Hukuru hwe torque yakakwana - matambudziko nemhinduro

1. Simba P rinoiswa kumucheto mumwe wedanda rine hurefu hwemamita maviri. Hukuru hwetorque hwakaita sei ? Mutsetse wekutenderera panzvimbo A.

Zvinozivikanwa:

Simba (F) = 10 N

Kureba kweAB (r _AB ) = 2 m

Simba F rakamira rakanangana nedanda.

Ruoko rwechiredzo (l ) = r _AB sin 90 ^o = (2 m)(1) = 2 m

Zvinodiwa: Kutenderera kwesimba remuchina wekutenderera

Solution:

Torque:

τ = F l = (10 N)(2 m) = 20 N m

Chiratidzo chekuwedzera nekuti danda rinotenderera richitenderera risingaenderane newachi.

2. Kureba kwedanda reAB i2 m uye hukuru hwesimba F i10 N. Hukuru hwetorque chii? Akisi yekutenderera panzvimbo A.

Zvinozivikanwa:

Simba (F) = 10 N

Kureba kweAB (r _AB ) = 2 m

Ruoko rwechibato (l ) = r _AB sin 60 ^o = (2 m)(0.5 √3 ) = √3 m

Zvinodiwa: Kutenderera kwesimba remuchina wekutenderera

Solution:

Torque:

τ = F l = (10 N)( √3 m) = 10 √3 N m

Chiratidzo chekuwedzera nekuti simba F rinoita kuti danda ritenderere richitenderera risingaenderane newachi.

3. Kureba kwedanda i2 m. Hukuru hweF ₁ i10 N uye hukuru hweF ₂ i15 N. Tsvaga torque yakakwana pakati pedanda.

Chinotenderera pakati pedanda.

Zvinozivikanwa:

Simba 1 (F ₁ ) = 10 N

Daro riri pakati peF ₁ nepakati pedanda (r ₁ ) = 1 m

Ruoko rwechiredzo 1 (l ₁ ) = r ₁ sin 90 ^o = (1 m)(1) = 1 m

Simba F ₁ rakamira rakanangana nedanda.

Simba 2 (F ₂ ) = 15 N

Kureba pakati peF2 _nepakati pedanda (r2 ₎ = 1 m

Simba F ₂ rakamira rakanangana nedanda.

Ruoko rwechiredzo 2 (l ₂ ) = r ₁ sin 90 ^o = (1 m)(1) = 1 m

Zvinodiwa: Kutenderera kwemhepo kunoenderana ne axis yekutenderera

Solution:

Torque 1:

τ ₁ = F ₁ l ₁ = (10 N)( 1 m) = 10 N m

Chiratidzo chekuwedzera nekuti simba reF ₁ rinoita kuti danda ritenderere richitenderera risingaenderane newachi.

Torque 2:

τ ₂ = F ₂ l ₂ = (15 N)( 1 m) = -15 N

Chiratidzo che minus nekuti simba F ₂ rinoita kuti danda ritenderere newachi.

Torque yemagetsi:

Σ τ = τ ₁ – τ ₂ = 10 – 15 = – 5 N m

Chiratidzo chekusiya ndechekuti danda rinotenderera newachi.

4. Kureba kwedanda reAB i2 m, hukuru hweF ₁ i10 N uye hukuru hweF ₂ i10 N. Sarudza torque yakakwana pakati pedanda.

Chinotenderera pakati pedanda.

Zvinozivikanwa:

Simba 1 (F ₁ ) = 10 Nn

Kureba pakati peF1 _nepakati pedanda (r1 ₎ = 1 m

Ruoko rwechitsiko 1 (l ₁ ) = r ₁ sin 60 ^o = (1 m)(0.5 √3 ) = 0.5 √3 m

Simba 2 (F ₂ ) = 10 N

Kureba pakati peF2 _nepakati pedanda (r2 ₎ = 1 m

Simba F ₂ rakamira rakanangana nedanda.

Ruoko rwechiredzo 2 (l ₂ ) = r ₂ sin 90 ^o = (1 m)(1) = 1 m

Zvinodiwa: Torque yakakwana pamusoro pe axis yekutenderera

Solution:

Torque 1:

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

Chiratidzo chekuwedzera nekuti simba F ₁ rinoita kuti danda ritenderere newachi.

Torque 2:

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

Chiratidzo che minus nekuti simba F ₂ rinoita kuti danda ritenderere newachi.

Torque yemagetsi:

Σ τ = τ ₁ – τ ₂ = 8.7 – 10 = – 1.3 N m

Chiratidzo chekusiya nekuti simba remagetsi rinoita kuti danda ritenderere newachi.

5. Kureba kwedanda i10 m, hukuru hweF ₁ i10 N, hukuru hweF ₂ i10 N uye hukuru hweF ₃ i15 N. Daro riri pakati pepoindi A nepoindi C i7.5 m. Simba F ₂ riri pakati pedanda. Sarudza torque ine simba pamusoro pepoindi C iri pa2.5 m kubva poindi B.

Nzvimbo yekutenderera iri panzvimbo C

Zvinozivikanwa:

Simba 1 (F ₁ ) = 10 N

Daro riri pakati peF ₁ nepoindi C (r ₁ ) = 2.5 m

Simba F ₁ rakamira rakanangana nedanda.

Ruoko rwechiredzo 1 (l ₁ ) = r ₁ sin 90 ^o = ( 2.5 m)( 1 ) = 2.5 m

Simba 2 (F ₂ ) = 10 N

Daro riri pakati peF ₂ nepoindi C (r ₂ ) = 2.5 m

Simba F2 _rakamira rakanangana nedanda.

Ruoko rwechiredzo 2 (l ₂ ) = r ₂ sin 90 ^o = ( 2.5 m)(1) = 2.5 m

Simba 3 (F ₃ ) = 15 N

Daro riri pakati peF ₃ nepoindi C (r ₃ ) = 7.5 m

Simba F3 _rakamira rakanangana nedanda.

Ruoko rwechiredzo 3 (l ₃ ) = r ₃ sin 90 ^o = (7.5 m)(1) = 7.5 m

Zvinodiwa: Torque yakakwana pamusoro pe axis yekutenderera

Solution:

Torque 1:

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

Chiratidzo chekuwedzera nekuti simba F ₁ rinoita kuti danda ritenderere newachi.

Torque 2:

τ ₂ = F ₂ l ₂ = (10 N)( 2.5 m) = 25 N m

Chiratidzo che " plus" nekuti simba re "F2 _" rinoita kuti danda ritenderere newachi.

Torque 3:

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

Chiratidzo che minus nekuti simba F ₃ rinoita kuti danda ritenderere newachi.

Torque yemagetsi:

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

Chiratidzo chekusiya nekuti simba remagetsi rinoita kuti danda ritenderere newachi.

6. Kureba kwedanda i10 m, hukuru hwaF₁ iri 10 N, hukuru hwaF₂ iri 10 N uye hukuru hweF₃ iri 10 N. Tsvaga torque ine mambure pamusoro penzvimbo A, iri 5 m kubva papoikushandiswa kwesimba F₁.

Kutenderera kwechikamu chepakati peA.

Zvinozivikanwa:

Simba 1 (F ₁ ) = 10 N

Daro riri pakati peF ₁ nepoindi A (r ₁ ) = 5 m

Ruoko rwechitsiko 1 (l ₁ ) = r ₁ sin 60 ^o = (5 m)(0.5 √3 ) = 2.5 √3 m

Simba 2 (F ₂ ) = 10 N

Daro riri pakati peF ₂ nepoindi A (r ₂ ) = 0

Simba F2 _rakamira rakanangana nedanda.

Ruoko rwechiredzo 2 (l ₂ ) = r ₂ sin 90 ^o = (0)(1) = 0

Simba 3 (F ₃ ) = 10 N

Daro riri pakati peF ₃ nepoindi A (r ₃ ) = 10 m

Ruoko rwechiredzo 3 (l ₃ ) = r ₃ sin 30 ^o = (10 m)(0.5) = 5 m

Zvinodiwa: torque yakakwana pamusoro pe axis yekutenderera

Solution:

Torque 1:

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

Chiratidzo chekuwedzera nekuti simba F ₁ rinoita kuti danda ritenderere newachi.

Torque 2:

τ ₂ = F ₂ l ₂ = (10 N)(0) = 0

Torque 3:

τ ₃ = F ₃ l ₃ = (10 N)( 5 m) = -50 N m

Chiratidzo che minus nekuti simba F ₃ rinoita kuti danda ritenderere newachi.

Torque yemagetsi:

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

Chiratidzo chekusiya nekuti simba remagetsi rinoita kuti danda ritenderere newachi.