Nguva yesimba - matambudziko nemhinduro

Nguva yesimba - matambudziko nemhinduro

1. Kana F _R iri simba guru reF ₁ , F ₂ , uye F ₃ , simba guru reF ₂ na x nderei?

Zvinozivikanwa:

Simba reNet (F)_R) = 40 N

Simba 1 (F ₁ ) = 10 N

Simba (F ₃ ) = 20 N

Zvinodiwa: Hukuru hwesimba F ₂ uye daro ra x

Solution:

Tsvaga hukuru hwesimba F ₂ :

Kumanikidza kunongedzera kumusoro, chiratidzo chekuramba uye chiratidzo chekuramba pasi, chiratidzo chekuramba.

ΣF = 0

– F _R + F ₁ + F ₂ – F ₃ = 0

– 40 + 10 + F ₂ – 20 = 0

– 30 + F ₂ – 20 = 0

– 50 + F ₂ = 0

F ₂ = 50 Newtons.

Chiratidzo chekuwedzera chinoratidza kuti divi resimba riri kumusoro.

Tsvaga x.

Sarudza A sechikamu chekutenderera.

τ ₁ = F ₁ l ₁ = (10 N)(1 m) = 10 Nm

Torque 1 inotenderera danda remwenje richipesana newachi saka tinoisa chiratidzo chakanaka kutorque 3.

τ ₂ = F ₂ x = (50)(x) = 50x Nm

Torque 1 inotenderera danda remwenje richipesana newachi saka tinoisa chiratidzo chakanaka kutorque 3.

τ ₃ = F ₃ x = (20 N)(1.75 m) = -35 Nm

Torque 2 inotenderera mwenje uchitenderera wachi saka tinoisa chiratidzo chekusashanda zvakanaka kutorque 2.

Nguva chaiyo yesimba :

Στ = 0

10 + 50x – 35 = 0

50x - 25 = 0

50x = 25

x = 25/50

x = 0.5 m

2. Masimba eF ₁ , F ₂ , F ₃ , uye F ₄ anoshanda patsvimbo yeABCD sezvakaratidzwa pamufananidzo. Kana huremu hwetsvimbo hukasatariswa, chii chiri kukura kwesimba, pamusoro pepoindi A.

Chikamu chekutenderera = poindi A.

Zvinozivikanwa:

Simba F₁ = 10 N, ruoko rwechirever l₁ = 0

Simba F ₂ = 4 N, ruoko rwechitsigiro l ₂ = 2 mamita

Simba F ₃ = 5 N, ruoko rwechitsigiro l ₃ = 3 mamita

Simba F ₄ = 10 N, ruoko rwechitsigiro l ₄ = 6 mamita

Zvinodiwa: nguva yesimba pamusoro penzvimbo A

Solution:

Nguva yesimba 1 (τ ₁ ) = F ₁ l ₁ = (10)(0) = 0

Nguva yesimba 2 (τ ₂ ) = F ₂ l ₂ = (4) (2) = -8 Nm

Nguva yesimba 3 (τ ₃ ) = F ₃ l ₃ = (5)(3) = 15 Nm

Nguva yesimba 4 (τ ₄ ) = F ₄ l ₄ = (10) (6) = -60 Nm

Kana torque ikatenderera tsvimbo inopesana newachi, tinopa chiratidzo chakanaka.

Kana torque ikatenderera tsvimbo newachi, tinoisa chiratidzo chekusaratidza.

Mhedzisiro yenguva yesimba:

τ = 0 – 8 Nm + 15 Nm – 60 Nm

τ = -68 Nm + 15 Nm

τ = -53 Nm

Chiratidzo chekudzima chinoratidza kuti nguva yesimba inotenderera tsvimbo newachi.

3. Masimba matatu anoshanda patsvimbo, F _A = ​​​​F _C = 10 N uye F _B = 20 N, sezvakaratidzwa mumufananidzo uri pazasi. Kana daro reAB = BC = 20 cm, chii chiri nguva yesimba pamusoro pepoindi C.

Zvinozivikanwa:

Kutenderera kwechikamu chepakati C.

Daro riri pakati peF _A ne axis yekutenderera (r _AC ) = 40 cm = 0,4 metres

Daro riri pakati peF _B ne axis yekutenderera (r _BC ) = 20 cm = 0.2 metres

Daro riri pakati peF _C ne axis yekutenderera (r _CC ) = 0 cm

F _A = ​​​​10 Newton

F _B = 20 Newton

FC ₌ 10 Newtons

Zvinodiwa: Mugumisiro wenguva yesimba pamusoro pepfungwa C.

Solution:

Nguva yesimba A:

Στ _A = (F _A )(r _AC chivi 90 ^o ) = (10 N)(0,4 m)(1) = -4 Nm

Chiratidzo chekudzima chinoratidza kuti nguva yesimba inotenderera tsvimbo newachi.

Nguva yesimba B:

Στ _B = (F _B )(r _BC chivi 90 ^o ) = (20 N)(0,2 m)(1) = 4 Nm

Chiratidzo chekuwedzera chinoratidza kuti nguva yesimba inotenderera tsvimbo inopesana newachi.

Nguva yesimba C:

Στ _C = (F _C )(r _CC chivi 90 ^o ) = (10 N)(0)(1) = 0

Mhedzisiro yenguva yesimba:

Στ = Στ ₁ + Στ ₂ + Στ ₃

Στ = -4 + 4 + 0

Στ = 0 Nm

4. Kureba kwetsvimbo ndeye 50 cm. Masimba matatu anoshanda patsvimbo, sezvakaratidzwa mumufananidzo uri pazasi. Kana axis yekutenderera iri poindi C, chii chinonzi net yemoment yesimba.

Zvinozivikanwa:

Kutenderera kwechikamu chepakati C.

Daro riri pakati peF ₁ ne axis yekutenderera (r ₁ ) = 30 cm = 0,3 metres

Daro riri pakati peF2 _ne axis yekutenderera (r2 ₎ = 10 cm = 0,1 metres

Daro riri pakati peF3 _ne axis yekutenderera (r3 ₎ = 20 cm = 0,2 metres

F ₁ = 10 Newton

F ₂ = 10 Newton

F ₃ = 10 Newton

Zvinodiwa: Zvinobva pakumanikidzwa kwechinhu pamusoro pepfungwa C.

Solution:

Nguva yesimba 1:

Στ ₁ = (F ₁ )(r ₁ chivi 90 ^o ) = (10 N)(0,3 m)(1) = -3 Nm

Chiratidzo chekudzima chinoratidza kuti nguva yesimba inotenderera tsvimbo newachi.

Nguva yesimba 2:

Στ ₂ = (F ₂ )(r ₂ chivi 90 ^o ) = (10 N)(0,1 m)(1) = 1 Nm

Chiratidzo chekuwedzera chinoratidza kuti nguva yesimba inotenderera tsvimbo inopesana newachi.

Nguva yesimba 3:

Στ ₃ = (F ₃ )(r ₃ chivi 30 ^o ) = (10 N)(0,2 m)(0,5) = -1 Nm

Chiratidzo chekudzima chinoratidza kuti nguva yesimba inotenderera tsvimbo newachi.

Mhedzisiro yenguva yesimba:

Στ = Στ ₁ + Στ ₂ + Στ ₃

Στ = -3 + 1 – 1

Στ = -3 Nm

Chiratidzo chekudzima chinoratidza kuti mhedzisiro yesimba inotenderera tsvimbo newachi.

5. Masimba matatu F ₁ , F ₂ , uye F ₃ anoshanda patsvimbo sezvakaratidzwa mumufananidzo uri pazasi. Kureba kwetsvimbo mamita mana. Ndeipi nguva yesimba pamusoro penzvimbo C?

(chivi 53 ^o = 0.8, cos 53 ^o = 0.6, AB = BC = CD = DE = mita imwe)

Zvinozivikanwa:

Kutenderera kwechikamu chepakati C.

Simba 1 (F ₁ ) = 5 Newton

Daro riri pakati pemutsetse wekuita weF1 _ne axis of rotation (r ₁ ) = 2 metres

Simba 2 (F ₂ ) = 0.4 Newton

Daro riri pakati pemutsetse wekuita weF2 _ne axis of rotation (r2 ₎ = 1 mita

Simba 3 (F ₃ ) = 4.8 Newton

Daro riri pakati pemutsetse wekuita weF3 ne axis of rotation (r ₃ ) ₌ 2 metres

Zvinodiwa: Nguva yesimba pamusoro pepfungwa C.

Solution:

Nguva yesimba 1:

τ ₁ = F ₁ r chivi 53 ^o = (5 N) (2 m) (0,8) = (10) (0,8) N = 8 N

Chiratidzo chekuwedzera chinoratidza kuti nguva yesimba inotenderera tsvimbo inopesana newachi.

Nguva yesimba 2:

τ ₂ = F ₂ r chivi 90 ^o = (0,4 N)(1 m)(1) = -0,4 N

Chiratidzo chekudzima chinoratidza kuti nguva yesimba inotenderera tsvimbo newachi.

Nguva yesimba 3:

τ ₃ = F ₃ r chivi 90 ^o = (4,8 N)(2 m)(1) = -9,6 N

Chiratidzo chekudzima chinoratidza kuti nguva yesimba inotenderera tsvimbo newachi.

Mhedzisiro yenguva yesimba:

Στ = τ ₁ – τ ₂ – τ ₃ = 8 – 0,4 – 9,6 = 8 – 10 = 2 Nm

Chiratidzo chekuwedzera chinoratidza kuti nguva yesimba inotenderera tsvimbo inopesana newachi.

6. Chii chinoitika panguva yekusimba pamusoro pedenderedzwa rekutenderera panzvimbo yeO nemasimba ari patsvimbo, sezvakaratidzwa mumufananidzo uri pazasi?

Zvinozivikanwa:

Mutsetse wekutenderera panzvimbo yeO.

Simba 1 (F ₁ ) = 6 Newton

Daro riri pakati pemutsetse wekuita weF1 _ne axis of rotation (r1 ₎ = 1 mita

Simba 2 (F ₂ ) = 6 Newton

Daro riri pakati pemutsetse wekuita weF2 _ne axis of rotation (r ₂ ) = 2 metres

Simba 3 (F ₃ ) = 4 Newton

Daro riri pakati pemutsetse wekuita weF3 _ne axis of rotation (r ₃ ) = 2 metres

Zvinodiwa: Mugumisiro wenguva yesimba pamusoro pepoindi C

Solution:

Nguva yesimba 1:

τ ₁ = F ₁ l ₁ = (6 N) (1 m) = 6 Nm

Chiratidzo chekuwedzera chinoratidza kuti nguva yesimba inotenderera tsvimbo inopesana newachi.

Nguva yesimba 2:

τ ₂ = F ₂ r ₂ chivi 30 ^o = (6 N)(2 m)(0,5)= 6 Nm

Chiratidzo chekuwedzera chinoratidza kuti nguva yesimba inotenderera tsvimbo inopesana newachi.

Nguva yesimba 3:

τ ₃ = F ₃ l ₃ = (4 N)(2 m) = -8 Nm

Chiratidzo chekudzima chinoratidza kuti nguva yesimba inotenderera tsvimbo newachi.

Mhedzisiro yenguva yesimba:

Στ = τ ₁ + τ ₂ – τ ₃ = 6 + 6 – 8 = 4 Nm

Chiratidzo chekuwedzera chinoratidza kuti nguva yesimba inotenderera tsvimbo inopesana newachi.