1. Resultant of two forces
Learning objectives
Resultant of parallel forces
Resultant of perpendicular forces
Resultant two forces at any angle

2. Resultant of two forces
A resultant force is a single force which can replace a set of forces acting on an object. It has exactly the same effect on the object as the original set.
Parallel forces
7 N
4 N
Resultant force = = 11 N
5 N
12 N
Resultant force = = 7 N

3. Resultant of Perpendicular forces
4 N
Resultant =
= 5 N
Angle  =
tan-1(3/4) =
36.90

4. Two forces at any angle a2 = b2 + c2 – 2b c cos A
Resultant R
5 N
8 N
5 N
300 
1500
300
8 N
Using cosine rule :
a2 = b2 + c2 – 2b c cos A
R2 = – 28 5 cos 150
R = 12.6 N
Use sine rule to find :
Giving: sin  =
 = 11.50

5. Example a2 = b2 + c2 – 2b c cos A Using cosine rule :
130°
15 N
25 N
15 N
Resultant
50° 
130°
25 N
Using cosine rule :
a2 = b2 + c2 – 2b c cos A
R2 = – 225 15 cos 50
R = 19.2 N
Use sine rule to find :
Giving: sin  =
 = 36.8°

6. Example
Find the magnitude of the resultant of the forces shown in the sketch, and the angle it make with the larger force.
8 N
500
5 N
5 N
Resultant 
130°
50°
8 N
By the cosine rule :
R2 = – 2 x 8 x 5 x cos 1300
Gives R = 11.9 N
By the sine rule :
Gives  = 18.80