Resolution of force
the splitting of single force into two forces is known as resolution of force .
The two split force are known as component of forces.
Let F be the force . It split into two forces . Say Fx and Fy .
Fx is the component of forces along x axis or horizontal.
Fy is the component of forces along y axis or vertically.
Based on angle between two component of forces are classify into following types-
- Mutually perpendicular component or orthogonal component .
- Non-mutually perpendicular component or non-orthogonal componet .
Mutually perpendicular component or orthogonal componet .
Two components aur said to be mutually perpendicular component or orthogonal component if the angle between two component force is 90 degree.
let F be the force . It's two components of forces are fx and fy . The component of force Fx lies on x-axis. The component of force Fy lies on y-axis. Let O be the point where all three force F,Fx,Fy are meeting.
Let's take a point ' a ' on x-axis and 'b' on y-axis .and 'c ' on line of action of force F.
The angle between two components of forces fx and fy is 90 degree.
The angle between two components of forces fx and f is
To know the magnitude of two components of forces fx and fy .
Join all the point o,a,b,c in such a way that it form a rectangle oacb .
In reactangle oacb
Where
oa=bc=Fx
ob=ac=Fy
oa=oc.cos
oa=Fcos
Fx=Fcos
simillarly ac=oc×sin
ac=Fsin
Fy=Fsin
the magnitude of two componet of force F is Fcos and Fsin
Non perpendicular component or non orthogonal componet .
two components aur said to be mutually non perpendicular component or non orthogonal component if the angle between two component force is not 90 degree.
let f be the force . it's two components of forces are fx and fy . the component of force fx lies on x-axis. the component of force fy lies on y-axis. let o be the point where all three force f,fx,fy are meeting.
let's take a point a on x-axis and b on y-axis .and c on line of action of force .
the angle between two components of forces fx and f is
the angle between two components of forces fy and f is
to know the magnitude of two components of forces fx and fy
join all the point o,a,b,c in such a way that it form a parallelogram oacb
in triangle oca
oa=bc=Fx
ob=ac=Fy
oc=F
angle of coa=ἀ
angle of oca= ἀ
angle of oac= ἀ +ẞ
applying sine rule in triangle oca we get
considering
