Forces, Elasticity and Newton's Laws

Q: Can I use total spring length in Hooke's Law calculations?

No. Hooke's Law uses extension, which is the difference between the stretched length of the spring and its original unstretched length, not the total length.

Q: Do Newton's Third Law force pairs cancel each other out?

No. Third law pairs act on different objects, so they never cancel. Cancelling forces act on the same object and are balanced, per Newton's First Law.

CIE IGCSE Physics· 1.5.1· 45 min read

1. Core: Types of Force and Weight Calculation★★☆☆☆⏱ 10 min

📘 Definition

Force

A push or pull that acts on an object due to interaction with another object, measured in newtons (N). Forces are either contact or non-contact.

Contact forces: Act only when objects touch: friction, air resistance, normal contact force, tension
Non-contact forces: Act at a distance: gravitational force, electrostatic force, magnetic force

📘 Definition

Mass and Weight

Mass is the amount of matter in an object (unit: kg, scalar, constant everywhere). Weight is the gravitational force acting on an object's mass (unit: N, vector, varies with gravitational field strength). The relationship is given by $W = m \times g$ .

Example:

A 5kg object has mass 5kg on Earth and the Moon, but weight 49N on Earth and 8N on the Moon.

📐 Worked Example

Calculate the weight of a 7.2 kg suitcase on Earth, where $g = 9.8 N / k g$ .

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Step 1: List known values: $m = 7.2 k g$ , $g = 9.8 N / k g$
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Step 2: Substitute into the weight formula:
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$W = m \times g = 7.2 \times 9.8 = 70.56 N$

Exam tip:

Use $g = 9.8 N / k g$ for calculations unless the question explicitly gives a different value.

2. Core: Elasticity and Load-Extension Graphs★★☆☆☆⏱ 10 min

📘 Definition

Elastic deformation

A change in the size or shape of an object caused by a force. A deformation is elastic if the object returns to its original size and shape once the force is removed, as happens with a spring stretched by small loads.

When you hang masses (loads) from a spring and measure how far it stretches (its extension), you can plot a load-extension graph with load on one axis and extension on the other. At Core level you need to be able to sketch, plot and interpret these graphs, but you are not required to use an equation.

📐 Worked Example

A student hangs increasing loads on a spring and records its extension each time. Describe qualitatively what the load-extension graph looks like and what it tells you about the spring.

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Step 1: For small loads the graph is a straight line through the origin, showing that equal increases in load give equal increases in extension.
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Step 2: For larger loads the line begins to curve, showing that the same increase in load now produces a larger increase in extension.
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Step 3: Interpret the straight part as the region where the spring stretches steadily, and the curved part as the region where the spring stretches more easily and may not return to its original length.

Exam tip:

On a load-extension graph, a straight line through the origin means extension increases in equal steps for equal increases in load; when the line curves, equal loads no longer give equal extensions.

3. Core: Newton's First and Third Laws of Motion★★☆☆☆⏱ 10 min

📘 Definition

Newton's First Law of Motion

An object remains at rest, or moves at constant speed in a straight line, unless acted on by a non-zero resultant force.

Example:

A book resting on a table stays still because upward normal contact force balances downward weight, so resultant force = 0.

📘 Definition

Newton's Third Law of Motion

When two objects interact, the forces they exert on each other are equal in size, opposite in direction, and act on different objects.

Example:

When you push a wall with a force of 20N, the wall pushes back on you with a 20N force in the opposite direction.

📐 Worked Example

Use Newton's First Law to explain why a passenger falls backward when a stationary bus suddenly accelerates forward.

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Step 1: Before acceleration, the passenger is stationary relative to the bus.
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Step 2: When the bus accelerates, the passenger's feet are pulled forward by friction with the bus floor, but their upper body has no resultant force acting on it immediately, so it stays stationary relative to the ground, making the passenger fall backward.

4. Extended: Newton's Second Law and Resultant Forces★★★★☆Extended only⏱ 15 min

📘 Definition

Newton's Second Law of Motion

$F_{r es u l t an t} = m \times a$

The resultant force acting on an object equals the object's mass multiplied by its acceleration, in the direction of the resultant force. $F$ = resultant force (N), $m$ = mass (kg), $a$ = acceleration (m/s²)

The resultant force is the single force that has the same effect as all individual forces acting on an object. Calculate it by adding forces acting in the same direction, and subtracting forces acting in opposite directions.

📐 Worked Example

A 3kg cart is pushed forward with a force of 15N, and experiences a friction force of 6N acting backward. Calculate the acceleration of the cart.

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Step 1: Calculate resultant force: $F = 15 N - 6 N = 9 N$ forward
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Step 2: Rearrange Newton's Second Law to solve for acceleration:
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$a = \frac{F}{m} = \frac{9}{3} = 3 m/s^2 \text{ forward}$

Exam tip:

Always state the direction of resultant force and acceleration in Extended responses to earn full marks.

5. Extended: Hooke's Law and the Spring Constant★★★★☆Extended only⏱ 12 min

📘 Definition

Hooke's Law

$F = k x$

The extension of an elastic object is directly proportional to the force applied, provided the limit of proportionality is not exceeded. $F$ = applied force (N), $k$ = spring constant (N/m), $x$ = extension (m).

Example:

A spring with $k = 100 N / m$ extends 0.01 m when 1 N of force is applied.

📘 Definition

Spring constant

$k = \frac{F}{x}$

The force per unit extension of a spring, measured in newtons per metre (N/m). A stiffer spring has a larger spring constant.

📐 Worked Example

A spring has an original length of 0.1 m. When a 6 N weight is hung from it, it stretches to a total length of 0.13 m. Calculate its spring constant, assuming the limit of proportionality is not reached.

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Step 1: Calculate extension: $x = 0.13 m - 0.1 m = 0.03 m$
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Step 2: Rearrange Hooke's Law to solve for $k$ :
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$k = \frac{F}{x} = \frac{6}{0.03} = 200 N/m$

Exam tip:

If a force-extension graph curves upward at higher forces, the limit of proportionality has been passed, so $F = k x$ no longer applies for those values.

6. Common Pitfalls

Wrong move:

Using total spring length instead of extension in Hooke's Law calculations

Why:

Hooke's Law uses the increase in length of the spring, not its total stretched length, so using total length gives an incorrect value for $x$ .

Correct move:

Subtract the original unstretched length of the spring from its stretched length to calculate extension before using $F = k x$ .

Wrong move:

Confusing mass and weight, using kg as the unit for weight

Why:

Mass is measured in kg, while weight is a force measured in N. Using the wrong unit leads to lost marks and incorrect force calculations.

Correct move:

Use $W = m g$ to convert mass in kg to weight in N whenever force calculations are required.

Wrong move:

Stating Newton's Third Law force pairs cancel each other out

Why:

Third law pairs act on two different interacting objects, so they never cancel. Cancelling balanced forces act on the same object.

Correct move:

When identifying Third Law pairs, confirm each force acts on a separate object, e.g. force of Earth on you, force of you on Earth.

Wrong move:

Applying Hooke's Law beyond the limit of proportionality

Why:

Once the limit of proportionality is exceeded, extension is no longer proportional to applied force, so $F = k x$ is no longer valid.

Correct move:

Only use $F = k x$ if the question confirms the limit of proportionality is not reached, or if the force-extension graph is linear.

Wrong move:

Assuming a positive resultant force acts on an object moving at constant speed

Why:

Newton's First Law states constant speed means there is no resultant force acting on the object, not a positive force.

Correct move:

If an object is stationary or moving at constant velocity, all forces acting on it are balanced, so resultant force = 0.

7. Quick Reference Cheatsheet

Concept	Formula	Key Rule	Tier
Weight	$W = m g$	Use $g = 9.8 N / k g$ unless stated otherwise	Core
Hooke's Law	$F = k x$	$x$ = extension, not total spring length	Extended
Newton's First Law		Zero resultant force = stationary / constant speed	Core
Newton's Third Law		Equal, opposite forces acting on different objects	Core
Newton's Second Law	$F = ma$	$F$ = resultant force, state direction of acceleration	Extended

8. Frequently Asked

What is the difference between mass and weight?

Mass is the amount of matter in an object, measured in kg, and is constant everywhere. Weight is the gravitational force acting on an object's mass, measured in N, and changes with gravitational field strength, e.g. on the Moon.

Can I use total spring length in Hooke's Law calculations?

No. Hooke's Law uses extension, which is the difference between the stretched length of the spring and its original unstretched length, not the total length.

When is Hooke's Law no longer valid?

Hooke's Law is invalid once the spring exceeds its limit of proportionality, after which extension is no longer proportional to applied force.

Do Newton's Third Law force pairs cancel each other out?

No. Third law pairs act on different objects, so they never cancel. Cancelling forces act on the same object and are balanced, per Newton's First Law.

Going deeper

official_document2026-2028 CIE IGCSE Physics 0625 SyllabusRefer to section 1.5 for forces content
practice_resourceStructured Forces Practice QuestionsNo MCQs, aligned to Core and Extended exam requirements

What's Next

Now that you have mastered forces, elasticity and Newton's laws, you are ready to apply these concepts to more advanced motion and energy topics in CIE IGCSE Physics 0625. Next, you will learn to analyse force-extension graphs to identify the limit of proportionality, and calculate work done by forces as part of the energy unit. You will also use Newton's laws to interpret motion graphs and solve real-world scenarios involving friction and air resistance, which are frequently tested in both Extended MCQ and theory papers. Practice structured response questions to build your ability to explain laws and calculations clearly, as this is where most marks are awarded in theory exams.