Resultant of two forces

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
Resultant force 7 4 11 N
Resultant force 12 - 5 7 N
3
Resultant of Perpendicular forces
Resultant
?

Resultant
5 N
Angle ?
tan-1(3/4)
36.90
4
Two forces at any angle
1500
a2 b2 c2 2?b ?c ?cos A
Using cosine rule
R2 82 52 2?8 ?5 ?cos 150
R 12.6 N
Use sine rule to find ?
Giving sin ? 0.198712
? 11.50
5
Example
a2 b2 c2 2?b ?c ?cos A
Using cosine rule
R2 252 152 2?25 ?15 ?cos 50
R 19.2 N
Use sine rule to find ?
Giving sin ? 0.5991
? 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.
?
130
By the cosine rule
R2 82 52 2 x 8 x 5 x cos 1300
Gives R 11.9 N
By the sine rule
Gives ? 18.80