Moment of force – problems and solutions
1. If FR is the net force of F1, F2, ו-F3, what is the magnitude of force F2 and x?
ידוע:
Net force (FR) = 40 N
כוח 1 (F1) = 10 N
Force (F3) = 20 N
מבוקש: The magnitude of force F2 and distance of x
פתרון:
Find the magnitude of force F2 :
Force points to upward, signed negative and force points to downward, signed negative.
ΣF = 0
- פR + ו1 + ו2 - פ3 = 0
– 40 + 10 + F2 - 20 = 0
– 30 + F2 - 20 = 0
– 50 + F2 = 0
F2 = 50 Newton.
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 מטר
2. Forces of F1, F2, F3, ו-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.
ידוע:
Force F1 = 10 N, the lever arm l1 = 0 
Force F2 = 4 N, the lever arm l2 = 2 מטר
Force F3 = 5 N, the lever arm l3 = 3 מטר
Force F4 = 10 N, the lever arm l4 = 6 מטר
מבוקש: the moment of force about point A
פתרון:
Moment of force 1 (τ1) = פ1 l1 = (10)(0) = 0
Moment of force 2 (τ2) = פ2 l2 = (4)(2) = -8 Nm
Moment of force 3 (τ3) = פ3 l3 = (5)(3) = 15 Nm
Moment of force 4 (τ4) = פ4 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 ו-FB = 20 N, as shown in figure below. If distance of AB = BC = 20 cm, what is the moment of force about point C.
ידוע:
The axis rotation at point C.
Distance between FA and the axis of rotation (rAC) = 40 ס"מ = 0,4 מטרים
Distance between FB and the axis of rotation (rBC) = 20 ס"מ = 0.2 מטרים
Distance between FC and the axis of rotation (rCC) = 0 ס"מ
FA = 10 ניוטון
FB = 20 ניוטון
FC = 10 ניוטון
מבוקש: The resultant of the moment of force about point C.
פתרון:
Moment of force A :
בA = (FA)(rAC בלי 90o) = (10 N)(0,4 m)(1) = -4 N.m
Minus sign indicates that the moment of force rotates rod clockwise.
Moment of force B :
בB = (FB)(rBC בלי 90o) = (20 N)(0,2 m)(1) = 4 N.m
Plus sign indicates that the moment of force rotates rod counterclockwise.
Moment of force C :
בC = (FC)(rCC בלי 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.
ידוע:
The axis rotation at point C.
Distance between F1 and the axis of rotation is (r1) = 30 ס"מ = 0,3 מטרים
Distance between F2 and the axis of rotation (r2) = 10 ס"מ = 0,1 מטרים
Distance between F3 and the axis of rotation (r3) = 20 ס"מ = 0,2 מטרים
F1 = 10 ניוטון
F2 = 10 ניוטון
F3 = 10 ניוטון
מבוקש: Resultant of moment of force about point C.
פתרון:
Moment of force 1 :
ב1 = (F1)(r1 בלי 90o) = (10 N)(0,3 m)(1) = -3 N.m
Minus sign indicates that the moment of force rotates rod clockwise.
Moment of force 2 :
ב2 = (F2)(r2 בלי 90o) = (10 N)(0,1 m)(1) = 1 N.m
Plus sign indicates that the moment of force rotates rod counterclockwise.
Moment of force 3 :
ב3 = (F3)(r3 בלי 30o) = (10 N)(0,2 m)(0,5) = -1 N.m
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, ו-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 53o = 0.8, קוס 53o = 0.6, AB = BC = CD = DE = 1 meter)
ידוע:
The axis of rotation at point C. 
כוח 1 (F1) = 5 ניוטון
The distance between the line of action of F1 with the axis of rotation (r1) = 2 מטרים
כוח 2 (F2) = 0.4 ניוטון
The distance between the line of action of F2 with the axis of rotation (r2) = מטר אחד
כוח 3 (F3) = 4.8 ניוטון
The distance between the line of action of F3 with the axis of rotation (r3) = 2 מטר
מבוקש: The moment of force about point C.
פתרון:
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 – ט2 – ט3 = 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?
ידוע:
The axis of rotation at point O. 
כוח 1 (F1) = 6 ניוטון
The distance between the line of action of F1 with the axis of rotation (r1) = מטר אחד
כוח 2 (F2) = 6 ניוטון
The distance between the line of action of F2 with the axis of rotation (r2) = 2 מטרים
כוח 3 (F3) = 4 ניוטון
The distance between the line of action of F3 with the axis of rotation (r3) = 2 מטרים
מבוקש: The resultant of the moment of force about point C
פתרון:
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 בלי 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 – ט3 = 6 + 6 – 8 = 4 N.m
Plus sign indicates that the moment of force rotates rod counterclockwise.
