Chitsanzo cha mphindi ya mphamvu

Zitsanzo 10 za Mafunso Okhudza Mphamvu

1. Kutalika kwa ndodo AB ndi mamita awiri ndipo kukula kwa mphamvu F ndi 10 Newtons. Dziwani mphindi ya kalembedwe kulowera ku mfundo A ndi komwe ndodo AB imazungulira!
Zokambirana
Mzere wozungulira uli pamalo A.

Amadziwika kuti:
Mphamvu (F) = 10 Newtons
Mtunda AB (r)_AB) = mamita 2
Mphamvu F imapanga ngodya ya 90^o motsutsana ndi ndodo AB.
Dzanja lamphamvu (l) = r_AB tchimo 90^o = (mamita awiri)(1) = mamita awiri
Anafunsa kuti: Mphamvu yozungulira mfundo A ndi komwe ndodo AB imazungulira

Yankho:
Nthawi ya mphamvu:
τ = F l = (10 N)(2 m) = 20 Newton metres
Mphamvu ya mphindi ndi yabwino chifukwa mphamvu F imapangitsa kuti ndodo ya AB izungulire mozungulira wotchi.

2. Kutalika kwa ndodo AB ndi mamita awiri ndipo kukula kwa mphamvu F ndi ma Newton 10. Dziwani nthawi ya mphamvu pafupi ndi mfundo A ndi komwe ndodo AB imazungulira!

Zokambirana
Mzere wozungulira ndiyomwe ili pamalo A.

Amadziwika kuti:
Mphamvu (F) = 10 Newtons
Mtunda AB (r)_AB) = mamita 2
Mphamvu F imapanga ngodya ya 60^o motsutsana ndi ndodo AB.
Dzanja lamphamvu (l) = r_AB tchimo 60^o = (mamita awiri)(0,5√3) = √mamita atatu
Anafunsa kuti: Torsi mfundo A ndi njira yozungulira ndodo AB

Yankho:
Nthawi ya mphamvu:
τ = F l = (10 N)(√3 m) = 10√3 mamita a Newton
Mphamvu ya mphindi ndi yabwino chifukwa mphamvu F imapangitsa kuti ndodo ya AB izungulire mozungulira wotchi.

3. Kutalika kwa ndodo AB ndi mamita awiri, kukula kwa mphamvu F1 _ndi ma Newton 10 ndipo kukula kwa mphamvu F2 _ndi ma Newton 15. Dziwani nthawi yomwe mphamvu imachokera pakati pa ndodo ndi komwe ndodo AB imazungulira !

Zokambirana
Mzere wozungulira uli pakati pa ndodo.
Amadziwika kuti:
Kalembedwe 1 (F)₁) = 10 Newton
Mtunda F₁ ndi pakati pa tsinde (r₁) = mamita 1
Kalembedwe F₁ kupanga ngodya ya 90^o kupita ku ndodo ya AB
Kalembedwe ka mkono 1 (l)₁) =r₁ tchimo 90^o = (mamita awiri)(1) = mamita awiri

Kalembedwe 2 (F)₂) = 15 Newton
Mtunda F₂ ndi pakati pa tsinde (r₂) = mamita 1
Kalembedwe F₂ kupanga ngodya ya 90^o kupita ku ndodo ya AB
Kalembedwe ka mkono 2 (l)₂) =r₂ tchimo 90^o = (mamita awiri)(1) = mamita awiri
Anafunsa kuti: Mphamvu yochokera pakati pa ndodo ndi komwe ndodo AB imazungulira
Yankho:
Mphamvu yachiwiri:
τ₁ =F₁ l₁ = (10 N)(1 m) = 10 Newton metres
Mphamvu ya mphindi ndi yabwino chifukwa mphamvu F imapangitsa kuti ndodo izungulire mozungulira wotchi.

Mphamvu yachiwiri:
τ₂ =F₂ l₂ = (15 N)(1 m) = -15 Newton mamita
Mphamvu ya mphamvu ndi yoipa chifukwa mphamvu F₂ zomwe zimapangitsa kuti ndodoyo izizungulira mozungulira wotchi.

Mphamvu yotsatira:
Στ = τ₁ – τ₂ = 10 – 15 = – 5 Newton meters
Mphamvu yomwe imabwera chifukwa cha mphamvu F imapangitsa kuti ndodo ya AB izungulire mozungulira wotchi.

4. Kutalika kwa ndodo AB ndi mamita awiri, kukula kwa mphamvu F ndi₁ ndi 10 Newton ndi kukula kwa mphamvu F₂ ndi 10 Newton. Dziwani nthawi yomwe mphamvu imachokera pakati pa ndodo ndi komwe ndodo AB imazungulira!
Zokambirana
Mzere wozungulira uli pakati pa ndodo.
Amadziwika kuti:
Kalembedwe 1 (F)₁) = 10 Newton
Mtunda F₁ ndi pakati pa tsinde (r₁) = mamita 1
Kalembedwe F₁ kupanga ngodya ya 60^o kupita ku ndodo ya AB
Kalembedwe ka mkono 1 (l)₁) =r₁ tchimo 60^o = (mamita 1)(0,5√3) = mamita 0,5√3

Kalembedwe 2 (F)₂) = 10 Newton
Mtunda F₂ ndi pakati pa tsinde (r₂) = mamita 1
Kalembedwe F₂ kupanga ngodya ya 90^o kupita ku ndodo ya AB
Kalembedwe ka mkono 2 (l)₂) =r₂ tchimo 90^o = (mamita awiri)(1) = mamita awiri
Anafunsa kuti: Mphamvu yochokera pakati pa ndodo ndi komwe ndodoyo imazungulira ndi komwe AB imazungulira
Yankho:
Mphamvu yachiwiri:
τ₁ =F₁ l₁ = (10 N)(0,5√3 m) = 5√3 = 8,7 mamita a Newton
Mphamvu ya mphindi ndi yabwino chifukwa mphamvu ya F1 imapangitsa kuti ndodo izungulire mozungulira wotchi.

Mphamvu yachiwiri:
τ₂ =F₂ l₂ = (10 N)(1 m) = -10 Newton mamita
Mphamvu ya mphamvu ndi yoipa chifukwa mphamvu F₂ zomwe zimapangitsa kuti ndodoyo izizungulira mozungulira wotchi.

Mphamvu yotsatira:
Στ = τ₁ – τ₂ = 8,7 – 10 = – 1,3 Newton meters
Mphamvu yomwe imabwera chifukwa cha mphamvu F imapangitsa kuti ndodo ya AB izungulire mozungulira wotchi.

5. Kutalika kwa ndodo AB ndi mamita awiri, kukula kwa mphamvu F ndi₁ ndi 10 Newton, kukula kwa mphamvu F₂ ndi 10 Newton ndi kukula kwa mphamvu F₃ ndi ma Newton 15. Mtunda pakati pa mfundo A ndi mfundo C ndi mamita 7,5. Mphamvu F₂ ili pakati pa ndodo AB. Dziwani nthawi yomwe mphamvu imachokera pa mfundo C yomwe ili mamita 2,5 kuchokera pa mfundo B! Komanso onani njira yomwe ndodo AB imazungulira.
Zokambirana
Mzere wozungulira uli pamalo C omwe ali mamita 2,5 kuchokera pamalo B.
Amadziwika kuti:
Kalembedwe 1 (F)₁) = 10 Newton
Mtunda F₁ ndi mfundo C (r₁) = mamita 2,5
Kalembedwe F₁ kupanga ngodya ya 90^o kupita ku ndodo ya AB
Kalembedwe ka mkono 1 (l)₁) =r₁ tchimo 90^o = (mamita awiri)(1) = mamita awiri

Kalembedwe 2 (F)₂) = 10 Newton
Mtunda F₂ ndi mfundo C (r₂) = mamita 2,5
Kalembedwe F₂ kupanga ngodya ya 90^o kupita ku ndodo ya AB
Kalembedwe ka mkono 2 (l)₂) =r₂ tchimo 90^o = (mamita awiri)(1) = mamita awiri

Kalembedwe 3 (F)₃) = 15 Newton
Mtunda F₃ ndi mfundo C (r₃) = mamita 7,5
Kalembedwe F₃ kupanga ngodya ya 90^o kupita ku ndodo ya AB
Kalembedwe ka mkono 3 (l)₃) =r₃ tchimo 90^o = (mamita awiri)(1) = mamita awiri
Anafunsa kuti: Mphamvu yochokera pa mfundo C ndi njira yozungulira ndodo AB.
Yankho:
Mphamvu yachiwiri:
τ₁ =F₁ l₁ = (10 N)(2,5 m) = 25 Newton metres
Mphamvu ya nthawi ndi yabwino chifukwa mphamvu F₁ zomwe zimapangitsa kuti ndodoyo izizungulira mozungulira wotchi.

Mphamvu yachiwiri:
τ₂ =F₂ l₂ = (10 N)(2,5 m) = 25 Newton metres
Mphamvu ya nthawi ndi yabwino chifukwa mphamvu F₂ zomwe zimapangitsa kuti ndodoyo izizungulira mozungulira wotchi.

Mphamvu yachiwiri:
τ₃ =F₃ l₃ = (15 N)(7,5 m) = -112,5 Newton mamita
Mphamvu ya mphamvu ndi yoipa chifukwa mphamvu F₃ zomwe zimapangitsa kuti ndodoyo izizungulira mozungulira wotchi.

Mphamvu yotsatira:
Στ = τ₁ + τ₂ – τ₃ = 25 + 25 – 112,5 = – 62,5 mamita a Newton
Mphamvu yomwe imabwera chifukwa cha mphamvu F imapangitsa kuti ndodo ya AB izungulire mozungulira wotchi.

6. Kutalika kwa ndodo AB ndi mamita awiri, kukula kwa mphamvu F ndi₁ ndi 10 Newton, kukula kwa mphamvu F₂ ndi 10 Newton ndi kukula kwa mphamvu F₃ ndi ma Newton 10. Dziwani nthawi yomwe mphamvu imachokera pa mfundo A yomwe ili mamita 5 kuchokera pomwe mphamvu F imagunda.₁Komanso dziwani komwe ndodo AB imazungulira.
Zokambirana
Mzere wozungulira uli pamalo A.
Amadziwika kuti:
Kalembedwe 1 (F)₁) = 10 Newton
Mtunda F₁ ndi mfundo A (r₁) = mamita 5
Kalembedwe F₁ kupanga ngodya ya 60^o kupita ku ndodo ya AB
Kalembedwe ka mkono 1 (l)₁) =r₁ tchimo 60^o = (mamita 5)(0,5√3) = mamita 2,5√3

Kalembedwe 2 (F)₂) = 10 Newton
Mtunda F₂ ndi mfundo A (r₂= = 0
Kalembedwe F₂ kupanga ngodya ya 90^o kupita ku ndodo ya AB
Kalembedwe ka mkono 2 (l)₂) =r₂ tchimo 90^o = (0)(1) = 0
Kalembedwe 3 (F)₃) = 10 Newton
Mtunda F₃ ndi mfundo A (r₃) = mamita 10
Kalembedwe F₃ kupanga ngodya ya 30^o kupita ku ndodo ya AB
Kalembedwe ka mkono 3 (l)₃) =r₃ tchimo 30^o = (mamita awiri)(0,5) = mamita awiri
Anafunsa kuti: Mphamvu yochokera pa mfundo A ndi komwe ndodo AB imazungulira.
Yankho:
Mphamvu yachiwiri:
τ₁ =F₁ l₁ = (10 N)(2,5√3 m) = 25√3 = 43,3 mamita a Newton
Mphamvu ya mphindi ndi yabwino chifukwa mphamvu ya F1 imapangitsa kuti ndodo izungulire mozungulira wotchi.

Mphamvu yachiwiri:
τ₂ =F₂ l₂ = (10 N)(0) = 0
Mphamvu ya mphindi ndi zero chifukwa mphamvu F₂ imagwirizana ndi mzere wozungulira

Mphamvu yachiwiri:
τ₃ =F₃ l₃ = (10 N)(5 m) = -50 Newton mamita
Mphamvu ya mphamvu ndi yoipa chifukwa mphamvu F₃ zomwe zimapangitsa kuti ndodoyo izizungulira mozungulira wotchi.

Mphamvu yotsatira:
Στ = τ₁ + τ₂ – τ₃ = 43,3 + 0 – 50 = – 6,7 mamita a Newton
Mphamvu yomwe imabwera chifukwa cha mphamvu F imapangitsa kuti ndodo ya AB izungulire mozungulira wotchi.

7. Mphamvu zitatu F₁, F₂, ndi F₃ imagwira ntchito pa ndodo monga momwe zasonyezedwera pachithunzi chotsatirachi. Ngati kulemera kwa ndodo sikunyalanyazidwa ndipo kutalika kwa ndodo ndi mamita 4, ndiye kuti mphamvu ya mphindi yozungulira mzere wozungulira pa mfundo C ndi…. (sin 53^o = 0,8, cos 53^o = 0,6, AB = BC = CD = DE = mita imodzi)

A. 12 Nm
B. 8 Nm
C. 6 Nm
D. 2 Nm
E. Zero

Zokambirana
Amadziwika kuti:
Mzere wozungulira uli pa mfundo C.
Kalembedwe 1 (F)₁) = 5 Newton
Mtunda pakati pa malo ogwirira ntchito F₁ ndi mzere wozungulira (r)₁) = mamita 2
Kalembedwe 2 (F)₂) = 0,4 Newton
Mtunda pakati pa malo ogwirira ntchito F2 ndi mzere wozungulira (r)₂) = mamita 1
Kalembedwe 3 (F)₃) = 4,8 Newton
Mtunda pakati pa malo ogwirira ntchito F₃ ndi mzere wozungulira (r)₃) = mamita 2
Funso: Mtengo wa mphamvu yozungulira mzere wozungulira pa mfundo C
Yankho:

Mphamvu Yoyamba:
Mphamvu ya mphindi 1 imapangitsa kuti ndodoyo izizungulira mozungulira wotchi kotero kuti mphamvu ya mphindi 1yo ili ndi chizindikiro chabwino.
Mphamvu Yoyamba:
Mphamvu ya mphindi 2 imapangitsa kuti ndodoyo izizungulira mozungulira mozungulira kotero kuti mphamvu ya mphindi 2 imakhala ndi chizindikiro choipa.
Mphamvu Yoyamba:
Mphamvu ya mphindi 3 imapangitsa kuti ndodoyo izizungulira mozungulira mozungulira kotero kuti mphamvu ya mphindi 3 imakhala ndi chizindikiro choipa.

Mphamvu yotsatira:
Kukula kwa mphamvu ya mphindi ndi mamita awiri a Newton. Mphamvu ya mphindi yolakwika imatanthauza kuti ndodoyo imazungulira motsutsa wotchi.
Yankho lolondola ndi D.

8. Kukula kwa mphamvu yomwe imabwera chifukwa cha mphamvu pa ndodo pa mfundo O ndi mphamvu zomwe zimagwira ntchito pa ndodo ngati kulemera kwake sikunyalanyazidwa ndi….

A. 7,5 Nm
B. 4 Nm
C. 3,5 Nm
D. 3 Nm
E. 2 Nm

Zokambirana
Amadziwika kuti:
Mzere wozungulira uli pa mfundo O.
Kalembedwe 1 (F)₁) = 6 Newton
Mtunda pakati pa malo ogwirira ntchito F₁ ndi mzere wozungulira (r)₁) = mamita 1
Kalembedwe 2 (F)₂) = 6 Newton
Mtunda pakati pa malo ogwirira ntchito F2 ndi mzere wozungulira (r)₂) = mamita 2
Kalembedwe 3 (F)₃) = 4 Newton
Mtunda pakati pa malo ogwirira ntchito F₃ ndi mzere wozungulira (r)₃) = mamita 2
Funso: Mtengo wa mphamvu yozungulira mzere wozungulira pa mfundo C
Yankho:
Mphamvu Yoyamba:
Mphamvu ya mphindi 1 imapangitsa kuti ndodoyo izizungulira mozungulira wotchi kotero kuti mphamvu ya mphindi 1yo ili ndi chizindikiro chabwino.
Mphamvu Yoyamba:
Mphamvu ya mphindi 2 imapangitsa kuti ndodoyo izizungulira mozungulira wotchi kotero kuti mphamvu ya mphindi 2yo ili ndi chizindikiro chabwino.
Mphamvu Yoyamba:
Mphamvu ya mphindi 3 imapangitsa kuti ndodoyo izizungulira mozungulira mozungulira kotero kuti mphamvu ya mphindi 3 imakhala ndi chizindikiro choipa.

Mphamvu yotsatira:
Kukula kwa mphamvu ndi mamita 4 a Newton. Mphamvu yabwino imatanthauza kuti ndodoyo imazungulira mozungulira wotchi.
Yankho lolondola ndi B.

9. Ndodo ndi yayitali mamita 8. Mphamvu zitatu zimagwira ntchito pa ndodo, monga momwe chithunzi chili pansipa chikusonyezera. Kukula kwa mphamvu yomwe imapangitsa ndodo kuzungulira pakati pake ndi…
A. 10 N m
B. 20 N m
C. 30 N m
D. 40 N m
E. 50 N m

Kukambirana:
Pakati pa ndodo pali pakati. Ndodoyo ndi yautali mamita 8, kotero pakati pa ndodoyo pali mamita 4 kuchokera kumapeto kwa ndodoyo.
Mphamvu Yamphamvu 1 = F₁ l₁ = (10 N)(4 m) = 40 N m
Moment of Force 1 ili ndi phindu labwino chifukwa Moment of Force 1 imapangitsa kuti ndodoyo izizungulira mozungulira wotchi.
Mphamvu Yamphamvu 2 = F₂ l₂ = (10 N)(2 m) = – 20 N m
Moment of Force 2 ili ndi phindu loipa chifukwa Moment of Force 2 imapangitsa kuti ndodoyo izizungulira mozungulira wotchi.
Mphamvu Yamphamvu 3 = F₃ l₃ = (15 N)(2 m) = – 30 N m
Moment of Force 3 ili ndi phindu loipa chifukwa Moment of Force 3 imapangitsa kuti ndodoyo izizungulira mozungulira wotchi.

Mphamvu Yotsatira Nthawi = 40 N m – 20 N m – 30 N m = – 10 N m

Mphamvu yomwe imabwera chifukwa cha mphamvu kapena mphamvu yomwe imabwera chifukwa cha mphamvuyo ili ndi phindu loipa, izi zikusonyeza kuti njira yozungulira ndodoyo ndi yozungulira wotchi.

Yankho lolondola ndi A.

10. Mphamvu F₁ = 10 N, F₂ = 15 N, F₃ = 15 N ndi F₄ = 10 N, ikugwira ntchito pa ndodo ABCD monga momwe zasonyezedwera pachithunzichi. Kutalika kwa ndodo ABCD ndi mamita 20. Ngati kulemera kwa ndodo sikunyalanyazidwa ndiye kuti mtengo wa mphamvu yozungulira mfundo D ndi...
A. 15 Nm
B. 18 Nm
C. 35 Nm
D. 63 Nm
E. 68 Nm

Kukambirana:
Cholinga cha funso ili ndikupeza phindu la mphamvu yomwe imachokera yomwe imapangitsa kuti ndodo izungulire, komwe pakati pa kuzungulira kuli pa mfundo D.
Mphamvu Yamphamvu 1 = F₁ l₁ = (10 N)(15 m) = 150 N m
Moment of Force 1 ili ndi phindu labwino chifukwa Moment of Force 1 imapangitsa kuti ndodoyo izizungulira mozungulira wotchi.
Mphamvu Yamphamvu 2 = F₂ l₂ = (15 N)(5 m) = -75 N m
Moment of Force 2 ili ndi phindu loipa chifukwa Moment of Force 2 imapangitsa kuti ndodoyo izizungulira mofanana ndi kuzungulira kwa wotchi.
Mphamvu Yamphamvu 3 = F₃ l₃ = (15 N)(0 m) = 0 N m

Nthawi ya Mphamvu 3 ndi zero chifukwa F₃ imagwirizana ndi mzere wozungulira.
Mphamvu Yamphamvu 4 = F₄ l₄ = (10 N)(5 m) = 50 N m
Moment of Force 4 ili ndi phindu labwino chifukwa Moment of Force 4 imapangitsa kuti ndodoyo izizungulira mozungulira wotchi.

Mphamvu Yotsatira Nthawi = 150 N m – 75 N m + 50 N m = 125 N m
Mphamvu yomwe imabwera chifukwa cha mphamvu kapena mphamvu yomwe imabwera chifukwa cha mphamvuyo imakhala ndi phindu labwino, motero njira yozungulira ndodoyo ndi yosiyana ndi njira yozungulira manja a wotchi.