Resultant of Forces Acting Along the Same Straight Line
When two or more forces act along the same straight line, the resultant force is the vector sum of these forces. This can be achieved by simply adding the magnitudes of the forces if they are in the same direction, or subtracting them if they are in opposite directions.
Steps to Determine the Resultant Force
Identify the direction of each force.
Assign positive and negative signs to the forces based on their directions.
Forces in one direction (e.g., to the right) are considered positive.
Forces in the opposite direction (e.g., to the left) are considered negative.
Sum the forces algebraically.
The resultant force is the sum of all the forces, taking their signs into account.
Example 1: Forces in the Same Direction
Consider two forces, F1 and F2, both acting to the right along a straight line.
F1=5 N (to the right)
F2=3 N (to the right)
The resultant force FR is:
FR=F1+F2=5N+3N=8N
Diagram:
mathematically,
Example 2: Forces in Opposite Directions
Consider two forces, F1 and F2, acting along the same line but in opposite directions.
F1=7N (to the right)
F2=4N (to the left)
Assigning signs based on direction:
F1=+7N
F2=−4N
The resultant force FRF_RFR is:
FR=F1+F2
=7N+(−4N)
=7N−4N
=3N(to the right)
Diagram:
Example 3: Multiple Forces
Consider three forces acting along the same line:
F1=10N (to the right)
F2=6N (to the left)
F3=4N (to the right)
Assigning signs based on direction:
F1=+10N
F2=−6N
F3=+4N
The resultant force FRF_RFR is:
FR=F1+F2+F3=10N+(−6N)+4N=10N−6N+4N=8N(to the right)
Diagram:
Summary
When forces act along the same straight line, the resultant force is the sum of the forces, considering their directions. Forces in the same direction are added, while forces in opposite directions are subtracted. This principle allows us to determine the net effect of multiple forces acting on an object along a single line.
