Moment of force – problems and solutions

Momento de forza: problemas e solucións

1. If F_R is the net force of F₁, F₂, e F₃, what is the magnitude of force F₂ and x?

Coñecido:

Net force (F_R) = 40 N Moment of force – problems and solutions 1

Forza 1 (F₁) = 10 N

Force (F₃) = 20 N

Quería: The magnitude of force F₂ and distance of x

Solución:

Find the magnitude of force F₂:

Force points to upward, signed negative and force points to downward, signed negative.

ΣF = 0

- F_R +F₁ +F₂ - F₃ = 0

– 40 + 10 + F₂- 20 = 0

– 30 + F₂- 20 = 0

– 50 + F₂= 0

F₂= 50 newtons.

Plus sign indicates that the direction of the force is upward.

Find x.

Choose A as the axis of rotation.

τ₁=F₁ l₁ = (10 N)(1 m) = 10 Nm

The torque 1 rotates beam counterclockwise so we assign positive sign to the torque 3.

τ₂=F₂ x = (50)(x) = 50x Nm

The torque 1 rotates beam counterclockwise so we assign positive sign to the torque 3.

τ₃=F₃ x = (20 N)(1.75 m) = -35 Nm

The torque 2 rotates beam clockwise so we assign negative sign to the torque 2.

The net of momento de forza :

Στ = 0

10 + 50x – 35 = 0

50x - 25 = 0

50x = 25

x = 25/50

x = 0.5 m

2. Forces of F₁, F₂, F₃, e F₄ acts on the rod of ABCD as shown in figure. If rod’s mass ignored, what is the magnitude of the moment of force, about point A.

The axis of rotation = points A.

Coñecido:

Forza F₁= 10 N, the lever arm l₁ = 0 Moment of force – problems and solutions 2

Forza F₂= 4 N, the lever arm l₂ = 2 metros

Forza F₃= 5 N, the lever arm l₃ = 3 metros

Forza F₄= 10 N, the lever arm l₄ = 6 metros

Buscase: the moment of force about point A

Solución:

Moment of force 1 (τ₁) = F₁ l₁ = (10)(0) = 0

Moment of force 2 (τ₂) = F₂ l₂ = (4)(2) = -8 Nm

Moment of force 3 (τ₃) = F₃ l₃ = (5)(3) = 15 Nm

Moment of force 4 (τ₄) = F₄ l₄ = (10)(6) = -60 Nm

If torque rotates rod counterclockwise then we assign positive sign.

Ver tamén Dous condutores paralelos que transportan correntes: problemas e solucións

If torque rotates rod clockwise then we assign negative sign.

A resultante do momento da forza:

τ = 0 – 8 Nm + 15 Nm – 60 Nm

τ = -68 Nm + 15 Nm

τ = -53 Nm

Minus sign indicates that the moment of force rotates rod clockwise.

3. Three forces act on a rod, F_A =F_C = 10 N e F_B = 20 N, as shown in figure below. If distance of AB = BC = 20 cm, what is the moment of force about point C.

Coñecido:

The axis rotation at point C. Moment of force – problems and solutions 3

Distance between F_A and the axis of rotation (r_AC) = 40 cm = 0,4 meters

Distance between F_B and the axis of rotation (r_BC) = 20 cm = 0.2 meters

Distance between F_C and the axis of rotation (r_CC) = 0 centímetros

F_A = 10 Newtons

F_B = 20 Newtons

F_C = 10 Newtons

Buscase: The resultant of the moment of force about point C.

Solución:

Moment of force A :

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

Minus sign indicates that the moment of force rotates rod clockwise.

Moment of force B :

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

Plus sign indicates that the moment of force rotates rod counterclockwise.

Moment of force C :

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

A resultante do momento da forza:

Στ = Στ₁ + Στ₂ + Στ₃

Στ = -4 + 4 + 0

Στ = 0 Nm

4. Length of a rod is 50 cm. Three forces act on the rod, as shown in figure below. If the axis of rotation is point C, what is the net of the moment of force.

Coñecido:

The axis rotation at point C. Moment of force – problems and solutions 4

Distance between F₁ and the axis of rotation is (r₁) = 30 cm = 0,3 meters

Ver tamén Conversión de unidades: problemas e solucións

Distance between F₂ and the axis of rotation (r₂) = 10 cm = 0,1 meters

Distance between F₃ and the axis of rotation (r₃) = 20 cm = 0,2 meters

F₁ = 10 Newtons

F₂ = 10 Newtons

F₃ = 10 Newtons

Buscase: Resultant of moment of force about point C.

Solución:

Moment of force 1 :

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

Minus sign indicates that the moment of force rotates rod clockwise.

Moment of force 2 :

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

Plus sign indicates that the moment of force rotates rod counterclockwise.

Moment of force 3 :

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

Minus sign indicates that the moment of force rotates rod clockwise.

A resultante do momento da forza:

Στ = Στ₁ + Στ₂ + Στ₃

Στ = -3 + 1 – 1

Στ = -3 Nm

Minus sign indicates that the resultant of the moment of force rotates rod clockwise.

5. Three forces F₁, F₂, e F₃ act on a rod as shown in figure below. Length of rod is 4 meters. What is the moment of force about point C.

(sin 53^o = 0.8, cos 53^o = 0.6, AB = BC = CD = DE = 1 metro)

Coñecido:

The axis of rotation at point C.

Forza 1 (F₁) = 5 Newtons

A distancia entre a liña de acción de F₁ co eixo de rotación (r₁) = 2 metros

Forza 2 (F₂) = 0.4 Newtons

A distancia entre a liña de acción de F₂ co eixo de rotación (r₂) = 1 metros

Forza 3 (F₃) = 4.8 Newtons

The distance between the line of action of F₃ with the axis of rotation (r₃) = 2 metro

Quería: The moment of force about point C.

Solución:

Moment of force 1 :

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

Plus sign indicates that the moment of force rotates rod counterclockwise.

Ver tamén Rolling motion - problems and solutions

Moment of force 2 :

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

Minus sign indicates that the moment of force rotates rod clockwise.

Moment of force 3 :

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

Minus sign indicates that the moment of force rotates rod clockwise.

A resultante do momento da forza:

Στ = τ₁ – τ₂ – τ₃ = 8 – 0,4 – 9,6 = 8 – 10 = 2 N.m

Plus sign indicates that the moment of force rotates rod counterclockwise.

6. What is the resultant of the moment of force about the axis of rotation at point O by forces acts on the rod, as shown in the figure below?

Coñecido:

O eixo de rotación no punto O.

Forza 1 (F₁) = 6 Newtons

A distancia entre a liña de acción de F₁ co eixo de rotación (r₁) = 1 metros

Forza 2 (F₂) = 6 Newtons

A distancia entre a liña de acción de F₂ co eixo de rotación (r₂) = 2 metros

Forza 3 (F₃) = 4 Newtons

A distancia entre a liña de acción de F₃ co eixo de rotación (r₃) = 2 metros

Quería: The resultant of the moment of force about point C

Solución:

Moment of force 1 :

τ₁=F₁ l₁ = (6 N)(1 m) = 6 Nm

Plus sign indicates that the moment of force rotates rod counterclockwise.

Moment of force 2 :

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

Plus sign indicates that the moment of force rotates rod counterclockwise.

Moment of force 3 :

τ₃=F₃ l₃ = (4 N)(2 m) = -8 Nm

Minus sign indicates that the moment of force rotates rod clockwise.

A resultante do momento da forza:

Στ = τ₁ + τ₂ – τ₃ = 6 + 6 – 8 = 4 Nm

Plus sign indicates that the moment of force rotates rod counterclockwise.