Draw two perpendicular forces tip to tail to form a right triangle. The resultant runs from the first tail to the last tip. Use Pythagoras to find its magnitude and measure its direction from the axis named in the question.
The 2027 SEC G3 Physics K323 syllabus covers force diagrams, resultant force and graphical problems involving a static point mass. This example finds the resultant of two forces and the third force needed for equilibrium.
- Draw both forces acting on the same object.
- Copy the arrows tip to tail without turning them.
- Give both the magnitude and direction of the resultant.
- Reverse the resultant to find the balancing force.
CHAPTER 1 OF 4 · Back to contents
Separate the force diagram from the addition diagram
On the free-body diagram, show the forces acting on the chosen object. In the addition diagram, you can slide a copy of one arrow so its tail meets the tip of the other. Keep its direction and length.
With perpendicular arrows, the two forces form the legs of a right triangle. The diagonal joining the start to the finish represents the net effect.
The stated direction needs a reference. An angle measured from east towards north differs from an angle measured from north towards east.
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Worked example | 6 N east and 8 N north
A point object is pulled by 6 N east and 8 N north. Draw the 6 N arrow first, then draw the 8 N arrow from its tip. The diagonal points north-east.
| Quantity | Magnitude | Direction |
|---|---|---|
| Resultant | 10 N | 53.1° north of east |
| Balancing force | 10 N | 53.1° south of west |
The magnitude is √(6² + 8²) = 10 N. The angle from east has opposite side 8 and adjacent side 6, so tan θ = 8/6 and θ ≈ 53.1°. Measured from north, the same resultant is 36.9° east of north.
A scale drawing at 1 cm for 2 N gives legs of 3 cm and 4 cm and a diagonal of 5 cm. Use a scale drawing if the question specifies a graphical method, and label the scale and measured angle.
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CHAPTER 3 OF 4 · Back to contents
Practise closing the force triangle
To keep the object in equilibrium, add a third force opposite to the resultant. Starting at the last tip in the addition diagram, draw an arrow back to the original tail. That closes the triangle.
With 5 N east and 12 N south, the resultant magnitude is 13 N. Its direction is about 67.4° south of east, and the balancing force is 13 N at 67.4° north of west.
Check the direction before rounding. If the larger component points south, the resultant in this practice question should be closer to south than to east.
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CHAPTER 4 OF 4 · Back to contents
Frequently asked questions
Why is the resultant of 6 N and 8 N smaller than 14 N?
The forces act at right angles. Adding their magnitudes directly would describe two forces pointing in the same direction.
Can I draw north first?
Yes. Keeping both arrows unchanged gives the same final tip whichever you place first.
Is the balancing force another name for the resultant?
The balancing force has the same magnitude and opposite direction. Adding it makes the net force zero.
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