Resultant of Forces

Adding two forces using the law of parallelogram.

Adding two forces using the law of triangles.

Adding more than two forces using the force polygon.

Find resultant of multiple concurrent forces acting on a point using analytical and graphical method.
Parallelogram Law:
The law of parallelogram of forces states that if two vectors acting on a particle at the same time be represented in magnitude and direction by the two adjacent sides of a parallelogram drawn from a point their resultant vector is represented in magnitude and direction by the diagonal of the parallelogram drawn from the same point.
Triangle Law:
If two forces acting simultaneously on a body are represented by the sides of a triangle taken in order, their resultant is represented by the closing side of the triangle taken in the opposite order.
Polygon Law:
Polygon law of vector addition states that if a number of vector are represented completely by the side of a polygon taken in order their resultant is fully represented by the closing side of the polygon taken in opposite order.
Solved Examples
Solved Example:
22201
The resultant of two equal vectors is equal to either of them. The angle between two vectors will be: (UP TGT Math 2016)
Solved Example:
22202
Find the resultant of the parallel force system as shown in the figure and locate the same with respect to point C:
Solved Example:
22203
The Law of Polygon of Forces states that: (ISRO Scientist Civil 2015)
Solved Example:
22204
Two forces 5 N and 20 N are acting at an angle of 120$^\circ$ between them. Find the resultant force in magnitude and direction.
Solved Example:
22205
If two concurrent forces A and B acting on a point are 200 N and 300 N. What is the magnitude of resultant force, if it makes an angle of 50$^\circ$ with each force? (Based on DSSSB AE Civil Sept 2021)
Solved Example:
22206
Two forces with equal magnitudes F act on a body and the magnitude of the resultant force is $\dfrac{F}{3}$. The angle between the two forces is:
Solved Example:
22207
If a rigid body is in equilibrium under the action of three forces, then:
Solved Example:
22208
D' Alembert's principle is used for: (UPPSC AE Civil 2019)
Solved Example:
22209
A ring is pulled by three forces as shown in the figure. Find the force F and the angle $\theta$ if the resultant of these forces is 100N acting in the vertical direction.
Solved Example:
22210
The algebraic sum of the resolved parts of a number of forces in a given direction is equal to the resolved part of their resultant in the same direction. This is as per the principle of:
Solved Example:
22211
The resolved part of the resultant of two forces inclined at an angle 9$^\circ$ in a given direction is equal to:
Solved Example:
22212
What is the magnitude of the resultant force of the two forces which are perpendicular to each other? The two forces are 20 units and 30 units respectively.
Solved Example:
22213
The resultant of two forces in a plane is 400 N at 120$^\circ$. If one of the forces is 200 N at 20$^\circ$ what is the other force?
Solved Example:
22214
Determine the resultant of the following forces: A = 600 N at 40$^\circ$, B = 800 N at 160$^\circ$ and C = 200 N at 300$^\circ$.
Solved Example:
22215
The equilibrant of the forces 10 N at 10$^\circ$ and 15 N at 100$^\circ$ is:
Solved Example:
22216
A point possesses simultaneously velocities whose measures are 4, 3, 2, and 1; the angle between the first and second is 30$^\circ$, between the second and third 90$^\circ$, and between the third and fourth 120$^\circ$; find the resultant velocity and angle to the direction of the first velocity? (AAI ATC Junior Executive March 2021 Shift I)