What is a resultant force?
When several forces act on an object, we can replace them with one resultant force that produces exactly the same effect. Because force is a vector, we must combine both magnitude and direction, not just add numbers blindly.
- Same direction: add the forces, e.g. 6 N and 4 N to the right give 10 N to the right.
- Opposite direction: subtract, e.g. 6 N right and 4 N left give 2 N to the right.
- Perpendicular (at 90°): use Pythagoras' theorem.
Key formula / 关键公式
For two perpendicular forces: F = √(Fx² + Fy²)
Direction: tan θ = Fy / Fx
Newton's second law: F = ma (F is the resultant force)
Resultant force and motion
A non-zero resultant force changes an object's motion: it accelerates, decelerates or changes direction. If the resultant force is zero, the object stays at rest or moves at constant velocity (equilibrium). The acceleration always points in the same direction as the resultant force.
Worked example / 例题
A box of mass 5 kg is pulled by a 30 N force forward while friction of 10 N acts backward. Find the acceleration.
Resultant force F = 30 − 10 = 20 N forward.
Using F = ma: a = F / m = 20 / 5 = 4 m s⁻² forward.
Worked example / 例题
Two forces, 3 N east and 4 N north, act on a point. Find the resultant.
F = √(3² + 4²) = √25 = 5 N, at angle tan θ = 4/3, θ ≈ 53° north of east.
Remember / 记住
- Force is a vector — direction matters.
- Resultant = 0 means rest or constant velocity.
- The acceleration is in the direction of the resultant force.