Moment of force – problems and solutions

Moment síly – problémy a řešení

1. If F_R is the net force of F₁F₂a F₃, what is the magnitude of force F₂ and x?

Známý:

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

Síla 1 (F₁) = 10 N

Force (F₃) = 20 N

Hledám: The magnitude of force F₂ and distance of x

Řešení:

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 Newtonů.

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 moment of force :

Στ = 0

10 + 50x – 35 = 0

50x - 25 = 0

50x = 25 XNUMX

x = 25/50

x = 0.5 m

2. Forces of F₁F₂F₃a 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.

Známý:

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

Síla F₂= 4 N, the lever arm l₂ = 2 metrů

Síla F₃= 5 N, the lever arm l₃ = 3 metrů

Síla F₄= 10 N, the lever arm l₄ = 6 metrů

Hledá se: the moment of force about point A

Řešení:

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.

Viz také Newtonovy pohybové zákony – problémy a řešení

If torque rotates rod clockwise then we assign negative sign.

The resultant of the moment of force :

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 a 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.

Známý:

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

Vzdálenost mezi F_A a osa otáčení (r_AC) = 40 cm = 0,4 metru

Vzdálenost mezi F_B a osa otáčení (r_BC) = 20 cm = 0.2 metru

Vzdálenost mezi F_C a osa otáčení (r_CC) = 0 cm

F_A = 10 Newtonů

F_B = 20 Newtonů

F_C = 10 Newtonů

Hledá se: The resultant of the moment of force about point C.

Řešení:

Moment of force A :

Svatý_A= (F_A)(r_AC bez 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 :

Svatý_B = (F_B)(r_BC bez 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 :

Svatý_C= (F_C)(r_CC bez 90^o) = (10 N)(0)(1) = 0

The resultant of the moment of force :

Στ = Στ₁ + Στ₂ + Στ₃

Στ = -4 + 4 + 0

Στ = 0 N.m

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.

Známý:

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

Vzdálenost mezi F₁ and the axis of rotation is (r₁) = 30 cm = 0,3 metru

Viz také Rezonance zvukových vln - problémy a řešení

Vzdálenost mezi F₂ a osa otáčení (r₂) = 10 cm = 0,1 metru

Vzdálenost mezi F₃ a osa otáčení (r₃) = 20 cm = 0,2 metru

F₁ = 10 Newtonů

F₂ = 10 Newtonů

F₃ = 10 Newtonů

Hledá se: Resultant of moment of force about point C.

Řešení:

Moment of force 1 :

Svatý₁ = (F₁)(r₁ bez 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 :

Svatý₂= (F₂)(r₂ bez 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 :

Svatý₃= (F₃)(r₃ bez 30^o) = (10 N)(0,2 m)(0,5) = -1 Nm

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

The resultant of the moment of force :

Στ = Στ₁ + Στ₂ + Στ₃

Στ = -3 + 1 – 1

Στ = -3 N.m

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

5. Three forces F₁F₂a 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.

(hřích 53^o = 0.8, cos 53^o = 0.6, AB = BC = CD = DE = 1 meter)

Známý:

The axis of rotation at point C.

Síla 1 (F₁) = 5 Newtonů

The distance between the line of action of F₁ with the axis of rotation (r₁) = 2 metry

Síla 2 (F₂) = 0.4 Newtonů

The distance between the line of action of F₂ with the axis of rotation (r₂) = 1 metrů

Síla 3 (F₃) = 4.8 Newtonů

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

Hledám: The moment of force about point C.

Řešení:

Moment of force 1 :

τ₁=F₁ r sin 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.

Viz také Měrné teplo a tepelná kapacita – problémy a řešení

Moment of force 2 :

τ₂=F₂ r sin 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 sin 90^o= (4,8 N)(2 m)(1) = -9,6 N

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

The resultant of the moment of force :

Στ = τ₁ – t₂ – t₃ = 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?

Známý:

The axis of rotation at point O.

Síla 1 (F₁) = 6 Newtonů

The distance between the line of action of F₁ with the axis of rotation (r₁) = 1 metrů

Síla 2 (F₂) = 6 Newtonů

The distance between the line of action of F₂ with the axis of rotation (r₂) = 2 metry

Síla 3 (F₃) = 4 Newtonů

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

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

Řešení:

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 bez 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.

The resultant of the moment of force :

Στ = τ₁ + τ₂ – t₃ = 6 + 6 – 8 = 4 N.m

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