 20 cm = 20/100 m = 0,2 m

Funso: Kuthamanga kwa gudumu (α) mozungulira

Yankho:

Werengerani mphindi ya mphamvu:

τ = FR = (6 Newton)(0,2 mamita) = 1,2 Newton mamita

Werengerani mphindi ya inertia:

Fomula ya nthawi ya inertia ya gudumu lolimba mu mawonekedwe a diski kapena mbale ndi 1/2 MR ² = 1/2 (5 kg)(0,2 m) ² = 1/2 (5 kg)(0,04 m ² ) = 1/2 (0,2) = 0,1 kg m ².

Werengerani kuthamanga kwa angular pogwiritsa ntchito njira yozungulira ya rotational dynamics:

τ = I α

α = τ / I = 1,2 / 0,1 = 12 rad s ^-2

Yankho lolondola ndi E.

6. Pulley yolimba ya disc yokhala ndi kulemera kwa 8 kg ndi radius ya 10 cm imakulungidwa m'mphepete mwa chingwe ndi katundu wa 4 kg womangiriridwa kumapeto amodzi (g = 10 ms ^-2 ). Kuthamanga kwa kuyenda pansi kwa katundu ndi...

A. 2,5 ms ^–2

B. 5,0 ms ^–2

C. 10,0 ms ^–2

D. 20,0 ms ^–2

E. 33,3 ms ^–2

Zokambirana

Amadziwika kuti:

Kulemera kwa pulley ya disc yolimba (m) = 8 kg

Ulalo wa pulley yolimba ya disc (r) = 10 cm = 0,1 mita

Kulemera kwa katundu (m) = 4 kg

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

Kulemera kwa katundu (w) = mg = (4 kg)(10 m/s ² ) = 40 kg m/s ² = 40 Newtons

Funso: Kuthamanga kwa kuyenda pansi kwa katundu

Yankho:

Werengerani nthawi ya inertia ya diski yolimba:

I = 1/2 MR ² = 1/2 (8 kg)(0,1 m) ² = (4 kg)(0,01 m ² ) = 0,04 kg m ²

Werengerani mphindi ya mphamvu:

τ = F r = (40 N) (0,1 m) = 4 Nm

Werengerani kuthamanga kwa angular pogwiritsa ntchito njira yachiwiri ya Newton yoyendetsera mozungulira:

Στ = I α

4 = 0,04 α

α = 4 / 0,04 = 100

Werengerani kufulumira kwa kuyenda pansi kwa katundu:

a = r α = (0,1) (100) = 10 m/s ²

Yankho lolondola ndi C.

7. Pulley yolimba yokhala ndi kulemera (M) ndi radius (R) monga momwe zasonyezedwera pachithunzichi! Malekezero amodzi a chingwe chopanda kulemera amazunguliridwa mozungulira pulley, malekezero ena a chingwe amapachikidwa ndi katundu wa m kg, kuthamanga kwa angular kwa pulley (α) ngati katunduyo watulutsidwa. Ngati chidutswa cha pulasitiki A chokhala ndi kulemera kwa 1⁄2 M chalumikizidwa ku pulley, kuti apange kuthamanga komweko kwa angular, katunduyo ayenera kupangidwa…. (Pulley ya I = 1/2 MR ² )

A. 3/4 m kg

B. 3/2 m kg

C. 2 m kg

D. 3 m kg

E. 4 m kg

Zokambirana

Amadziwika kuti :

kulemera kwa katundu = m

Kulemera kwa katundu = w = mg

Unyinji wa pulley yolimba = M

Ulalo wa pulley yolimba = R

Kuthamanga kwa angular kwa pulley = α

Anafunsa :

Ngati kulemera kwa pulley kukukwera kufika pa M + M/2 = 3M/2 ndipo kuthamanga kwa angular kwa pulley = α, kodi kulemera kwa katunduyo ndi kotani?

Yankho :

Nthawi ya inertia ya pulley yopanda pulasitiki:

Ine = 1/2 MR ² = 0,5 MR ²

Nthawi ya inertia ya pulley + plasticine:

Ine = 1/2 (3M/2) R ² = (3M/4) R ² = 0,75M R ²

Nthawi ya mphamvu:

τ = FR

Lamulo lachiwiri la Newton la kayendedwe ka kuzungulira:

Στ = I α

w R = I α

mg R = I α

α = mg R / I

Kuti pakhale kuthamanga komweko kwa angular, kulemera kwa katundu kuyenera kupangidwa….. M'malo mwa α mu equation 2 ndi α mu equation 1:

Yankho lolondola ndi B.

8.. Pulley yopangidwa ndi chinthu cholimba yokhala ndi chingwe chozungulira mbali yake yakunja ikuwonetsedwa monga momwe zasonyezedwera pachithunzichi. Kukangana kwa pulley ndi chingwe ndi kukangana pa mzere wake wozungulira sizimaganiziridwa. Ngati katunduyo ukutsika ndi kuthamanga kosalekeza kwa ms ^-2 , ndiye kuti mtengo wa mphindi ya inertia ya pulley ndi wofanana ndi….

A. I = τ α R

B. I = τ α ^-1 R

C. I = τ a R

D. I = τ a ^-1 R ^-1

E. I = τ a R ^-1

Zokambirana

Amadziwika kuti:

Mphamvu = w = mg

Dzanja lamphamvu = R

Kuthamanga kwa angular = α

Kuthamanga kwa katundu = a ms ^-2

Funso: Nthawi ya inertia ya pulley (I)

Yankho:

Ubale pakati pa kufulumira kwa mzere ndi kufulumira kwa angular:

a = R α

α = a / R

Nthawi ya inertia imawerengedwa pogwiritsa ntchito fomula iyi:

τ = I α

I = τ: α = τ : a / R = τ (R / a) = τ R a ^-1

Palibe yankho lolondola.

9. Pulley yopangidwa ndi chinthu cholimba yokhala ndi chingwe chozungulira mbali yake yakunja ikuwonetsedwa monga momwe zasonyezedwera pachithunzichi. Kukangana kwa pulley sikunyalanyazidwa. Ngati mphindi ya inertia ya pulley I = β ndipo chingwecho chikukokedwa ndi mphamvu yosalekeza F, ndiye kuti mtengo wa F ndi wofanana ndi….

A. F = α .β .R

B. F = α. β ^2. R

C. F = α . (β . R) ^-1

D. F = α . β . (R) ^-1

E. F = R. (α. β) ^-1

Zokambirana

Amadziwika kuti:

Mphamvu yokoka = F

Nthawi ya inertia ya pulley = β

Kuthamanga kwa angular kwa pulley = α

Utali wa Pulley = R

Funso: Mtengo wa F ndi wofanana ndi….

Yankho:

Fomula yachiwiri ya lamulo la Newton yoyendetsera kayendedwe ka kuzungulira:

Στ = β α ———- Equation 1

Kufotokozera kwa fomula:

Στ = Mphindi wotsatira wa mphamvu (torque)

β = Nthawi ya kutopa

α = Kuthamanga kwa Angular

Mphamvu yomwe imagwira ntchito pa pulley imabwera chifukwa cha izi:

Στ = FR ———-> Equation 2

Kufotokozera kwa fomula:

F = mphamvu yokoka

R = Mtunda kuchokera pamalo pomwe mphamvu F imagwira ntchito mpaka ku mzere wozungulira = utali wa pulley

Sinthani Στ mu equation 1 ndi Στ mu equation 2:

Στ = β . α

F. R = β. α

F = (β . α) / R

F = β . α . (R ^-1 )

Yankho lolondola ndi D.

Mphamvu Yozungulira

10. Tinthu tolemera magalamu 0,2 timayenda mozungulira ndi liwiro lokhazikika la 10 rad s ^-1 . Ngati utali wa njira ya tinthuto ndi 3 cm, ndiye kuti mphamvu ya angular ya tinthuto ndi...

A. 3 × 10 ^–7 kg m ² s ^-1

B. 9 × 10 ^–7 kg m ² s ^-1

C. 1,6 × 10 ^–6 kg m ² s ^-1

D. 1,8 × 10 ^–4 kg m ² s ^-1

E. 4,5 × 10 ^–3 kg m ² s ^-1

Zokambirana

Amadziwika kuti:

Kulemera kwa tinthu tating'onoting'ono (m) = 0,2 magalamu = 2 x 10 ^-4 kg

Liwiro la angular (ω) = 10 rad s ^-1

Utali wa njira ya tinthu (r) = 3 cm = 3 x 10 ^-2 mamita

Anafunsa: Mphamvu ya angular ya tinthu

Yankho:

Fomula ya angular momentum:

L = Ine ω

Kufotokozera: I = angular momentum, I = mphindi ya inertia, ω = angular velocity

Nthawi ya kulephera kwa tinthu tating'onoting'ono:

Ine = mr ² = (2 x 10 ^-4 )(3 x 10 ^-2 ) ² = (2 x 10 ^-4 )(9 x 10 ^-4 ) = 18 x 10 ^-8

Mphamvu ya angular ndi:

L = I ω = (18 x 10 ^-8 )(10 rad s ^-1 ) = 18 x 10 ^-7 kg m ² s ^-1

Palibe yankho lolondola.

11. Wovina amazungulira ndi manja ake atatambasulidwa kufika pa 160 cm. Kenako, manja ake amapindidwa kufika pa 80 cm pa zigongono. Ngati liwiro la wovinayo likhalabe lofanana, ndiye kuti mphamvu yake yolunjika ndi...

A. akadali

B. imakhala theka la kukula koyambirira

C. imakhala 3/4 ya kukula koyambirira

D. imakhala kawiri kuposa yoyamba

E. imakhala nthawi zinayi kuposa yoyamba

Zokambirana

Amadziwika kuti:

Ulalo wozungulira 1 (r1 ₎ = 160 cm

Ulalo wozungulira 2 (r2 ₎ = 80 cm

Liwiro la angular 1 (ω ₁ ) = ω

Liwiro la angular 1 (ω ₂ ) = ω

Anafunsa: Linear momentum

Yankho:

Liwiro la mzere 1:

v ₁ = r ₁ ω ₁ = (160 cm) ω

Liwiro la mzere 2:

v ₂ = r ₂ ω ₂ = (80 cm) ω

Mphamvu yolunjika 1:

p = mv ₁ = m (160 cm) ω

Mphamvu yolunjika 2:

p = mv ₂ = m (80 cm) ω

Kotero mphamvu yolunjika imakhala 1/2 nthawi yoyambirira.

Yankho lolondola ndi B.

Gwero la funso:

Mafunso a National Examination Physics a Senior High School/Vocational High School