Mafunso a chitsanzo cha torque

10 Mafunso a chitsanzo cha torque

1. Kulemera kwa ndodo AB kunganyalanyazidwe. Ngati F_R ndi zotsatira za mphamvu zitatu F₁, F₂ ndi F₃, kenako kukula kwa mphamvu F₂ ndipo mtunda x ndi …

A. 50 N pansi ndi 0,5 m kumanzere kwa A

B. 50 N mmwamba ndi 0,5 m kumanja kwa A

C. 50 N mmwamba ndi 0,75 m kumanzere kwa A

D. 50 N pansi ndi 0,75 m kumanja kwa A

E. 50 N mmwamba ndi 0,2 m kumanja kwa A

Zokambirana

Amadziwika kuti:

Mphamvu yochokera (F)_R) = 40 N

F₁ = 10 n

F₃ = 20 n

Anafunsa kuti: Kukula kwa mphamvu F₂ ndi mtunda x

Yankho:

Werengerani kukula kwa mphamvu F₂ :

Gaya Mphamvu yolunjika mmwamba ndi yabwino, mphamvu yolunjika pansi ndi yoipa.

ΣF = 0 (ndodo siimaima ndipo siisuntha)

- F_R +F₁ +F₂ - F₃ = 0

– 40 + 10 + F₂ - 20 = 0

– 30 + F₂ - 20 = 0

– 50 + F₂ = 0

F₂ = 50 Newton, ndi zabwino chifukwa chakuti mphamvuyo ikupita mmwamba.

Werengerani mtunda x:

Sankhani mfundo A ngati mzere wozungulira.

τ₁ =F₁ l₁ = (10 N)(1 m) = 10 Nm

Mphamvu yoyamba ndi yabwino chifukwa imapangitsa kuti kuzungulira kwa ndodo AB kukhale kotsutsana ndi wotchi.

τ₂ =F₂ x = (50)(x) = 50x Nm

Mphamvu yoyamba ndi yabwino chifukwa imapangitsa kuti kuzungulira kwa ndodo AB kukhale kotsutsana ndi wotchi.

τ₃ =F₃ x = (20 N)(1,75 m) = -35 Nm

Mphamvu ya 1 ndi yoipa chifukwa imayambitsa kuzungulira kwa ndodo AB mbali imodzi ndi kuzungulira kwa wotchi.

Torque Yotsatira:

Στ = 0 (ndodo imakhala chete ndipo sizungulira)

10 + 50x – 35 = 0

50x - 25 = 0

50x = 25

x = 25/50

x = mamita 0,5

Yankho lolondola ndi B.

2. Kalembedwe F₁, F₂, F₃, ndi F₄ imagwira ntchito pa ndodo ABCD monga momwe zasonyezedwera pachithunzichi! Ngati kulemera kwa ndodo sikunyalanyazidwa, ndiye kuti mtengo wake mphindi ya kalembedwe Kupita ku mfundo A ndi…..

A. 15 Nm

B. 18 Nm

C. 35 Nm

D. 53 Nm

E. 68 Nm

Zokambirana

Mzere wozungulira ndi mfundo A.

Amadziwika kuti:

Kalembedwe F₁ = 10 N, mkono wa mphamvu l₁ = 0

Kalembedwe F₂ = 4 N, mkono wa mphamvu l₂ = 2 mita

Kalembedwe F₃ = 5 N, mkono wa mphamvu l₃ = 3 mita

Kalembedwe F₄ = 10 N, mkono wa mphamvu l₄ = 6 mita

Anafunsa kuti: Mphindi ya mphamvu yokhudza mfundo A

Yankho:

Mphamvu ya mphindi 1 (τ₁) = F₁ l₁ = (10)(0) =

Mphamvu ya mphindi 2 (τ₂) = F₂ l₂ = (4)(2) = -8 Nm

Mphamvu ya mphindi 3 (τ₃) = F₃ l₃ = (5)(3) = 15 Nm

Mphamvu ya mphindi 4 (τ₄) = F₄ l₄ = (10)(6) = -60 Nm

Mphamvu imakhala yabwino ngati mphamvuyo ipangitsa kuti ndodoyo izizungulira mozungulira wotchi.

Mphamvu imakhala yoipa ngati mphamvuyo ipangitsa kuti ndodoyo izizungulira mozungulira wotchi.

Mphamvu yotsatira:

τ = 0 - 8 Nm + 15 Nm - 60 Nm

τ = -68 Nm + 15 Nm

τ = -53 Nm

Chizindikiro choyipa chimatanthauza kuti ndodoyo imazungulira mozungulira wotchi.

Yankho lolondola ndi D.

3. Ndodo yomwe kulemera kwake sikunyalanyazidwa imakhudzidwa ndi mphamvu zitatu F_A =F_C = 10 N ndi F_B = 20 N monga momwe chithunzichi chikusonyezera. Ngati mtunda AB = BC = 20 cm, ndiye kuti kukula kwa mphamvu ya mphindi pafupifupi C ndi…

A. 0 Nm

B. 1 Nm

C. 4 Nm

D. 6 Nm

E. 8 Nm

Zokambirana

Ndizodziwika kuti :

Axis kuzungulira yomwe ili pamalo C.

Mtunda pakati pa F_A ndi mzere wozungulira (r)_AC) = 40 cm = 0,4 mamita

Mtunda pakati pa F_B ndi mzere wozungulira (r)_BC) = 20 cm = 0,2 mamita

Mtunda pakati pa F_C ndi mzere wozungulira (r)_CC) = 0 cm

F_A = 10 Newton

F_B = 20 Newton

F_C = 10 Newton

Anafunsa Mphamvu yochokerapo ngati ndodoyo yazunguliridwa pa mzere wa C

Yankhani :

Werengerani nthawi ya mphamvu yopangidwa ndi mphamvu iliyonse.

Nthawi ya mphamvu A

Στ_A = (F_A)(r_AC tchimo 90^o) = (10 N)(0,4 m)(1) = -4 Nm

Mphamvu ya A ndi yoipa chifukwa njira yozungulira ndodo yomwe imayendetsedwa ndi mphamvu ya A imayenda mozungulira wotchi.

Mphamvu B

Στ_B = (F_B)(r_BC tchimo 90^o) = (20 N)(0,2 m)(1) = 4 Nm

Mphamvu ya B ndi yabwino chifukwa njira yozungulira ndodo yomwe imachitika chifukwa cha mphamvu ya B ndi yotsutsana ndi wotchi.

Mphamvu ya C

Στ_C = (F_C)(r_CC tchimo 90^o) = (10 N)(0)(1) = 0

Mphamvu ya C imalembedwa ndi 0 chifukwa cha mphamvu ya F_C imagwirizana ndi mzere wozungulira

Mphamvu yochokerapo

Στ = Στ₁ + Στ₂ + Στ₃

Στ = -4 + 4 + 0

Στ = 0 Nm

Yankho lolondola ndi A.

4. Ndodo yautali wa masentimita 50 imayikidwa ndi mphamvu zitatu zofanana, monga momwe zasonyezedwera pachithunzi chotsatirachi. Ngati ndodoyo yazunguliridwa mozungulira mfundo yozungulira pa mfundo C, kukula kwa mphamvu yonse ndi...

A. 1 Nm

B. 3 Nm

C. 4 Nm

D. 5 Nm

E. 6 Nm

Zokambirana

Ndizodziwika kuti :

Mzere wozungulira uli pamalo C.

Mtunda pakati pa F₁ ndi mzere wozungulira (r)₁) = 30 cm = 0,3 mamita

Mtunda pakati pa F₂ ndi mzere wozungulira (r)₂) = 10 cm = 0,1 mamita

Mtunda pakati pa F₃ ndi mzere wozungulira (r)₃) = 20 cm = 0,2 mamita

F₁ = 10 Newton

F₂ = 10 Newton

F₃ = 10 Newton

Anafunsa Mphamvu yochokerapo ngati ndodoyo yazunguliridwa pa mzere wa C

Yankhani :

Werengerani nthawi ya mphamvu yopangidwa ndi mphamvu iliyonse.

Nthawi ya mphamvu 1

Στ₁ = (F₁)(r₁ tchimo 90^o) = (10 N)(0,3 m)(1) = -3 Nm

Mphamvu ya mphindi 1 ndi yoipa chifukwa njira yozungulira ndodo yomwe imachitika chifukwa cha mphamvu ya mphindi 1 ili mbali imodzi ndi momwe manja a wotchi amazungulira.

Nthawi ya mphamvu 2

Στ₂ = (F₂)(r₂ tchimo 90^o) = (10 N)(0,1 m)(1) = 1 Nm

Mphamvu ya 2 ndi yabwino chifukwa njira yozungulira ndodo yomwe imachitika chifukwa cha mphamvu ya 2 imayenda mozungulira wotchi.

Nthawi ya mphamvu 3

Στ₃ = (F₃)(r₃ tchimo 30^o) = (10 N)(0,2 m)(0,5) = -1 Nm

Mphamvu ya mphindi 3 ndi yoipa chifukwa njira yozungulira ndodo yomwe imachitika chifukwa cha mphamvu ya mphindi 3 ili mbali imodzi ndi momwe manja a wotchi amazungulira.

Mphamvu yochokerapo

Στ = Στ₁ + Στ₂ + Στ₃

Στ = -3 + 1 – 1

Στ = -3 Nm

Kukula kwa mphamvu yochokera ku mphamvu ndi mamita atatu a Newton. Chizindikiro chotsutsa cha mphamvu yochokera ku mphamvu chimatanthauza kuti njira yozungulira ndodo yomwe imayendetsedwa ndi mphamvu yochokera ku mphamvuyo ndi yofanana ndi njira yozungulira dzanja la wotchi.

Yankho lolondola ndi B.

5. 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

Anafunsa kuti: Mtengo wa mphamvu yozungulira mzere wozungulira pa mfundo C

Yankho:

Mphamvu Yoyamba:

τ₁ =F₁ tchimo 53^o = (5 N)(2 m)(0,8) = (10)(0,8) N = 8 N

Mphamvu ya mphindi 1 imapangitsa kuti ndodoyo izizungulira mozungulira wotchi kotero kuti mphamvu ya mphindi 1yo ili ndi chizindikiro chabwino.

Mphamvu Yoyamba:

τ₂ =F₂ tchimo 90^o = (0,4 N)(1 m)(1) = -0,4 N

Mphamvu ya mphindi 2 imapangitsa kuti ndodoyo izizungulira mozungulira mozungulira kotero kuti mphamvu ya mphindi 2 imakhala ndi chizindikiro choipa.

Mphamvu Yoyamba:

τ₃ =F₃ tchimo 90^o = (4,8 N)(2 m)(1) = -9,6 N

Mphamvu ya mphindi 3 imapangitsa kuti ndodoyo izizungulira mozungulira mozungulira kotero kuti mphamvu ya mphindi 3 imakhala ndi chizindikiro choipa.

Mphamvu yotsatira:

∑τ = τ₁ – τ₂ – τ₃ = 8 – 0,4 – 9,6 = 8 – 10 = -2 Nm

Kukula kwa mphamvu ya mphindi ndi mamita awiri a Newton. Mphamvu ya mphindi yolakwika imatanthauza kuti ndodoyo imazungulira motsutsa wotchi.

Yankho lolondola ndi D.

6. 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

Anafunsa kuti: Mtengo wa mphamvu yozungulira mzere wozungulira pa mfundo C

Yankho:

Mphamvu Yoyamba:

τ₁ =F₁ l₁ = (6 N)(1 m) = 6 Nm

Mphamvu ya mphindi 1 imapangitsa kuti ndodoyo izizungulira mozungulira wotchi kotero kuti mphamvu ya mphindi 1yo ili ndi chizindikiro chabwino.

Mphamvu Yoyamba:

τ₂ =F₂ r₂ tchimo 30^o = (6 N)(2 m)(0,5)= 6 Nm

Mphamvu ya mphindi 2 imapangitsa kuti ndodoyo izizungulira mozungulira wotchi kotero kuti mphamvu ya mphindi 2yo ili ndi chizindikiro chabwino.

Mphamvu Yoyamba:

τ₃ =F₃ l₃ = (4 N)(2 m) = -8 Nm

Mphamvu ya mphindi 3 imapangitsa kuti ndodoyo izizungulira mozungulira mozungulira kotero kuti mphamvu ya mphindi 3 imakhala ndi chizindikiro choipa.

Mphamvu yotsatira:

∑τ = τ₁ + τ₂ – τ₃ = 6 + 6 – 8 = 4 Nm

Kukula kwa mphamvu ndi mamita 4 a Newton. Mphamvu yabwino imatanthauza kuti ndodoyo imazungulira mozungulira wotchi.

Yankho lolondola ndi B.

7. Ndodo AB, yomwe kulemera kwake sikunyalanyazidwa, imayikidwa mopingasa ndipo imagwira ntchito ndi mphamvu zitatu monga momwe zasonyezedwera pachithunzichi. Nthawi yomwe mphamvu imagwira ntchito 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
Ndizodziwika kuti :
Mzere wozungulira kapena pivot uli pamalo a D.
F₁ = 10 N ndi l₁ =r₁ uchi θ = (40 cm)(uchi 53^o) = (0,4 m)(0,8) = 0,32 mamita
F₂ = 10√2 N ndi l₂ =r₂ uchi θ = (20 cm)(uchi 45^o) = (0,2 m)(0,5√2) = 0,1√2 mamita
F₃ = 20 N ndi l₃ =r₁ uchi θ = (10 cm)(uchi 90^o) = (0,1 m)(1) = 0,1 mamita
Anafunsa : Mphamvu yochokerapo
Yankhani :

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

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

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

8. Ndodo AB, yomwe kulemera kwake sikunyalanyazidwa, imayikidwa mopingasa ndipo imagwira ntchito ndi mphamvu zitatu monga momwe zasonyezedwera pachithunzichi. Nthawi yomwe mphamvu imagwira ntchito 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
Ndizodziwika kuti :
Mzere wozungulira uli pa D.
Mtunda pakati pa F₁ 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 F₃ ndi mzere wozungulira (r)_CD) = 10 cm = 0,1 m
F₁ = 10 Newton
F₂ = 10√2 Newton
F₃ = 20 Newton
Tchimo 53^o = 0,8
Anafunsa Mphamvu yochokerapo ngati ndodo yazunguliridwa pa mzere wa D
Yankhani :

Werengerani nthawi ya mphamvu yopangidwa ndi mphamvu iliyonse.
Nthawi ya mphamvu 1
Mphamvu ya 1 ndi yabwino chifukwa njira yozungulira ndodo yomwe imachitika chifukwa cha mphamvu ya 1 imayenda mozungulira wotchi.
Nthawi ya mphamvu 2
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
Mphamvu ya 3 ndi yabwino chifukwa njira yozungulira ndodo yomwe imachitika chifukwa cha mphamvu ya 3 imayenda mozungulira wotchi.
Mphamvu yochokerapo
Yankho lolondola ndi D.

9. Ndodo yomwe kulemera kwake sikunyalanyazidwa imakhudzidwa ndi mphamvu zitatu F_A =F_C = 10 N ndi F_B = 20 N monga momwe chithunzichi chikusonyezera. Ngati mtunda AB = BC = 20 cm, ndiye kuti kukula kwake mphindi ya kalembedwe kuyika mfundo C ndi…

A. 0 Nm
B. 1 Nm
C. 4 Nm
D. 6 Nm
E. 8 Nm

Zokambirana
Ndizodziwika kuti :
Mzere wozungulira uli pamalo C.
Mtunda pakati pa F_A ndi mzere wozungulira (r)_AC) = 40 cm = 0,4 mamita
Mtunda pakati pa F_B ndi mzere wozungulira (r)_BC) = 20 cm = 0,2 mamita
Mtunda pakati pa F_C ndi mzere wozungulira (r)_CC) = 0 cm
F_A = 10 Newton
F_B = 20 Newton
F_C = 10 Newton
Anafunsa Mphamvu yochokerapo ngati ndodoyo yazunguliridwa pa mzere wa C
Yankhani :
Werengerani nthawi ya mphamvu yopangidwa ndi mphamvu iliyonse.
Nthawi ya mphamvu A
Mphamvu ya A ndi yoipa chifukwa njira yozungulira ndodo yomwe imayendetsedwa ndi mphamvu ya A imayenda mozungulira wotchi.
Mphamvu B
Mphamvu ya B ndi yabwino chifukwa njira yozungulira ndodo yomwe imachitika chifukwa cha mphamvu ya B ndi yotsutsana ndi wotchi.
Mphamvu ya C

Mphamvu ya C imalembedwa ndi mtengo wa 0 chifukwa gaya F_C imagwirizana ndi mzere wozungulira
Mphamvu yochokerapo
Yankho lolondola ndi A.

10. Ndodo yautali wa masentimita 50 ili ndi mphamvu zitatu zofanana monga momwe zasonyezedwera pachithunzi chotsatirachi. Ngati ndodoyo yazunguliridwa mozungulira pivot pa mfundo C, ndiye kuti kukula kwa mphamvu yonse ndi...

A. 1 Nm
B. 3 Nm
C. 4 Nm
D. 5 Nm
E. 6 Nm
Zokambirana
Ndizodziwika kuti :
Mzere wozungulira uli pamalo C.
Mtunda pakati pa F₁ ndi mzere wozungulira (r)₁) = 30 cm = 0,3 mamita
Mtunda pakati pa F₂ ndi mzere wozungulira (r)₂) = 10 cm = 0,1 mamita
Mtunda pakati pa F₃ ndi mzere wozungulira (r)₃) = 20 cm = 0,2 mamita
F₁ = 10 Newton
F₂ = 10 Newton
F₃ = 10 Newton
Anafunsa Mphamvu yochokerapo ngati ndodoyo yazunguliridwa pa mzere wa C
Yankhani :
Werengerani nthawi ya mphamvu yopangidwa ndi mphamvu iliyonse.
Nthawi ya mphamvu 1
Mphamvu ya mphindi 1 ndi yoipa chifukwa njira yozungulira ndodo yomwe imachitika chifukwa cha mphamvu ya mphindi 1 ili mbali imodzi ndi momwe manja a wotchi amazungulira.
Nthawi ya mphamvu 2
Mphamvu ya 2 ndi yabwino chifukwa njira yozungulira ndodo yomwe imachitika chifukwa cha mphamvu ya 2 imayenda mozungulira wotchi.
Nthawi ya mphamvu 3
Mphamvu ya mphindi 3 ndi yoipa chifukwa njira yozungulira ndodo yomwe imachitika chifukwa cha mphamvu ya mphindi 3 ili mbali imodzi ndi momwe manja a wotchi amazungulira.
Mphamvu yochokerapo
Kukula kwa mphamvu yochokera ku mphamvu ndi mamita atatu a Newton. Chizindikiro chotsutsa cha mphamvu yochokera ku mphamvu chimatanthauza kuti njira yozungulira ndodo yomwe imayendetsedwa ndi mphamvu yochokera ku mphamvuyo ndi yofanana ndi njira yozungulira dzanja la wotchi.
Yankho lolondola ndi B.

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