Forces and Newton's Laws

Scalar and Vector Quantities

Scalar quantities have magnitude (size) only.

• Examples: speed, distance, mass, temperature, time, energy

Vector quantities have both magnitude and direction.

• Examples: velocity, displacement, force, acceleration, momentum, weight

This distinction matters because when adding vectors, direction must be considered.

Types of Force

Contact forces — only act when objects are touching:

• Friction
• Normal contact force (reaction force)
• Tension
• Air resistance (drag)
• Upthrust (buoyancy)

Non-contact forces — act at a distance (through fields):

• Gravitational force (gravity)
• Electrostatic force (between charges)
• Magnetic force

Weight and Mass

Mass (kg) — a measure of the amount of matter in an object. Scalar. Does not change with location.

Weight (N) — the gravitational force on an object. Vector. Depends on gravitational field strength (g).

$$W = mg$$

Where:

• W = weight (N)
• m = mass (kg)
• g = gravitational field strength (N/kg); on Earth's surface g ≈ 9.8 N/kg (WJEC uses 9.8 or 10)

Example: A 60 kg student. Weight = 60 × 9.8 = 588 N (on Earth).

Resultant Force

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

Calculating resultant force:

• Forces in the same direction: add them
• Forces in opposite directions: subtract smaller from larger; direction = direction of larger force
• Forces at right angles: use Pythagoras' theorem (HT) or scale drawing

Example: A car experiences 3000 N driving force and 1800 N friction. Resultant = 3000 − 1800 = 1200 N forward

Newton's Three Laws of Motion

Newton's First Law

"An object remains at rest or moves at constant velocity unless acted upon by a resultant force."

• If resultant force = 0: object is in equilibrium (stationary or constant velocity)
• A moving object at constant velocity has balanced forces (e.g., skydiver at terminal velocity)

Newton's Second Law

"The acceleration of an object is directly proportional to the resultant force and inversely proportional to its mass."

$$F = ma$$

Where:

• F = resultant force (N)
• m = mass (kg)
• a = acceleration (m/s²)

Example: A resultant force of 1500 N acts on a 500 kg car. a = F/m = 1500/500 = 3 m/s²

Newton's Third Law

"For every action, there is an equal and opposite reaction."

When object A exerts a force on object B, object B exerts an equal and opposite force on A.

• Same type of force
• Equal magnitude
• Opposite direction
• Acting on different objects

Example: A rocket pushes exhaust gases downward (action) → gases push rocket upward (reaction).

Free Body Diagrams

A free body diagram shows all forces acting ON an object (arrows showing direction and comparative magnitude). Used to identify the resultant force.

WJEC tip: Draw arrows proportional to force size; label each force (weight, normal contact force, friction, thrust, drag, etc.).