Ihe atụ nke oge ike

Ihe atụ iri nke ajụjụ ndị a na-ajụkarị gbasara ike.

1. Ogologo mkpanaka AB bụ mita 2, oke ike F bụkwa Newton 10. Chọpụta oge nke ejiji gaa n'ebe A na ntụziaka nke ntụgharị nke mkpanaka AB!
Ihe atụ nke oge ike 1Mkparịta ụka
Axis nke ntụgharị dị na isi A.

A maara na:
Ike (F) = Newtons 10
Anya AB (r)AB) = mita 2
Ike F na-emepụta akụkụ nke 90o megide mkpara AB.
Ogwe aka ike (l) = rAB mmehie 90o = (mita 2)(1) = mita 2
A jụrụ: Oge ike gbasara isi ihe A na ntụziaka nke ntụgharị nke mkpanaka AB

Azịza:
Oge ike:
τ = F l = (10 N)(2 m) = mita 20 Newton
Oge ike dị mma n'ihi na ike F na-eme ka mkpanaka AB na-atụgharị gaa n'akụkụ aka nri.

2. Ogologo mkpanaka AB bụ mita 2, oke ike F bụkwa Newton 10. Chọpụta oge ike gbasara isi ihe A na ntụziaka nke mkpanaka AB!

Mkparịta ụka
Axis nke ntụgharị bụIhe atụ nke oge ike 2dị na isi A.

A maara na:
Ike (F) = Newtons 10
Anya AB (r)AB) = mita 2
Ike F na-emepụta akụkụ nke 60o megide mkpara AB.
Ogwe aka ike (l) = rAB mmehie 60o = (mita 2)(0,5√3) = √mita 3
A jụrụ: Torque gaa na isi A na ntụziaka nke ntụgharị nke mkpanaka AB

Azịza:
Oge ike:
τ = F l = (10 N)(√3 m) = 10√3 mita Newton
Oge ike dị mma n'ihi na ike F na-eme ka mkpanaka AB na-atụgharị gaa n'akụkụ aka nri.

3. Ogologo mkpanaka AB bụ mita 2, oke ike F1 bụ Newton 10 na oke ike F2 bụ Newton 15. Chọpụta oge ike sitere na ya gbasara ebe etiti mkpanaka ahụ na ntụziaka nke ntụgharị mkpanaka AB!

Mkparịta ụka
Ihe atụ nke oge ike 4Axis nke ntụgharị dị n'etiti mkpanaka ahụ.
A maara na:
Ụdị nke abụọ (F)1) = 10 Newton
Ogologo F1 na etiti nke ogwe osisi ahụ (r)1) = mita 1
Ụdị F1 ịmepụta akụkụ nke 90o megide mkpanaka AB
Ụdị ogwe aka 1 (l)1) = r1 mmehie 90o = (mita 1)(1) = mita 1

Ụdị nke abụọ (F)2) = 15 Newton
Ogologo F2 na etiti nke ogwe osisi ahụ (r)2) = mita 1
Ụdị F2 ịmepụta akụkụ nke 90o megide mkpanaka AB
Ụdị ogwe aka 2 (l)2) = r2 mmehie 90o = (mita 1)(1) = mita 1
A jụrụ: Oge ike sitere na etiti mkpanaka ahụ na ntụziaka nke ntụgharị nke mkpanaka AB
Azịza:
Oge ike nke 1:
τ1 = F.1 l1 = (10 N)(1 m) = mita 10 Newton
Oge ike dị mma n'ihi na ike F na-eme ka mkpanaka ahụ tụgharịa gaa n'akụkụ aka nri.

Oge ike nke 2:
τ2 = F.2 l2 = (15 N)(1 m) = -15 Mita Newton
Oge ike adịghị mma n'ihi na ike F2 na-eme ka mkpanaka ahụ na-atụgharị aka elekere.

Oge ike sitere na ya:
Στ = τ1 – τ2 = 10 – 15 = – 5 Mita Newton
Oge ike a na-enweta adịghị mma n'ihi na ike F nke sitere na ya na-eme ka mkpanaka AB na-atụgharị gaa n'aka nri.

4. Ogologo mkpanaka AB bụ mita 2, oke ike F bụ1 bụ 10 Newton na oke ike F2 bụ 10 Newton. Chọpụta oge ike sitere na ya gburugburu etiti mkpanaka ahụ na ntụziaka nke ntụgharị nke mkpanaka AB!
Ihe atụ nke oge ike 6Mkparịta ụka
Axis nke ntụgharị dị n'etiti mkpanaka ahụ.
A maara na:
Ụdị nke abụọ (F)1) = 10 Newton
Ogologo F1 na etiti nke ogwe osisi ahụ (r)1) = mita 1
Ụdị F1 ịmepụta akụkụ nke 60o megide mkpanaka AB
Ụdị ogwe aka 1 (l)1) = r1 mmehie 60o = (mita 1)(0,5√3) = mita 0,5√3

Ụdị nke abụọ (F)2) = 10 Newton
Ogologo F2 na etiti nke ogwe osisi ahụ (r)2) = mita 1
Ụdị F2 ịmepụta akụkụ nke 90o megide mkpanaka AB
Ụdị ogwe aka 2 (l)2) = r2 mmehie 90o = (mita 1)(1) = mita 1
A jụrụ: Oge ike sitere na ya gbasara etiti mkpanaka ahụ na ntụziaka nke ntụgharị nke mkpanaka AB
Azịza:
Oge ike nke 1:
τ1 = F.1 l1 = (10 N)(0,5√3 m) = 5√3 = 8,7 Mita Newton
Oge ike dị mma n'ihi na ike F1 na-eme ka mkpanaka ahụ tụgharịa gaa n'akụkụ aka nri.

Oge ike nke 2:
τ2 = F.2 l2 = (10 N)(1 m) = -10 Mita Newton
Oge ike adịghị mma n'ihi na ike F2 na-eme ka mkpanaka ahụ na-atụgharị aka elekere.

Oge ike sitere na ya:
Στ = τ1 – τ2 = 8,7 – 10 = – 1,3 Mita Newton
Oge ike a na-enweta adịghị mma n'ihi na ike F nke sitere na ya na-eme ka mkpanaka AB na-atụgharị gaa n'aka nri.

5. Ogologo mkpanaka AB bụ mita 10, oke ike F bụ1 bụ 10 Newton, oke ike F2 bụ 10 Newton na oke ike F3 bụ Newtons iri na ise. Anya dị n'etiti isi ihe A na isi ihe C bụ mita 7,5. Ike F2 dị n'etiti mkpanaka AB. Chọpụta oge ike sitere na isi C nke dị mita 2,5 site na isi B! Chọpụtakwa ụzọ ntụgharị nke mkpanaka AB.
Ihe atụ nke oge ike 8Mkparịta ụka
Axis nke ntụgharị dị na isi C nke dị mita 2,5 site na isi B.
A maara na:
Ụdị nke abụọ (F)1) = 10 Newton
Ogologo F1 na isi C (r)1) = mita 2,5
Ụdị F1 ịmepụta akụkụ nke 90o megide mkpanaka AB
Ụdị ogwe aka 1 (l)1) = r1 mmehie 90o = (mita 2,5)(1) = mita 2,5

Ụdị nke abụọ (F)2) = 10 Newton
Ogologo F2 na isi C (r)2) = mita 2,5
Ụdị F2 ịmepụta akụkụ nke 90o megide mkpanaka AB
Ụdị ogwe aka 2 (l)2) = r2 mmehie 90o = (mita 2,5)(1) = mita 2,5

Ụdị nke abụọ (F)3) = 15 Newton
Ogologo F3 na isi C (r)3) = mita 7,5
Ụdị F3 ịmepụta akụkụ nke 90o megide mkpanaka AB
Ụdị ogwe aka 3 (l)3) = r3 mmehie 90o = (mita 7,5)(1) = mita 7,5
A jụrụ: Oge ike sitere na isi ihe C na ntụziaka nke ntụgharị nke mkpanaka AB.
Azịza:
Oge ike nke 1:
τ1 = F.1 l1 = (10 N)(2,5 m) = mita 25 Newton
Oge ike dị mma n'ihi na ike F1 na-eme ka mkpanaka ahụ na-atụgharị n'akụkụ aka ekpe.

Oge ike nke 2:
τ2 = F.2 l2 = (10 N)(2,5 m) = mita 25 Newton
Oge ike dị mma n'ihi na ike F2 na-eme ka mkpanaka ahụ na-atụgharị n'akụkụ aka ekpe.

Oge ike nke 3:
τ3 = F.3 l3 = (15 N)(7,5 m) = -112,5 Mita Newton
Oge ike adịghị mma n'ihi na ike F3 na-eme ka mkpanaka ahụ na-atụgharị aka elekere.

Oge ike sitere na ya:
Στ = τ1 + τ2 – τ3 = 25 + 25 – 112,5 = – 62,5 Mita Newton
Oge ike a na-enweta adịghị mma n'ihi na ike F nke sitere na ya na-eme ka mkpanaka AB na-atụgharị gaa n'aka nri.

6. Ogologo mkpanaka AB bụ mita 10, oke ike F bụ1 bụ 10 Newton, oke ike F2 bụ 10 Newton na oke ike F3 bụ Newton iri. Chọpụta oge ike sitere na isi A nke dị mita ise site na isi ike F.1Chọpụtakwa ebe mkpara AB ga-esi na-agbagharị.
Mkparịta ụka
Ihe atụ nke oge ike 11Axis nke ntụgharị dị na isi A.
A maara na:
Ụdị nke abụọ (F)1) = 10 Newton
Ogologo F1 na isi A (r)1) = mita 5
Ụdị F1 ịmepụta akụkụ nke 60o megide mkpanaka AB
Ụdị ogwe aka 1 (l)1) = r1 mmehie 60o = (mita 5)(0,5√3) = mita 2,5√3

Ụdị nke abụọ (F)2) = 10 Newton
Ogologo F2 na isi A (r)2) = 0
Ụdị F2 ịmepụta akụkụ nke 90o megide mkpanaka AB
Ụdị ogwe aka 2 (l)2) = r2 mmehie 90o = (0)(1) = 0
Ụdị nke abụọ (F)3) = 10 Newton
Ogologo F3 na isi A (r)3) = mita 10
Ụdị F3 ịmepụta akụkụ nke 30o megide mkpanaka AB
Ụdị ogwe aka 3 (l)3) = r3 mmehie 30o = (mita 10)(0,5) = mita 5
A jụrụ: Oge ike sitere na isi ihe A na ntụziaka nke ntụgharị nke mkpanaka AB.
Azịza:
Oge ike nke 1:
τ1 = F.1 l1 = (10 N)(2,5√3 m) = 25√3 = 43,3 Mita Newton
Oge ike dị mma n'ihi na ike F1 na-eme ka mkpanaka ahụ tụgharịa gaa n'akụkụ aka nri.

Oge ike nke 2:
τ2 = F.2 l2 = (10 N)(0) = 0
Oge ike bụ efu n'ihi na ike F2 na-adaba na axis nke ntụgharị

Oge ike nke 3:
τ3 = F.3 l3 = (10 N)(5 m) = -50 Mita Newton
Oge ike adịghị mma n'ihi na ike F3 na-eme ka mkpanaka ahụ na-atụgharị aka elekere.

Oge ike sitere na ya:
Στ = τ1 + τ2 – τ3 = 43,3 + 0 – 50 = – 6,7 Mita Newton
Oge ike a na-enweta adịghị mma n'ihi na ike F nke sitere na ya na-eme ka mkpanaka AB na-atụgharị gaa n'aka nri.

7. Ike atọ F1, F.2, na F3 na-arụ ọrụ na mkpanaka ahụ dịka egosiri na eserese na-esonụ. Ọ bụrụ na a leghara oke nke mkpanaka ahụ anya ma ogologo mkpanaka ahụ bụ mita 4, mgbe ahụ uru nke oge ike gbasara axis nke ntụgharị na isi C bụ…. (mmehie 53o = 0,8, cos 53o = 0,6, AB = BC = CD = DE = 1 mita)
Mkparịta ụka nke ule mba nke afọ 2014 maka Fiziksị nke ụlọ akwụkwọ sekọndrị - Moment of Force (Torque) 8a

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

Mkparịta ụka
A maara na:
Axis nke ntụgharị dị na isi C.
Ụdị nke abụọ (F)1) = 5 Newton
Anya dị n'etiti ebe ọrụ F1 na axis nke ntụgharị (r)1) = mita 2
Ụdị nke abụọ (F)2) = 0,4 Newton
Anya dị n'etiti ebe ọrụ F2 na axis nke ntụgharị (r)2) = mita 1
Ụdị nke abụọ (F)3) = 4,8 Newton
Anya dị n'etiti ebe ọrụ F3 na axis nke ntụgharị (r)3) = mita 2
Ajụjụ: Uru nke oge ike gbasara axis nke ntụgharị na isi ihe C
Azịza:

Oge Ike nke 1:
Mkparịta ụka nke ule mba nke afọ 2014 maka Fiziksị nke ụlọ akwụkwọ sekọndrị - Moment of Force (Torque) 8bOge ike nke 1 na-eme ka mkpanaka ahụ tụgharịa gaa n'akụkụ aka nri ka oge ike nke 1 wee nwee ihe ịrịba ama dị mma.
Oge Ike nke 2:
Mkparịta ụka nke ule mba nke 2014 maka Fizik nke ụlọ akwụkwọ sekọndrị - Moment of force (torque) 8cOge ike nke 2 na-eme ka mkpanaka ahụ tụgharịa gaa n'akụkụ nke ntụgharị aka elekere ka oge ike nke 2 wee nwee akara ọjọọ.
Oge Ike nke 3:
Mkparịta ụka nke ule mba nke 2014 maka Fiziksị nke ụlọ akwụkwọ sekọndrị - Moment of Force (Torque) 8dOge ike nke 3 na-eme ka mkpanaka ahụ tụgharịa gaa n'akụkụ nke ntụgharị aka elekere ka oge ike nke 3 wee nwee akara ọjọọ.

Oge ike sitere na ya:
Mkparịta ụka nke ule mba nke afọ 2014 maka Fiziksị nke ụlọ akwụkwọ sekọndrị - Moment of Force (Torque) 8eOke nke oge ike bụ mita Newton abụọ. Oge ike na-adịghị mma pụtara na mkpanaka ahụ na-agbagharị n'akụkụ aka ekpe.
Azịza ziri ezi bụ D.

8. Oke ike sitere na oge ike dị n'axis na isi ihe O site n'aka ike ndị na-arụ ọrụ na mkpanaka ahụ ma ọ bụrụ na eleghara oke ya anya bụ….
Mkparịta ụka nke ule mba nke 2014 maka Fizik nke ụlọ akwụkwọ sekọndrị - Moment of force (torque) 8f

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

Mkparịta ụka
A maara na:
Axis nke ntụgharị dị na isi O.
Ụdị nke abụọ (F)1) = 6 Newton
Anya dị n'etiti ebe ọrụ F1 na axis nke ntụgharị (r)1) = mita 1
Ụdị nke abụọ (F)2) = 6 Newton
Anya dị n'etiti ebe ọrụ F2 na axis nke ntụgharị (r)2) = mita 2
Ụdị nke abụọ (F)3) = 4 Newton
Anya dị n'etiti ebe ọrụ F3 na axis nke ntụgharị (r)3) = mita 2
Ajụjụ: Uru nke oge ike gbasara axis nke ntụgharị na isi ihe C
Azịza:
Oge Ike nke 1:
Mkparịta ụka nke ule mba nke 2014 maka Fizik nke ụlọ akwụkwọ sekọndrị – Moment of force (torque) 8gOge ike nke 1 na-eme ka mkpanaka ahụ tụgharịa gaa n'akụkụ aka nri ka oge ike nke 1 wee nwee ihe ịrịba ama dị mma.
Oge Ike nke 2:
Mkparịta ụka nke ule mba nke 2014 maka Fizik nke ụlọ akwụkwọ sekọndrị – Oge ike (torque) awa 8Oge ike nke 2 na-eme ka mkpanaka ahụ tụgharịa gaa n'akụkụ aka nri ka oge ike nke 2 wee nwee ihe ịrịba ama dị mma.
Oge Ike nke 3:
Mkparịta ụka nke ule mba nke afọ 2014 maka Fiziksị nke ụlọ akwụkwọ sekọndrị - Moment of Force (Torque) 8iOge ike nke 3 na-eme ka mkpanaka ahụ tụgharịa gaa n'akụkụ nke ntụgharị aka elekere ka oge ike nke 3 wee nwee akara ọjọọ.

Oge ike sitere na ya:
Mkparịta ụka nke ule mba nke afọ 2014 maka Fiziksị nke ụlọ akwụkwọ sekọndrị – Moment of force (torque) 8jOke nke oge ike bụ mita Newton anọ. Oge ike dị mma pụtara na mkpanaka ahụ na-agbagharị n'akụkụ aka ekpe.
Azịza ziri ezi bụ B.

9. O nwere mita asatọ n'ogologo. Ike atọ na-arụ ọrụ n'ogwe ahụ, dịka egosiri na foto dị n'okpuru. Oke nke oge ike nke na-eme ka ogwe ahụ gbaa gburugburu n'etiti ya bụ…
A. 10 N m
B. 20 N m
C. 30 N m
D. 40 N m
E. 50 N m

Mkparịta ụka:
Ihe atụ nke Oge Ike - UnEtiti mkpanaka ahụ dị n'etiti. Ogidi ahụ dị mita asatọ n'ogologo, ya mere etiti mkpanaka ahụ dị mita anọ site na nsọtụ mkpanaka ahụ.
Oge Ike 1 = F1 l1 = (10 N)(4 m) = 40 N m
Oge Ike 1 nwere uru dị mma n'ihi na Oge Ike 1 na-eme ka mkpanaka ahụ tụgharịa gaa n'akụkụ aka nri.
Oge Ike 2 = F2 l2 = (10 N)(2 m) = – 20 N m
Oge Ike nke 2 nwere uru na-adịghị mma n'ihi na Oge Ike nke 2 na-eme ka mkpanaka ahụ tụgharịa n'akụkụ aka nri.
Oge Ike 3 = F3 l3 = (15 N)(2 m) = – 30 N m
Oge Ike nke 3 nwere uru na-adịghị mma n'ihi na Oge Ike nke 3 na-eme ka mkpanaka ahụ tụgharịa n'akụkụ aka nri.

Oge Ike nke si na ya pụta = 40 N m – 20 N m – 30 N m = – 10 N m

Oge ike ma ọ bụ ike nke sitere na ya nwere uru na-adịghị mma, nke a na-egosi na ntụziaka nke ntụgharị nke mkpanaka ahụ dị n'akụkụ aka nri.

Azịza ziri ezi bụ A.

10. Ike F1 = 10 N, F2 = 15 N, F3 = 15 N na F4 = 10 N, na-arụ ọrụ na mkpara ABCD dịka egosiri na eserese ahụ. Ogologo mkpara ABCD bụ mita 20. Ọ bụrụ na eleghara oke nke mkpara ahụ anya, mgbe ahụ uru nke oge ike gbasara isi ihe D bụ...
A. 15 Nm
B. 18 Nm
C. 35 Nm
D. 63 Nm
E. 68 Nm

Ajụjụ ihe atụ nke Torque - ule mba - 2Mkparịta ụka:
Ebumnuche nke ajụjụ a bụ ịchọta uru nke oge ike sitere na ya nke na-eme ka mkpanaka ahụ na-agbagharị, ebe etiti ntụgharị dị na isi ihe D.
Oge Ike 1 = F1 l1 = (10 N)(15 m) = 150 N m
Oge Ike 1 nwere uru dị mma n'ihi na Oge Ike 1 na-eme ka mkpanaka ahụ tụgharịa gaa n'akụkụ aka nri.
Oge Ike 2 = F2 l2 = (15 N)(5 m) = -75 N m
Oge Ike nke 2 nwere uru na-adịghị mma n'ihi na Oge Ike nke 2 na-eme ka mkpanaka ahụ tụgharịa n'otu ụzọ ahụ dịka ntụgharị aka elekere.
Oge Ike 3 = F3 l3 = (15 N)(0 m) = 0 N m

Oge Ike nke 3 bụ efu n'ihi na F3 na-adaba na axis nke ntụgharị.
Oge Ike 4 = F4 l4 = (10 N)(5 m) = 50 N m
Oge nke Ike 4 nwere uru dị mma n'ihi na Oge nke Ike 4 na-eme ka mkpanaka ahụ tụgharịa gaa n'akụkụ aka nri.

Oge Ike nke si na ya pụta = 150 N m – 75 N m + 50 N m = 125 N m
Oge ike ma ọ bụ ike nke sitere na ya nwere uru dị mma, ya mere ntụziaka nke ntụgharị nke mkpanaka ahụ dị iche na ntụziaka nke ntụgharị nke aka elekere.

 

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