Newton's three laws (mark-scheme form)
First Law: with zero resultant force an object stays at rest or moves at constant velocity. Second Law: a resultant force gives acceleration in its direction; ( = resultant force in N, = mass in kg, = acceleration in m/s²). Third Law: if A exerts a force on B, B exerts an equal, opposite force on A — same type, on two DIFFERENT objects. E.g. a resultant of 3600 N on 1800 kg gives m/s².
Weight is a force; mass is matter
Mass = the amount of matter; a scalar in kg; the same everywhere. Weight = the force of gravity on an object; a vector in N; , where = gravitational field strength (10 N/kg on Earth, 9.8 N/kg for precise work). It varies with location (less on the Moon). Trap: "how heavy it is" is not accepted — the mark-scheme form is "force due to gravity, in N". E.g. kg: N.
Free-body diagrams and resultant force
A free-body diagram shows ALL forces on ONE object as arrows, each (1) labelled with its name (weight, normal reaction, friction, tension, thrust, air resistance), (2) pointing correctly, (3) a length proportional to its size. Resultant force = the vector sum: add same-direction forces, subtract opposing ones. At rest or constant velocity the resultant = 0 (weight = normal reaction, thrust = drag); a non-zero resultant means the object accelerates.
Drawn from real examiner reports.
Third Law pair on the same object
Newton's Third Law pairs ALWAYS act on two DIFFERENT objects. "The forces on the car are equal and opposite" describes balanced forces (First Law), not the Third Law. If the ground pushes up on a foot, the pair is the foot pushing down on the ground — not the person's weight. Reciting "every action has an equal and opposite reaction" on its own earns only 1 mark.
June 2024 Paper 2PR Q5(a) — more than half of all candidates scored zero. The examiner noted that candidates who merely recited "every action has an equal and opposite reaction" only scored 1 mark; they needed to name the force direction explicitly AND confirm the forces act on two different objects.
Mass (kg) vs weight (N) confused
"The weight of the block is 5 kg" is wrong — 5 kg is the mass; its weight is N. If a quantity is in kg it is mass; if in N it is a force (weight, thrust, friction). The weight definition trap: "pull of gravity" or "heaviness" scores zero — the mark scheme needs "force due to gravity on an object, in N".
November 2024 Paper 2P Q3 — some candidates confused momentum, moment, force, and energy when asked to apply Newton's Third Law in a collision context, suggesting underlying confusion about what a force is.
Free-body arrows unlabelled or mis-sized
Every arrow needs a force-name label, and lengths must be proportional (weight = normal reaction on a flat surface). Draw each arrow from the correct point — weight from the centre; normal reaction and friction at the surface. Include air resistance on moving objects. Do NOT add the resultant as an extra arrow: it is the sum of the forces, not a force itself.
June 2024 Paper 2PR examiner's summary — examiners consistently note that candidates should take care when drawing diagrams to add labels and draw accurately, and should draw a labelled diagram to accompany descriptions wherever possible.
First Law balance vs Third Law pair
Balanced forces (First Law) act on the SAME object in opposite directions, giving zero resultant — e.g. a book's weight and the table's normal reaction, both on the book. A Third Law pair acts on TWO DIFFERENT objects — e.g. the book's weight (Earth on book) and the book's gravitational pull on the Earth. Weight and normal reaction are never a Third Law pair.
Using thrust alone in F = ma
When thrust and resistance are both given, the in is the resultant force — subtract first. E.g. thrust 1800 N, resistance 600 N, mass 300 kg gives a resultant of 1200 N, so m/s². Using 1800 N alone gives 6 m/s², which is wrong.
Third Law: name the type and both objects
A full Third Law answer has four elements: equal magnitude; opposite direction; the same type of force; acting on two DIFFERENT objects. Template: "the force of A on B is equal and opposite to the force of B on A." Never stop at "equal and opposite".
Find the resultant force before F = ma
Before using , combine the forces into one resultant — add those along the motion, subtract those opposing it. The resultant, not the driving force, goes into . Quoting the thrust alone is a frequent, avoidable error.
Explain acceleration with the F = ma scaffold
For "explain why it accelerates": state the resultant force (thrust − drag), say a non-zero resultant causes acceleration (Second Law), then compute with if numbers are given. For terminal velocity, the resultant falls to zero, so the acceleration falls to zero.
| Quantity | Symbol | Formula | Unit |
|---|---|---|---|
| Resultant force | newton, N | ||
| Weight | newton, N | ||
| Gravitational field strength | — | N/kg (= m/s²) |
Where = resultant force (N), = mass (kg), = acceleration (m/s²), = weight (N), = gravitational field strength (10 N/kg on Earth for estimates; 9.8 m/s² for precise calculations).
The three laws at a glance:
| Law | Statement | Key word |
|---|---|---|
| First | Zero resultant force → object stays at rest or moves at constant velocity | Resultant = 0 |
| Second | Non-zero resultant force → acceleration; | Cause = change in motion |
| Third | Force of A on B = equal magnitude, opposite direction to force of B on A | Different objects |
State Newton's First Law of motion.
A box of cereal has a mass of 0.75 kg.
Calculate the weight of the box on the surface of the Earth.
(Gravitational field strength on Earth N/kg)
Give the unit of your answer.
