Resultant Forces

The resultant force is the single force that has the same effect as all the forces acting on an object combined.

Forces along a line

When forces act in the same direction, add them. When they act in opposite directions, subtract the smaller from the larger. The resultant acts in the direction of the larger force.

Example: A car engine produces a forward force of 3000 N. Friction and air resistance together produce a backward force of 1200 N.

Resultant = 3000 - 1200 = 1800 N forward.

Effect of the resultant force

Resultant force	Effect on motion
Zero	Object stays at rest or continues at constant velocity
Non-zero, in direction of motion	Object accelerates
Non-zero, opposite to motion	Object decelerates

Worked example

Two people push a box in opposite directions. Person A pushes with 50 N to the right. Person B pushes with 35 N to the left. Calculate the resultant force.

Resultant = 50 - 35 = 15 N to the right.

The box accelerates to the right.

Supplement: forces at angles

When two forces act at right angles, the resultant is found using a scale drawing or calculation. Draw the two forces as adjacent sides of a rectangle; the diagonal gives the resultant in both size and direction.

For perpendicular forces $F_1$ and $F_2$:

$\text{Resultant} = \sqrt{F_1^2 + F_2^2}$

Common errors and how to correct them

Adding all forces without considering direction. Forces in opposite directions must be subtracted, not added. Always assign a positive direction and keep signs consistent.

Stating “no resultant force means no forces.” Balanced forces are still present; their resultant is zero.

How to apply this in an exam

Always state the size and direction of the resultant. If the question asks about the effect on motion, link the resultant force to Newton’s first or second law.