Forces: revision notes and practice

What you will learn

• Identify forces and calculate their resultant along a line.
• Relate resultant force to acceleration and distinguish weight from mass.
• Explain balanced forces, action–reaction pairs and force measurements.

Key rules

Combine forces along a line

Add forces in the same direction and subtract forces in opposite directions. State the direction of the resultant.

Newton’s second law

F = ma. F is resultant force in N, m is mass in kg, and a is acceleration in m/s². If resultant force is zero, velocity does not change.

Weight

Weight W = mg. Mass is in kg; weight is a force in N. Use the gravitational field strength g supplied, in N/kg.

Worked examples

Example 1: A 3 kg object has forces of 18 N right and 6 N left. Find its acceleration.

1. Resultant force = 18 − 6 = 12 N right.
2. a = F/m = 12 ÷ 3 = 4 m/s² right.

4 m/s² right

Example 2: Find the weight of a 4 kg object where g = 9.8 N/kg.

1. Use W = mg.
2. W = 4 × 9.8 = 39.2 N.

39.2 N

A practice question

An object of mass 11 kg accelerates at 5 m/s². Calculate the magnitude of its resultant force.

1. A force describes an interaction

Forces act when objects interact. Contact examples include friction, tension and a support force; non-contact examples include gravitational, magnetic and electrostatic forces. Every force has a magnitude and direction, so force is a vector. Use newtons, N, rather than kilograms when reporting it.

A force diagram shows forces acting on the object you have chosen. Arrows point in the force directions, and labels explain their causes. Longer arrows can represent larger forces. Keep forces on different objects in separate diagrams so you do not combine an object's weight with a force it exerts elsewhere.

2. Find the resultant before calculating acceleration

The resultant is one force with the same overall effect as the combined forces on an object. Along one line, add forces in the same direction and subtract opposing forces. If 18 N acts right and 7 N acts left, the resultant is 11 N right. Include direction in the final answer.

Choose right as positive and the calculation is +18 + (−7) = +11 N. Higher extension for AQA: non-parallel vectors need an appropriate scale diagram or resolution into perpendicular components. Do not simply subtract magnitudes when the forces act at different angles.

3. Balanced forces do not necessarily stop motion

Zero resultant force means no change in velocity. An object at rest stays at rest; an object already moving continues at constant velocity. A car travelling steadily on a straight road may have a driving force balancing resistive forces. The presence of motion does not prove there is an unbalanced forward force.

An unbalanced force can change speed or direction. In the ideal model, removing a driving force while resistance remains makes the object slow. If all forces balanced instead, it would keep its velocity. Higher extension for AQA: inertia describes the tendency to maintain rest or uniform motion.

4. Newton's second law links cause and change

For a constant-mass object, F = ma uses resultant force. With 12 N resultant and mass 3 kg, acceleration is 4 m/s² in the resultant direction. Rearrange to a = F/m or m = F/a. An individual pulling force is insufficient if friction or another force also matters.

For fixed mass, doubling resultant force doubles acceleration. For fixed resultant force, doubling mass halves acceleration. These comparisons hold when the other conditions are unchanged. A moving 5 kg trolley can have zero resultant force: its acceleration is zero even though its velocity need not be.

Fresultant = ma; F in N, m in kg, a in m/s²

5. Weight changes with gravitational field strength

Mass describes how much matter an object contains and is measured in kilograms. Weight is the gravitational force on it, measured in newtons. Calculate W = mg using the gravitational field strength g in N/kg. A 6 kg object weighs 58.8 N where g = 9.8 N/kg.

The same object's mass stays 6 kg in a different gravitational field, while its weight changes. A newton meter measures force; a balance is used to determine mass. Rearrange to m = W/g when weight is given. Do not put grams directly into an equation requiring kilograms.

W = mg; m = W/g

6. Action and reaction act on different objects

Newton's third law describes an interaction pair: forces of equal size and opposite direction act on the two interacting objects. A foot pushes backwards on the ground; the ground pushes forwards on the foot. These forces do not cancel on the person because they act on different objects.

For a book resting on a table, the upward support and downward weight balance on the book. They are not a third-law pair: both act on the book. The interaction partner of the table's upward force on the book is the book's downward force on the table.

7. Springs reveal force and extension

For a spring below its limit of proportionality, force is proportional to extension: F = ke. Extension is stretched length minus original length, not the full length. A 100 N/m spring extended by 0.04 m experiences 4 N. Convert centimetres to metres before substituting.

A force–extension graph is straight through the origin in this proportional region; its gradient is k when force is vertical. Past the limit of proportionality, the straight-line rule no longer applies. Permanent deformation is a separate issue: do not assume every non-linear extension automatically means the object cannot recover.

F = ke; k in N/m, extension e in m

8. Explain a practical and a falling object

In a teacher-supervised trolley investigation, vary resultant force while keeping total accelerated mass constant, then vary mass while keeping force constant. Use measured acceleration and repeated trials. Account for friction and include all moving masses in the model; the hanging mass alone is not automatically the entire accelerated mass.

A falling object initially has weight larger than upward air resistance, so it accelerates downwards. Resistance grows as speed rises. When resistance balances weight, the resultant and acceleration become zero: the object continues at terminal velocity. Moments, pressure and Higher momentum are further forces content beyond this introductory guide.

Check your understanding

How to earn the marks

• Use the resultant force and state its direction before applying F = ma.
• Distinguish zero velocity from zero acceleration; balanced forces allow steady motion.
• For third-law pairs, name both objects and the same interaction.
• For a spring, calculate extension from the original length and check the proportional region.

A common mistake

An object can move at constant velocity when forces are balanced. Zero resultant force does not necessarily mean zero velocity.

Course context and official specifications

This guide covers selected skills. Some extensions are Higher content; choose your official tier separately from practice difficulty in the app. These are original questions and explanations.

• AQA GCSE Physics — 4.5.1.3; 4.5.6.2.2

  The core calculations in this bank are selected separate Physics skills. Foundation and Higher content differ within these larger sections; this is not complete topic coverage.

• Edexcel GCSE Physics — 2.15–2.19; 9.1–9.5

  The core calculations in this bank are selected separate Physics skills. Foundation and Higher content differ within these larger sections; this is not complete topic coverage.

• OCR Gateway GCSE Physics A — P2.2i; P2.3; PM2.2i; PM2.3iii

  The core calculations in this bank are selected separate Physics skills. Foundation and Higher content differ within these larger sections; this is not complete topic coverage.

• OCR Twenty First Century GCSE Physics B — P4.1; P4.3.12

  The core calculations in this bank are selected separate Physics skills. Foundation and Higher content differ within these larger sections; this is not complete topic coverage.

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