Resultant Forces

When several forces act on an object, they combine to make a single overall force. This single force is called the resultant force. It tells you what the object will do next.

Key idea and definition

Resultant force is the single force that has the same effect as all the forces acting together. The unit of force is the newton (N).

If the forces are along one straight line, add forces in the same direction and subtract forces in opposite directions. Choose one direction as positive.

In symbols: $F_{\text{resultant}} = \sum (\text{forces with + or − signs})$.

Balanced and unbalanced forces

If the resultant force is zero, the forces are balanced and the object is in equilibrium. It stays at rest or continues in a straight line at constant speed.

If the resultant force is not zero, the object accelerates in the direction of the resultant (its speed or direction changes).

How to find a resultant (one dimension)

• Draw arrows for each force, showing direction.
• Choose a positive direction (e.g. right is +).
• Add forces in the + direction, subtract forces in the − direction.
• Give the size and the direction of the result.

Effects of a resultant force

• Same direction as motion: speed increases.
• Opposite direction: speed decreases.
• At right angles (perpendicular): direction changes (turning), even if speed stays the same.

Common misconceptions

• Zero resultant does not mean “no forces.” It means forces cancel (balanced).
• An object can keep moving at constant speed without a push if the resultant is zero.
• Forces have direction; always state it with your answer.