Contact and non-contact forces | GCSE Physics Revision

Hooke's Law: Force and Extension

Hooke's Law states that the force applied to a spring is directly proportional to its extension, expressed as F = ke, where F is force (N), k is the spring constant (N/m), and e is the extension (m).
The spring constant k is unique to each object and measures its stiffness — a lower k means the object is more elastic and easier to stretch, while a higher k means it is stiffer and harder to stretch.
Extension is calculated by subtracting the natural (unstretched) length from the stretched length of the spring.

1. Hooke's Law: Force and ExtensionAQA

Notes

Hooke's Law states that the force applied to a spring is directly proportional to its extension, expressed as F = ke, where F is force (N), k is the spring constant (N/m), and e is the extension (m).
The spring constant k is unique to each object and measures its stiffness — a lower k means the object is more elastic and easier to stretch, while a higher k means it is stiffer and harder to stretch.
Extension is calculated by subtracting the natural (unstretched) length from the stretched length of the spring.

Elastic Potential Energy

Elastic potential energy is the energy stored in an object when it is stretched or compressed, calculated using KaTeX parse error: Unexpected character: ' ' at position
7: E_e =

̲rac{1}{2}ke^2, where k is the spring constant and e is the extension.

It is only the extension e that is squared in the equation, not the entire expression.
When a spring is stretched, energy is transferred into its elastic potential energy store, and when released, this energy converts to another form such as kinetic energy.

3. ̲rac{1}{2}ke^2, where k is the spring constant and e is the extension.AQA

Notes

It is only the extension e that is squared in the equation, not the entire expression.
When a spring is stretched, energy is transferred into its elastic potential energy store, and when released, this energy converts to another form such as kinetic energy.

Worked Example: Finding the Spring Constant

To find the spring constant, first calculate the extension by subtracting the natural length from the stretched length (e.g. 0.8 − 0.6 = 0.2 m).
Rearranging Hooke's Law gives KaTeX parse error: Unexpected character: ' ' at position 5: k =

̲rac{F}{e}, so substituting F = 14 N and e = 0.2 m yields

k = 70 N/m.

Worked Example: Calculating Elastic Potential Energy

Using the values from the previous example (k = 70 N/m, e = 0.2 m), the elastic potential energy is calculated as KaTeX parse error: Unexpected character: ' ' at position 7: E_e =

̲rac{1}{2} \time….

Always ensure the extension is squared before multiplying by the other values to avoid calculation errors.

Force-Extension Graphs

On a force-extension graph, the gradient of the straight (linear) section of the line is equal to the spring constant k .
The area under the force-extension graph represents the energy transferred to the spring, which equals the elastic potential energy stored.
The graph is only linear (straight) while the spring obeys Hooke's Law; beyond this point the relationship breaks down.

8. Force-Extension GraphsAQA

Notes

On a force-extension graph, the gradient of the straight (linear) section of the line is equal to the spring constant k .
The area under the force-extension graph represents the energy transferred to the spring, which equals the elastic potential energy stored.
The graph is only linear (straight) while the spring obeys Hooke's Law; beyond this point the relationship breaks down.

The Elastic Limit and Hooke's Law

The elastic limit (also called the limit of proportionality) is the point beyond which a material no longer obeys Hooke's Law and the force-extension relationship is no longer linear.
Beyond the elastic limit, the spring may be permanently deformed and will not return to its original shape when the force is removed.

9. The Elastic Limit and Hooke's LawAQA

Notes

The elastic limit (also called the limit of proportionality) is the point beyond which a material no longer obeys Hooke's Law and the force-extension relationship is no longer linear.
Beyond the elastic limit, the spring may be permanently deformed and will not return to its original shape when the force is removed.

and Pull

What Is a Force?
A force is a push or a pull on an object that always arises from an interaction between two objects.
Forces have both a size (measured in Newtons) and a direction, making them vectors, which is why they are always represented as arrows.
Every force arrow carries a two-part label: what the force is and which object is exerting it (e.g. the pull of the Earth on the mug).

10. and PullAQA

Notes

What Is a Force?
A force is a push or a pull on an object that always arises from an interaction between two objects.
Forces have both a size (measured in Newtons) and a direction, making them vectors, which is why they are always represented as arrows.
Every force arrow carries a two-part label: what the force is and which object is exerting it (e.g. the pull of the Earth on the mug).

Contact Forces

A contact force only acts when two objects are touching — if a gap opens between them, the force disappears.
Examples of contact forces include friction, air resistance, tension in a rope or spring, and the normal contact force.
The normal contact force is the push of a surface on an object, and it always acts at right angles (perpendicular) to that surface.
Even a solid wooden table dents by a tiny, invisible amount when a book rests on it, and that dent is what produces the normal contact force pushing the book upwards.

11. Contact ForcesAQA

Notes

A contact force only acts when two objects are touching — if a gap opens between them, the force disappears.
Examples of contact forces include friction, air resistance, tension in a rope or spring, and the normal contact force.
The normal contact force is the push of a surface on an object, and it always acts at right angles (perpendicular) to that surface.
Even a solid wooden table dents by a tiny, invisible amount when a book rests on it, and that dent is what produces the normal contact force pushing the book upwards.

Non-Contact Forces

A non-contact force still acts across a gap between two objects, so the objects do not need to be touching.
The three non-contact forces at GCSE are gravity, the electrostatic force (between charged objects), and magnetism.
Each non-contact force acts through a field — a region of space where an object experiences a force without being touched.
A fridge magnet is a classic example: even with a small gap between the magnet and the door, the magnetic pull still acts, confirming it is a non-contact force.

12. Non-Contact ForcesAQA

Notes

A non-contact force still acts across a gap between two objects, so the objects do not need to be touching.
The three non-contact forces at GCSE are gravity, the electrostatic force (between charged objects), and magnetism.
Each non-contact force acts through a field — a region of space where an object experiences a force without being touched.
A fridge magnet is a classic example: even with a small gap between the magnet and the door, the magnetic pull still acts, confirming it is a non-contact force.

The Gap Test

The gap test is the key method for deciding whether a force is contact or non-contact: imagine a small gap between the two objects and ask whether the force would vanish.
If the force disappears when the gap opens, it is a contact force; if it still acts across the gap, it is a non-contact force.
A common exam mistake is classifying non-contact forces as contact forces (e.g. listing gravity when asked for a contact force on a cyclist), so always apply the gap test before writing your answer.

13. The Gap TestAQA

Notes

The gap test is the key method for deciding whether a force is contact or non-contact: imagine a small gap between the two objects and ask whether the force would vanish.
If the force disappears when the gap opens, it is a contact force; if it still acts across the gap, it is a non-contact force.
A common exam mistake is classifying non-contact forces as contact forces (e.g. listing gravity when asked for a contact force on a cyclist), so always apply the gap test before writing your answer.

Interaction Pairs (Newton's Third Law Pairs)

Every interaction between two objects produces exactly two forces — one on each object — never just one.
The two forces in an interaction pair are always equal in size, opposite in direction, and act on two different objects.
To find the partner force, swap the two object names in the sentence: the force of A on B pairs with the force of B on A.
A useful technique is to give each object its own column and file each force under the object it acts on — a genuine interaction pair always straddles both columns.

14. Interaction Pairs (Newton's Third Law Pairs)AQA

Notes

Every interaction between two objects produces exactly two forces — one on each object — never just one.
The two forces in an interaction pair are always equal in size, opposite in direction, and act on two different objects.
To find the partner force, swap the two object names in the sentence: the force of A on B pairs with the force of B on A.
A useful technique is to give each object its own column and file each force under the object it acts on — a genuine interaction pair always straddles both columns.

Common Exam Mistakes with Interaction Pairs

A common error is pairing the weight of an object with the normal contact force acting on it — both forces act on the same object, so they cannot be an interaction pair.
The true partner of the Earth's pull on a mug (its weight) is the pull of the mug on the Earth, which acts upwards on the Earth.
The true partner of the shelf's push on the mug is the push of the mug on the shelf, which acts on the shelf.
Examiner reports note that very few candidates could correctly name the missing force in an interaction pair, so practising the sentence-swap method is essential.

15. Common Exam Mistakes with Interaction PairsAQA

Notes

A common error is pairing the weight of an object with the normal contact force acting on it — both forces act on the same object, so they cannot be an interaction pair.
The true partner of the Earth's pull on a mug (its weight) is the pull of the mug on the Earth, which acts upwards on the Earth.
The true partner of the shelf's push on the mug is the push of the mug on the shelf, which acts on the shelf.
Examiner reports note that very few candidates could correctly name the missing force in an interaction pair, so practising the sentence-swap method is essential.

Why Interaction Pairs Never Cancel Out

Interaction pairs cannot cancel each other out because the two forces act on different objects, so they never appear in the same object's force column.
When you stand still, the Earth pulls you down with 600 N and you pull the Earth up with 600 N, but these forces act on different objects so there is no contest between them.
You remain stationary because the floor pushes up on you with a normal contact force — this balances your weight, both forces acting on you.

16. Why Interaction Pairs Never Cancel OutAQA

Notes

Interaction pairs cannot cancel each other out because the two forces act on different objects, so they never appear in the same object's force column.
When you stand still, the Earth pulls you down with 600 N and you pull the Earth up with 600 N, but these forces act on different objects so there is no contest between them.
You remain stationary because the floor pushes up on you with a normal contact force — this balances your weight, both forces acting on you.

Identifying Interaction Pairs: Worked Example

For a swimmer pushing off a pool wall, the genuine interaction pair is the wall's push on the swimmer and the swimmer's push on the wall — the same two objects with forces swapped.
The other suggested pairings (e.g. the swimmer's weight with the water's upthrust) fail because both forces in each case act on the same object (the swimmer), not on two different objects.
Examiner reports show that just over half of candidates could correctly identify an interaction pair in a multiple-choice question, so checking that each force acts on a different object is the key habit to develop.

17. Identifying Interaction Pairs: Worked ExampleAQA

Notes

For a swimmer pushing off a pool wall, the genuine interaction pair is the wall's push on the swimmer and the swimmer's push on the wall — the same two objects with forces swapped.
The other suggested pairings (e.g. the swimmer's weight with the water's upthrust) fail because both forces in each case act on the same object (the swimmer), not on two different objects.
Examiner reports show that just over half of candidates could correctly identify an interaction pair in a multiple-choice question, so checking that each force acts on a different object is the key habit to develop.

Forces on a Moving Cyclist

A cyclist freewheeling downhill experiences four forces: weight (non-contact), the push of the road (contact), air resistance (contact), and friction from the road on the tyres (contact).
When the cyclist brakes, an additional contact force appears: friction between the brake blocks and the wheel rims.
Examiner reports show that only around 20% of students could correctly name an additional contact force when braking, with many incorrectly giving non-contact forces instead.

18. Forces on a Moving CyclistAQA

Notes

A cyclist freewheeling downhill experiences four forces: weight (non-contact), the push of the road (contact), air resistance (contact), and friction from the road on the tyres (contact).
When the cyclist brakes, an additional contact force appears: friction between the brake blocks and the wheel rims.
Examiner reports show that only around 20% of students could correctly name an additional contact force when braking, with many incorrectly giving non-contact forces instead.

Electrostatic Force and Tension: Quick Examples

A rubbed balloon clinging to a wall demonstrates the electrostatic non-contact force — it still attracts the wall when held slightly away, confirming no touch is needed.
When a tow rope pulls a car, the partner of the rope's pull on the car is the pull of the car on the rope, and this partner force acts on the rope, not on the car.
Tension in a rope is a contact force because it would vanish if the rope were cut and the objects separated.

19. Electrostatic Force and Tension: Quick ExamplesAQA

Notes

A rubbed balloon clinging to a wall demonstrates the electrostatic non-contact force — it still attracts the wall when held slightly away, confirming no touch is needed.
When a tow rope pulls a car, the partner of the rope's pull on the car is the pull of the car on the rope, and this partner force acts on the rope, not on the car.
Tension in a rope is a contact force because it would vanish if the rope were cut and the objects separated.

AQA student objectives

All · Most · Some

Key knowledge

Hooke's Law: Force and Extension

Elastic Potential Energy

̲rac{1}{2}ke^2, where k is the spring constant and e is the extension.

Worked Example: Finding the Spring Constant

̲rac{F}{e}, so substituting F = 14 N and e = 0.2 m yields

Worked Example: Calculating Elastic Potential Energy

̲rac{1}{2} \time….

Force-Extension Graphs

The Elastic Limit and Hooke's Law

and Pull

Contact Forces

Non-Contact Forces

The Gap Test

Interaction Pairs (Newton's Third Law Pairs)

Common Exam Mistakes with Interaction Pairs

Why Interaction Pairs Never Cancel Out

Identifying Interaction Pairs: Worked Example

Forces on a Moving Cyclist

Electrostatic Force and Tension: Quick Examples