Newton's laws (P2.2)

Gateway A's flagship physics topic. Expect at least one calculation using F = ma, a free-body diagram, and a 6-mark question on safety / stopping distances or momentum.

Newton's three laws

Newton's First Law — inertia

A body continues at rest, or moves at a constant velocity in a straight line, unless acted on by a resultant force.

In other words: if forces are balanced (resultant force = 0), velocity is constant. The body could be stationary or moving at the same speed in the same direction.

Example: a parachutist at terminal velocity. Weight downward = drag upward → resultant = 0 → constant velocity.

Newton's Second Law — F = ma

F (N) = m (kg) × a (m/s²)

The resultant force on a body is proportional to its mass and to its acceleration. Always use resultant force in this equation — not the size of any one force.

Inertial mass: a measure of how difficult it is to change a body's velocity. Higher mass → harder to accelerate.

Newton's Third Law — action–reaction pairs

For every action there is an equal and opposite reaction.

Important: the action and reaction forces act on different objects. So they don't cancel each other out on a single body.

Example: a book on a table. The book pushes down on the table (action); the table pushes up on the book (reaction). The pair are equal in size, opposite in direction, on different bodies.

Resultant force and balanced forces

Forces are vectors — they have direction. To find a resultant on a single line:

• If forces in the same direction: add.
• If forces in opposite directions: subtract.

If the resultant = 0, forces are balanced. The object is either stationary or moving at constant velocity.

If the resultant ≠ 0, forces are unbalanced. The object accelerates in the direction of the resultant.

Free-body diagrams

Draw the body as a dot or rectangle. Draw arrows for every force acting on the body — never forces it exerts on others. Label every force with name and (if known) magnitude.

Common labels:

• Weight (W or mg) — always downward.
• Normal contact force (N or R) — perpendicular to surface.
• Friction (F or f) — opposes motion, parallel to surface.
• Drag (air resistance) — opposes motion through fluid.
• Thrust / push / tension — applied force.

Worked F = ma examples

Example 1. A 1,200 kg car accelerates at 2.5 m/s². Find the resultant force.

• F = m × a = 1,200 × 2.5 = 3,000 N.

Example 2. A 70 kg cyclist experiences a forward force of 200 N from pedalling and a 60 N backward drag/friction.

• Resultant = 200 − 60 = 140 N.
• a = F / m = 140 / 70 = 2 m/s².

Example 3. A 60 kg lift descends at constant velocity. The cable tension is 588 N. What is the cable tension if the lift then accelerates downward at 1.5 m/s²?

• Constant velocity: T = mg = 60 × 9.8 ≈ 588 N. ✓
• Accelerating down at 1.5 m/s²: resultant force on lift is downward, magnitude m × a = 60 × 1.5 = 90 N.
• Resultant = mg − T (downward), so T = mg − ma = 588 − 90 = 498 N.

Stopping distance

stopping distance = thinking distance + braking distance

• Thinking distance is the distance travelled during the driver's reaction time. Increased by tiredness, alcohol, drugs, distractions.
• Braking distance is the distance after the brakes are applied. Increased by greater speed, worn tyres, wet/icy roads, worn brakes.

Doubling the speed roughly quadruples the braking distance (because KE ∝ v²).

Common Gateway-paper mistakes

1. Using a single force in F = ma instead of the resultant.
2. Forgetting that constant velocity ≠ zero force — it means zero RESULTANT force.
3. Mixing up Newton's pair: writing that weight and normal contact force are a Newton-third-law pair (they are NOT — both act on the same body).
4. Confusing mass (kg) with weight (N): W = mg.
5. Forgetting to convert g to kg in F = ma calculations.