Boholo ba torque ea net - mathata le litharollo

1. Matla P a sebediswa pheletsong e nngwe ya lehlasedi le bolelele ba 2 m. Boholo ba lehlasedi ke bofe? torqueMothapo oa potoloho ntlheng ea A.

Tse tsejoang:

Matla (F) = 10 N

Bolelele ba AB (r)_AB) = 2 m

Matla a F a otlolohile ho lehlaseli.

Letsoho la lever (l)) =r_AB sebe 90^o = (2 m)(1) = 2 m

Oa Batla: Torque e potolohileng axis ea potoloho

Tharollo:

Torque:

τ = F l = (10 N)(2 m) = 20 N m

Letšoao la ho eketsa ka lebaka la lehlaseli e potoloha ho potoloha ho ya ka lehlakoreng le leng.

2. Bolelele ba lehlaseli AB ke 2 m mme boholo ba matla F ke 10 N. Boholo ba torque ke bofe? Mothapo wa potoloho ntlheng ya A.

Tse tsejoang:

Matla (F) = 10 N

Bolelele ba AB (r)_AB) = 2 m

Letsoho la lever (l)) =r_AB sebe 60^o = (2 m)(0.53) = 3 m

Oa Batla: Torque e potolohileng axis ea potoloho

Tharollo:

Torque:

τ = F l = (10 N)(3 m) = 103 N m

Letšoao la ho eketsa hobane matla F a baka mahlaseli e potoloha ho potoloha ho ya ka lehlakoreng le leng.

3. Bolelele ba lehlaseli ke 2 m. Boholo ba F₁ ke 10 N le boholo ba F₂ ke 15 N. Fumana torque ea letlooa bohareng ba lehlaseli.

Mothapo oa potoloho bohareng ba lehlaseli.

Tse tsejoang:

Matla a 1 (F)₁) = 10 N

The distanta pakeng tsa F₁ le bohareng ba lehlaseli (r₁) = 1 m

Letsoho la lever 1 (l)₁) =r₁ sebe 90^o = (1 m)(1) = 1 m

Matla F₁ e otlolohile ho lehlaseli.

Matla a 2 (F)₂) = 15 N

Sebaka se pakeng tsa F₂ le bohareng ba lehlaseli (r₂) = 1 m

Matla F₂ e otlolohile ho lehlaseli.

Letsoho la lever 2 (l)₂) =r₁ sebe 90^o = (1 m)(1) = 1 m

Ho batloa: Ttorque ea letlooa e potolohang mothapo oa potoloho

Tharollo:

Torque 1:

τ₁ =F₁ l₁ = (10 N)(1 m) = 10 N m

Letšoao la ho eketsa ka lebaka la matla a F₁ e baka lehlaseli e potoloha ho potoloha ho ya ka lehlakoreng le leng.

Torque 2:

τ₂ =F₂ l₂ = (15 N)(1 m) = -15 N

Letšoao la ho tlosa hobane matla a F₂ e etsa hore lehlaseli le e potoloha ka ho ya ka oache.

Torque ea letlooa:

Στ = τ₁ – τ₂ = 10 – 15 = – 5 N m

Letšoao la ho tlosa hobane lehlaseli ho e potoloha ka ho ya ka oache.

4. Bolelele ba lehlaseli AB ke 2 m, Boholo ba F₁ ke 10 N le boholo ba F₂ is 10 N. Fumana torque ea letlooa bohareng ba lehlaseli.

Mothapo oa potoloho bohareng ba lehlaseli.

Tse tsejoang:

Matla a 1 (F)₁) = 10 Nn

Sebaka se pakeng tsa F₁ le bohareng ba lehlaseli (r₁) = 1 m

Letsoho la lever 1 (l)₁) =r₁ sebe 60^o = (1 m)(0.53= 0.53 m

Matla a 2 (F)₂) = 10 N

Sebaka se pakeng tsa F₂ le bohareng ba lehlaseli (r₂) = 1 m

Matla F₂ e otlolohile ho lehlaseli.

Letsoho la lever 2 (l)₂) = r₂ sebe 90^o = (1 m)(1) = 1 m

Ho batloa: Torque ea letlooa e mabapi le axis ea potoloho

Tharollo:

Torque 1:

τ₁ =F₁ l₁ = (10 N)(0.53 m) = 5√3 = 8.7 Nm

Letšoao la ho eketsa hobane matla a F₁ e etsa hore lehlaseli le e potoloha ka ho ya ka oache.

Torque 2:

τ₂ =F₂ l₂ = (10 N)(1 m) = -10 N m

Letšoao la ho tlosa hobane matla a F₂ e etsa hore lehlaseli le e potoloha ka ho ya ka oache.

Torque ea letlooa:

Στ = τ₁ – τ₂ = 8.7 – 10 = – 1.3 N m

Letšoao la ho tlosa hobane matla a letlooa a etsa hore lehlaseli le e potoloha ka ho ya ka oache.

5. Bolelele ba lehlaseli ke 10 m, boholo ba F₁ ke 10 N, boholo ba F₂ ke 10 N le boholo ba F₃ ke 15 N. Sebaka se pakeng tsa ntlha A le ntlha C ke 7.5 m. Matla F₂ e fumanehang bohareng ba lehlaseli. Fumana torque ea letlooa mabapi le ntlha ea C e fumanehang ho 2.5 m ho tloha ntlheng ea B.

Mokhahlelo oa potoloho o sebakeng sa C

Tse tsejoang:

Matla a 1 (F)₁) = 10 N

Sebaka se pakeng tsa F₁ le ntlha C (r₁) = 2.5 m

Matla F₁ e otlolohile ho lehlaseli.

Letsoho la lever 1 (l)₁) =r₁ sebe 90^o = (2.5 m)(1) = 2.5 m

Matla a 2 (F)₂) = 10 N

Sebaka se pakeng tsa F₂ le ntlha C (r₂) = 2.5 m

Matla a F₂ e otlolohile ho lehlaseli.

Letsoho la lever 2 (l)₂) = r₂ sebe 90^o = (2.5 m(1) = 2.5 m

Matla a 3 (F)₃) = 15 N

Sebaka se pakeng tsa F₃ le ntlha C (r)₃) = 7.5 m

Matla a F₃ e otlolohile ho lehlaseli.

Letsoho la lever 3 (l)₃) = r₃ sebe 90^o = (7.5 m)(1) = 7.5 m

Ho batloa: Torque ea letlooa e mabapi le axis ea potoloho

Tharollo:

Torque 1:

τ₁ =F₁ l₁ = (10 N)(2.5 m) = 25 N m

Letšoao la ho eketsa hobane matla a F₁ e etsa hore lehlaseli le e potoloha ka ho ya ka oache.

Torque 2:

τ₂ =F₂ l₂ = (10 N)(2.5 m) = 25 N m

Tletshwao la hae le eketsehileng hobane matla a F₂ e etsa hore lehlaseli le e potoloha ka ho ya ka oache.

Torque 3:

τ₃ =F₃ l₃ = (15 N)(7.5 m) = -112..5 N m

Letšoao la ho tlosa hobane matla a F₃ e etsa hore lehlaseli le e potoloha ka ho ya ka oache.

Torque ea letlooa:

Στ = τ₁ + τ₂ – τ₃ = 25 + 25 - 112.5 = – 62.5 N m

Letšoao la ho tlosa hobane matla a letlooa a etsa hore lehlaseli le e potoloha ka ho ya ka oache.

6. Bolelele ba lehlaseli ke 10 m, boholo ba F₁ ke 10 N, boholo ba F₂ ke 10 N le boholo ba F₃ ke 10 N. Fumana torque ea letlooa mabapi le ntlha ea A, e fumanehang 5 m ho tloha point ea ts'ebeliso ea matla F₁.

Mokhahlelo oa potoloho ntlheng ea A.

Tse tsejoang:

Matla a 1 (F)₁) = 10 N

Sebaka se pakeng tsa F₁ le ntlha A (r)₁) = 5 m

Letsoho la lever 1 (l)₁) =r₁ sebe 60^o = (5 m)(0.53= 2.53 m

Etsa matla 2 (F)₂) = 10 N

Sebaka se pakeng tsa F₂ le ntlha A (r)₂= 0

Matla a F₂ e otlolohile ho lehlaseli.

Letsoho la lever 2 (l)₂) = r₂ sebe 90^o = (0)(1) = 0

Matla a 3 (F)₃) = 10 N

Sebaka se pakeng tsa F₃ le ntlha A (r)₃) = 10 m

Letsoho la lever 3 (l)₃) = r₃ sebe 30^o = (10 m)(0.5) = 5 m

Ho batloa: torque ea letlooa e potolohileng motsoako oa potoloho

Tharollo:

Torque 1:

τ₁ =F₁ l₁ = (10 N)(2.5√3 limithara) = 25√3 = 43.3 N m

Letšoao la ho eketsa hobane matla a F₁ e etsa hore lehlaseli le e potoloha ka ho ya ka oache.

Torque 2:

τ₂ =F₂ l₂ = (10 N)(0) = 0

Torque 3:

τ₃ =F₃ l₃ = (10 N)(5 m) = -50 N m

Letšoao la ho tlosa hobane matla a F₃ e etsa hore lehlaseli le e potoloha ka ho ya ka oache.

Torque ea letlooa:

Στ = τ₁ + τ₂ – τ₃ = 43.3 + 0 - 50 = – 6.7 N m

Letšoao la ho tlosa hobane matla a letlooa a etsa hore lehlaseli le e potoloha ka ho ya ka oache.