Qüvvə anı – problemlər və həllər
1. If FR is the net force of F1, F2, və F3, what is the magnitude of force F2 and x?
Məlumdur:
Net force (FR) = 40 N
Qüvvə 1 (F)1) = 10 N
Force (F3) = 20 N
İstenilen: Qüvvənin böyüklüyü F2 and distance of x
Həll yolu:
Find the magnitude of force F2 :
Force points to upward, signed negative and force points to downward, signed negative.
ΣF = 0
- FR +F1 +F2 - F3 = 0
– 40 + 10 + F2 - 20 = 0
– 30 + F2 - 20 = 0
– 50 + F2 = 0
F2 = 50 Nyuton.
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
x = 25/50
x = 0.5 m
2. Forces of F1, F2, F3, və 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.
Məlumdur:
F qüvvəsi1 = 10 N, the lever arm l1 = 0 
F qüvvəsi2 = 4 N, the lever arm l2 = 2 metr
F qüvvəsi3 = 5 N, the lever arm l3 = 3 metr
F qüvvəsi4 = 10 N, the lever arm l4 = 6 metr
İstənilən: the moment of force about point A
Həll yolu:
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.
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, FA =FC = 10 N və FB = 20 N, as shown in figure below. If distance of AB = BC = 20 cm, what is the moment of force about point C.
Məlumdur:
The axis rotation at point C.
F arasındakı məsafəA və fırlanma oxu (rAC) = 40 sm = 0,4 metr
F arasındakı məsafəB və fırlanma oxu (rBC) = 20 sm = 0.2 metr
F arasındakı məsafəC və fırlanma oxu (rCC) = 0 sm
FA = 10 Nyuton
FB = 20 Nyuton
FC = 10 Nyuton
İstənilən: The resultant of the moment of force about point C.
Həll yolu:
Moment of force A :
ΣτA = (FA)(rAC günah 90o) = (10 N)(0,4 m)(1) = -4 Nm
Minus sign indicates that the moment of force rotates rod clockwise.
Moment of force B :
ΣτB = (FB)(rBC günah 90o) = (20 N)(0,2 m)(1) = 4 Nm
Plus sign indicates that the moment of force rotates rod counterclockwise.
Moment of force C :
ΣτC = (FC)(rCC günah 90o) = (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.
Məlumdur:
The axis rotation at point C.
F arasındakı məsafə1 and the axis of rotation is (r1) = 30 sm = 0,3 metr
F arasındakı məsafə2 və fırlanma oxu (r2) = 10 sm = 0,1 metr
F arasındakı məsafə3 və fırlanma oxu (r3) = 20 sm = 0,2 metr
F1 = 10 Nyuton
F2 = 10 Nyuton
F3 = 10 Nyuton
İstənilən: Resultant of moment of force about point C.
Həll yolu:
Moment of force 1 :
Στ1 = (F1)(r1 günah 90o) = (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 günah 90o) = (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 günah 30o) = (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 F1, F2, və 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.
(günah 53o = 0.8, cos 53o = 0.6, AB = BC = CD = DE = 1 meter)
Məlumdur:
The axis of rotation at point C. 
Qüvvə 1 (F)1) = 5 Nyuton
The distance between the line of action of F1 with the axis of rotation (r1) = 2 metr
Qüvvə 2 (F)2) = 0.4 Nyuton
The distance between the line of action of F2 with the axis of rotation (r2) = 1 metr
Qüvvə 3 (F)3) = 4.8 Nyuton
The distance between the line of action of F3 with the axis of rotation (r3) = 2 metr
İstenilen: The moment of force about point C.
Həll yolu:
Moment of force 1 :
τ1 =F1 r sin 53o = (5 N)(2 m)(0,8) = (10)(0,8) N = 8 N
Plus sign indicates that the moment of force rotates rod counterclockwise.
Moment of force 2 :
τ2 =F2 r sin 90o = (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 90o = (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 – 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?
Məlumdur:
The axis of rotation at point O. 
Qüvvə 1 (F)1) = 6 Nyuton
The distance between the line of action of F1 with the axis of rotation (r1) = 1 metr
Qüvvə 2 (F)2) = 6 Nyuton
The distance between the line of action of F2 with the axis of rotation (r2) = 2 metr
Qüvvə 3 (F)3) = 4 Nyuton
The distance between the line of action of F3 with the axis of rotation (r3) = 2 metr
İstenilen: The resultant of the moment of force about point C
Həll yolu:
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 günah 30o = (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 – τ3 = 6 + 6 – 8 = 4 N.m
Plus sign indicates that the moment of force rotates rod counterclockwise.
