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⚡ Resultant Forces

Spec 6.5.1.4 📗 Foundation
📖 In-Depth Theory

What Is a Resultant Force?

When MULTIPLE FORCES act on an object, they can be replaced by a SINGLE RESULTANT FORCE that has the same effect.
Finding the resultant:
FORCES IN THE SAME DIRECTION: add magnitudes.
FORCES IN OPPOSITE DIRECTIONS: subtract smaller from larger; direction = that of larger force.
FORCES AT RIGHT ANGLES: use Pythagoras; direction from trigonometry or scale drawing.
BALANCED FORCES (resultant = 0):
If resultant force = 0, the object is either:
Stationary (at rest), OR
Moving at CONSTANT VELOCITY (constant speed in a straight line).
This is Newton's First Law.
UNBALANCED FORCES (resultant ≠ 0):
If resultant force ≠ 0, the object ACCELERATES (changes speed or direction).

Free Body Diagrams

A FREE BODY DIAGRAM shows all forces acting ON a single object as arrows:
Length ∝ magnitude of force.
Arrow points in direction of force.
Object represented as a box or dot at the centre.
EXAMPLES:
Stationary book on table:
↑ Normal contact force (upward)
↓ Weight (downward)
Resultant = 0 → balanced → stationary ✓
Car accelerating forward:
→ Driving force (forward, larger)
← Friction + air resistance (backward, smaller)
Resultant = driving force − resistance → forwards → accelerates ✓
Skydiver in free fall (before terminal velocity):
↓ Weight (downward)
↑ Air resistance (upward, smaller)
Resultant = weight − air resistance → downward → accelerates downward

Equilibrium and Resultant

An object is in EQUILIBRIUM when the resultant force is zero:
All forces balance — no net force.
Object stays still or moves at constant velocity.
When forces are UNBALANCED:
Resultant force in the direction of motion → object SPEEDS UP.
Resultant force opposite to direction of motion → object SLOWS DOWN.
Resultant force perpendicular to motion → object CHANGES DIRECTION.
SCALE DRAWING METHOD:
Draw vectors head-to-tail to scale.
Resultant = vector from tail of first to head of last.
Measure magnitude with ruler (× scale factor).
Measure direction with protractor.
TERMINAL VELOCITY:
As a falling object speeds up → air resistance increases.
Eventually air resistance = weight → resultant = 0 → constant velocity = terminal velocity.
For skydivers: terminal velocity ≈ 55 m/s (120 mph) before parachute.
⚠️ Common Mistake

A resultant force of ZERO does NOT mean the object is stationary — it means CONSTANT VELOCITY (which includes stationary). An object moving at constant speed in a straight line also has zero resultant force.

📌 Key Note

Resultant = single force with same effect as all forces combined. Balanced (zero resultant): stationary or constant velocity. Unbalanced: acceleration. Free body diagrams: arrows from object, length = magnitude. Terminal velocity: air resistance = weight → zero resultant → constant speed.

🎯 Matching Activity — Resultant Force and Motion

Match each situation to the correct description of the resultant force and motion. — drag the symbols on the right to match the component names on the left.

Resultant = 0, stationary
Drop here
Resultant = 0, moving
Drop here
Resultant forward
Drop here
Terminal velocity
Drop here
Car at constant speed on motorway — driving force equals resistance
Skydiver at constant speed — weight = air resistance, zero resultant
Book on table — weight balanced by normal contact force
Car accelerating — driving force greater than air resistance + friction
🎯 Test Yourself
Question 1 of 2
1. A car travels at constant speed along a straight road. What does this tell us about the forces on the car?
2. A skydiver jumps from a plane. Initially they accelerate. Later they reach terminal velocity. Why do they stop accelerating?
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