What is the Resolution of Forces?
Resolution of forces is essentially the technique by which a given quantity of force is divided into a variable number of components; it is done in such a way that the effect on the body remains constant. In general, it is done in two mutually perpendicular directions.
Resolution of Forces into Components
The process of splitting up a given force into different components without changing its effect on the body is called the resolution of a force. If a force 'F' is resolved or replaced by two forces using the principle of resolution of forces, it will together produce the same effect as that of force 'F'. These forces are known as the components of the force 'F'.
Resolution of Forces into Rectangular Components
The rectangular component of any force is two components such that they are perpendicular to each other, and the resultant of the two components will give the resultant force. Let us consider a force 'F' inclined at an angle 'θ' to the horizontal as shown in the figure below. X and Y are two axes passing through 'O' and perpendicular to each other.
Applying the principle of resolution of forces, resolve the force 'F' into Fx and Fy. The polygon constructed with these two components as adjacent sides will form a rectangle OABC, therefore, the components are known as rectangular components. For the sign convention of components of forces, conventional co-ordinate directions are considered.
Y-component (Fy) ↑ Positive ↓ Negative
Determine the X and Y components of the force shown in the figure.
Consider the triangle OAB,
cos θ = OA/OB
OA = OB cosθ
OA = Fx
OB = F
Fx = F cosθ
Sin θ = AB/OB
AB = OB sinθ
AB = Fy
OB = F
Fy = F sinθ
The two rectangular components of the force 'F' after resolution of force are:
Fx = F cosθ
Fy = F sinθ
Applying the principle of the resolution,
1. Component along X-direction
Fx = 20 cos30°
Fx = 17.32N
2. Component along Y-direction
Fy = 20 sin30º
Fy = 10N
Triangular Parallelogram Law of Forces
In the Triangular Law of Forces, If two forces acting simultaneously on a body are represented in magnitude and direction by two sides of a triangle in order, then the third side represents the resultant of the two forces in the opposite direction and magnitude.
The resultant of two concurrent and coplanar forces, i.e, forces lying in the same plane whose line of action passes through a single point may be obtained using the theorem of the parallelogram of forces which states that "If two forces acting at a point are represented by the sides of a parallelogram drawn from the point in magnitude and direction, their resultant force is represented by the diagonal of the parallelogram drawn through that point in magnitude and direction."
Resolution of Forces MCQs
1. A force of 50N is acting at a point making an angle 35o with the horizontal. Determine the components of this force in X and Y directions.
Component along X-direction
Fx = 50 cos 95o = 40.95N
Component along Y-direction
Fy = 50 sin 35o = 28.68N
2. Find the resultant for the given force system using the principle of superposition of forces.
∑Fx = 0
30 + 15 cos 60o – 25 cos 30o = 15.85N
∑Fy = 0
50 + 15 sin 60o + 25 sin 30o = 75.5N
Resultant Force (R) = √(Fx2+ Fy2)
= 15.852+ 75.52
3. Resolve the 400 N force acting on a block as shown into horizontal and vertical components.
Angle of inclination of 400 kN force with respect to horizontal x-axis = 40o-20o = 20o
Component along Horizontal axis = 400 cos 20o = 375.35N
Component along Vertical axis = -400 sin 20o = -136.8N
|Important Topics for Gate Exam|
|Non-Newtonian Fluids||Open Loop Control System|
|Pattern Allowances||Poissons Ratio|
|Pressure Measurement||Prestressed Concrete|
|Prestressing Systems||Principle of Conservation of Energy|
|Properties of Aggregate||Properties of Concrete|