In this article, we’ll cover finding the resultant force in a system of forces by working through a sample problem.
First, take a look at our article on finding the resultant force, which we could call the basic introduction to this topic.
See: How Is the Resultant Force Calculated
Finding the Resultant Force in a System of Forces
The forces acting on various objects aren’t always in the same direction or on the same coordinate plane. Sometimes several forces acting on an object may be in completely opposite directions.
Let’s explain this topic with a sample problem:
QUESTION: Find the resultant of the force system shown in the figure using the projection method.
We’ll start by finding each force’s x and y projections (components) one by one. In other words, we’ll find the Fx and Fy of each force.
For an explanation supported by example questions on how to find component forces, also see: Finding Component Forces
Next, we’ll find the total Fx and total Fy.
Total Fx = 127 Newtons
Total Fy = 113 Newtons
As a result, we’ve found the resultant force (R) of 4 forces acting on the object in different directions and lines of action, along with the angle it makes with the coordinate plane.
Vector Addition
The resultant force is a single equivalent force obtained by vectorially summing all the forces acting on the system.
Parallelogram Method
The resultant of two forces can also be found graphically using the parallelogram rule.
Equilibrium Condition
For an object to be in equilibrium, the resultant of all forces acting on it must be zero.
Related Questions
Directly adding forces at different angles is complicated and error-prone. Breaking each force into its horizontal and vertical axes reduces the addition to simple numerical sums, making it easier to calculate the result correctly.
The magnitude of the resultant force alone doesn’t tell you which direction the object will move in or be affected. The angle completes the result by specifying exactly which direction this resultant force acts in.
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