Isikhathi samandla - izinkinga nezixazululo

1. Uma u-F_R amandla e-F₁, F₂, kanye F₃, ubukhulu bamandla F buyini?₂ kanye no-x?

Kwaziwa:

Amandla aphelele (F)_R) = 40 N Isikhathi samandla - izinkinga nezixazululo 1

Amandla 1 (F)₁) = 10 N

Amandla (F)₃) = 20 N

Okufunayo: Ubukhulu bamandla F₂ kanye nebanga lika-x

Isixazululo:

Thola ubukhulu bamandla F₂:

Phoqa amaphuzu aye phezulu, okusayinwe okungekuhle kanye nokuphoqa amaphuzu aye phansi, okusayinwe okungekuhle.

ΣF = 0

- F_R +F₁ +F₂ - F₃ = 0

– 40 + 10 + F₂- 20 = 0

– 30 + F₂- 20 = 0

– 50 + F₂= 0

F₂= AmaNewton angu-50.

Uphawu olune-plus lubonisa ukuthi isiqondiso samandla siphezulu.

Thola u-x.

Khetha u-A njenge-axis yokujikeleza.

τ₁=F₁ l₁ = (10 N)(1 m) = 10 Nm

I-torque 1 ijikeleza umsebe ngokuphikisana newashi ngakho-ke sibeka uphawu oluhle ku-torque 3.

τ₂=F₂ x = (50)(x) = 50x Nm

I-torque 1 ijikeleza umsebe ngokuphikisana newashi ngakho-ke sibeka uphawu oluhle ku-torque 3.

τ₃=F₃ x = (20 N)(1.75 m) = -35 Nm

I-torque 2 ijikeleza ngomsebe ngokwewashi ngakho-ke sibeka uphawu olubi ku-torque 2.

Inethi ye umzuzu wamandla :

Στ = 0

10 + 50x – 35 = 0

50x - 25 = 0

50x 25

x = 25/50

x = 0.5 m

2. Amandla ka-F₁, F₂, F₃, kanye F₄ isebenza endukwini ye-ABCD njengoba kuboniswe esithombeni. Uma isisindo senduku singanakwa, ubukhulu besikhathi samandla buyini, mayelana nephuzu A.

I-axis yokujikeleza = iphuzu A.

Kwaziwa:

Amandla F₁= 10 N, ingalo ye-lever l₁ = 0 Isikhathi samandla - izinkinga nezixazululo 2

Amandla F₂= 4 N, ingalo ye-lever l₂ = 2 amamitha

Amandla F₃= 5 N, ingalo ye-lever l₃ = 3 amamitha

Amandla F₄= 10 N, ingalo ye-lever l₄ = 6 amamitha

Kufunwa: umzuzu wamandla mayelana nephuzu A

Isixazululo:

Isikhathi samandla 1 (τ₁) = F₁ l₁ = (10)(0) = 0

Isikhathi samandla 2 (τ₂) = F₂ l₂ = (4)(2) = -8 Nm

Isikhathi samandla 3 (τ₃) = F₃ l₃ = (5)(3) = 15 Nm

Isikhathi samandla 4 (τ₄) = F₄ l₄ = (10)(6) = -60 Nm

Uma i-torque ijikeleza induku ngokuphambene newashi khona-ke sibeka uphawu oluhle.

Bhekafuthi Ukusheshisa imisebe - izinkinga nezixazululo

Uma i-torque ijikeleza induku ngokwewashi, khona-ke sibeka uphawu olubi.

Umphumela wesikhathi samandla:

τ = 0 – 8 Nm + 15 Nm – 60 Nm

τ = -68 Nm + 15 Nm

τ = -53 Nm

Uphawu lokususa lubonisa ukuthi umzuzu wamandla ujikeleza induku ngokwewashi.

3. Amandla amathathu asebenza endukwini, F_A =F_C = 10 N kanye no-F_B = 20 N, njengoba kuboniswe esithombeni esingezansi. Uma ibanga lika-AB = BC = 20 cm, yisiphi isikhathi samandla mayelana nephuzu C.

Kwaziwa:

I-axis yokujikeleza endaweni C. Isikhathi samandla - izinkinga nezixazululo 3

Ibanga eliphakathi kuka-F_A kanye ne-axis yokujikeleza (r)_AC) = 40 cm = 0,4 amamitha

Ibanga eliphakathi kuka-F_B kanye ne-axis yokujikeleza (r)_BC) = 20 cm = 0.2 amamitha

Ibanga eliphakathi kuka-F_C kanye ne-axis yokujikeleza (r)_CC= 0cm

F_A = 10 uNewton

F_B = 20 uNewton

F_C = 10 uNewton

Kufunwa: Umphumela wesikhathi samandla mayelana nephuzu C.

Isixazululo:

Isikhathi samandla A:

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

Uphawu lokususa lubonisa ukuthi umzuzu wamandla ujikeleza induku ngokwewashi.

Isikhathi samandla B:

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

Uphawu lwe-Plus lubonisa ukuthi umzuzu wamandla ujikeleza induku ngokuphambene newashi.

Isikhathi samandla C:

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

Umphumela wesikhathi samandla:

Στ = Στ₁ + Στ₂ + Στ₃

Στ = -4 + 4 + 0

Στ = 0 Nm

4. Ubude benduku bungama-50 cm. Amandla amathathu asebenza endukuni, njengoba kuboniswe esithombeni esingezansi. Uma i-axis yokujikeleza iyiphuzu C, iyini inetha lomzuzu wamandla.

Kwaziwa:

I-axis yokujikeleza endaweni C. Isikhathi samandla - izinkinga nezixazululo 4

Ibanga eliphakathi kuka-F₁ futhi i-axis yokujikeleza ingu-(r)₁) = 30 cm = 0,3 amamitha

Bhekafuthi Amasondo axhunywe ngamabhande - izinkinga nezixazululo

Ibanga eliphakathi kuka-F₂ kanye ne-axis yokujikeleza (r)₂) = 10 cm = 0,1 amamitha

Ibanga eliphakathi kuka-F₃ kanye ne-axis yokujikeleza (r)₃) = 20 cm = 0,2 amamitha

F₁ = 10 uNewton

F₂ = 10 uNewton

F₃ = 10 uNewton

Kufunwa: Umphumela wesikhathi samandla mayelana nephuzu C.

Isixazululo:

Isikhathi samandla 1:

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

Uphawu lokususa lubonisa ukuthi umzuzu wamandla ujikeleza induku ngokwewashi.

Isikhathi samandla 2:

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

Uphawu lwe-Plus lubonisa ukuthi umzuzu wamandla ujikeleza induku ngokuphambene newashi.

Isikhathi samandla 3:

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

Uphawu lokususa lubonisa ukuthi umzuzu wamandla ujikeleza induku ngokwewashi.

Umphumela wesikhathi samandla:

Στ = Στ₁ + Στ₂ + Στ₃

Στ = -3 + 1 – 1

Στ = -3 Nm

Uphawu lokususa lubonisa ukuthi umphumela womzuzu wamandla ujikeleza induku ngokwewashi.

5. Amandla amathathu F₁, F₂, kanye F₃ isenzo endukwini njengoba kuboniswe esithombeni esingezansi. Ubude benduni bungamamitha angu-4. Iyini isikhathi samandla mayelana nephuzu C?

(isono 53^o = 0.8, cos 53^o = 0.6, AB = BC = CD = DE = imitha elingu-1)

Kwaziwa:

I-axis yokujikeleza endaweni C.

Amandla 1 (F)₁) = 5 Newton

Ibanga eliphakathi komugqa wesenzo sika-F₁ nge-axis yokujikeleza (r₁) = amamitha angu-2

Amandla 2 (F)₂) = 0.4 Newton

Ibanga eliphakathi komugqa wesenzo sika-F₂ nge-axis yokujikeleza (r₂) = 1 amamitha

Amandla 3 (F)₃) = 4.8 Newton

Ibanga eliphakathi kwemigqa yesenzo se- F₃ nge-axis yokujikeleza (r₃) = 2 imitha

Okufunayo: Isikhathi samandla mayelana nephuzu C.

Isixazululo:

Isikhathi samandla 1:

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

Uphawu lwe-Plus lubonisa ukuthi umzuzu wamandla ujikeleza induku ngokuphambene newashi.

Bhekafuthi Izinga lokushisa nokushisa - izinkinga nezixazululo

Isikhathi samandla 2:

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

Uphawu lokususa lubonisa ukuthi umzuzu wamandla ujikeleza induku ngokwewashi.

Isikhathi samandla 3:

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

Uphawu lokususa lubonisa ukuthi umzuzu wamandla ujikeleza induku ngokwewashi.

Umphumela wesikhathi samandla:

Στ = τ₁ – τ₂ – τ₃ = 8 – 0,4 – 9,6 = 8 – 10 = 2 Nm

Uphawu lwe-Plus lubonisa ukuthi umzuzu wamandla ujikeleza induku ngokuphambene newashi.

6. Uyini umphumela wesikhathi samandla mayelana ne-axis yokujikeleza endaweni ethi O ngamandla enza entongeni, njengoba kuboniswe esithombeni esingezansi?

Kwaziwa:

I-axis yokujikeleza endaweni ethi O.

Amandla 1 (F)₁) = 6 Newton

Ibanga eliphakathi komugqa wesenzo sika-F₁ nge-axis yokujikeleza (r₁) = 1 amamitha

Amandla 2 (F)₂) = 6 Newton

Ibanga eliphakathi komugqa wesenzo sika-F₂ nge-axis yokujikeleza (r₂) = amamitha angu-2

Amandla 3 (F)₃) = 4 Newton

Ibanga eliphakathi komugqa wesenzo sika-F₃ nge-axis yokujikeleza (r₃) = amamitha angu-2

Okufunayo: Umphumela wesikhathi samandla mayelana nephuzu C

Isixazululo:

Isikhathi samandla 1:

τ₁=F₁ l₁ = (6 N)(1 m) = 6 Nm

Uphawu lwe-Plus lubonisa ukuthi umzuzu wamandla ujikeleza induku ngokuphambene newashi.

Isikhathi samandla 2:

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

Uphawu lwe-Plus lubonisa ukuthi umzuzu wamandla ujikeleza induku ngokuphambene newashi.

Isikhathi samandla 3:

τ₃=F₃ l₃ = (4 N)(2 m) = -8 Nm

Uphawu lokususa lubonisa ukuthi umzuzu wamandla ujikeleza induku ngokwewashi.

Umphumela wesikhathi samandla:

Στ = τ₁ + τ₂ – τ₃ = 6 + 6 – 8 = 4 Nm

Uphawu lwe-Plus lubonisa ukuthi umzuzu wamandla ujikeleza induku ngokuphambene newashi.