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1.4 Elasticity

PHYSICS • Form 5 • Chapter 1: Force and Motion II

1.4 Elasticity

Learn how elastic materials return to their original shape and size, how force affects the extension of a spring, and how elastic potential energy is stored in a stretched spring.

Learning Objectives

  • State the meaning of elasticity.
  • Explain the relationship between force and extension of a spring.
  • Use Hooke’s law, F = kx.
  • Determine spring constant and elastic potential energy.
  • Compare spring arrangements in series and in parallel.

How a Spring Stretches and Stores Energy

See how force changes the extension of a spring, how Hooke’s law is used, and how the graph shows spring constant and elastic potential energy.

Elasticity infographic showing extension of a spring, Hooke's law, force against extension graph, spring constant and elastic potential energy

Stretch the Spring

Move the force slider. Compare the spring and graph side by side.

Spring setup Original length l₀ Extended length l 10 N Extension x F
F against x graph F / Nx / m current point area = Eₚ Gradient = spring constant, k
10 N
small forcelarge force

Fixed values: k = 100 N m⁻¹, l₀ = 0.20 m.

Original length, l₀0.20 m
Extended length, l0.30 m
Extension, x0.10 m
 

Safe elastic region

More force makes the spring extend more. The spring can still return to its original length.

FormulaF = kx
Eₚ0.50 J
x = l − l₀0.10 m

Short Explanation

What is Elasticity?

Elasticity is the property of a material that enables an object to return to its original shape and size after the force applied on it is removed.

Elastic and Non-Elastic Examples

A spring, sponge and elastic cord can return to their original shape or length. Plasticine changes shape but does not return to its original shape.

Hooke’s Law

The extension of a spring is directly proportional to the force applied on the spring, provided that the elastic limit is not exceeded. F = kx

Elastic Potential Energy

Elastic potential energy is the work done to stretch the spring. It is equal to the area under the graph of force against extension.

Factor Change in Factor Effect on Spring Constant
Material of spring Different material Changes according to the type of material
Length of spring Shorter spring Higher spring constant
Length of spring Longer spring Lower spring constant
Diameter of spring Smaller diameter Higher spring constant
Diameter of spring Larger diameter Lower spring constant
Thickness of spring wire Wire with smaller diameter Lower spring constant
Thickness of spring wire Wire with larger diameter Higher spring constant

Try to Answer First

Answer in your mind, then press “Check Answer”.

1

What is the meaning of elasticity?

Check Answer
Answer: Elasticity is the property of a material that enables an object to return to its original shape and size after the force applied on it is removed.
2

State Hooke’s law.

Check Answer
Answer: The extension of a spring is directly proportional to the force applied on the spring, provided that the elastic limit is not exceeded.
3

A spring extends by 6 mm when stretched by a force of 12 N. Calculate the spring constant.

Check Answer
Answer: \(k = \dfrac{F}{x}\), so \(k = \dfrac{12}{6} = 2\ \mathrm{N\,mm^{-1}}\).

Common Mistakes

  • !Thinking that all materials are elastic.
  • !Saying that plasticine is elastic because its shape can be changed.
  • !Mixing up original length, extended length and extension.
  • !Forgetting that the gradient of the F against x graph gives the spring constant.
  • !Thinking that elastic potential energy is the gradient of the graph instead of the area under the graph.

Concept Misunderstandings

Misunderstanding

Any object that changes shape is elastic.

Correct Concept

An object is elastic only if it returns to its original shape and size after the force is removed.

Misunderstanding

Spring constant is the area under the graph.

Correct Concept

Spring constant is the gradient of the graph of force, F, against extension, x.

Misunderstanding

Elastic potential energy is the gradient of the graph.

Correct Concept

Elastic potential energy is the area under the graph of force, F, against extension, x.

Summary

  • Elasticity is the ability of a material to return to its original shape and size after the force is removed.
  • Hooke’s law states that extension is directly proportional to force if the elastic limit is not exceeded.
  • The spring constant can be calculated using \(k = \dfrac{F}{x}\) or from the gradient of the graph of F against x.
  • Elastic potential energy is the area under the graph of F against x.
  • The spring constant is affected by material, spring length, spring diameter and thickness of spring wire.

Short Activity

Objective: Identify elasticity, Hooke’s law, spring constant and elastic potential energy.

A. Objective Quiz

1 Which material does not return to its original shape after the force is removed?

2 Hooke’s law can be written as:

B. Fill in the Blanks

3 The extension of a spring is the increase in of the spring.

4 Elastic potential energy is equal to the under the graph of F against x.

C. Matching / Drag and Drop

Drag each term to the correct meaning. If using a phone, tap the answer first, then tap the matching box.

Choices
Hooke’s law
Elasticity
Spring constant
Elastic potential energy
Meanings
1 Returns to original shape and size
2 Extension is directly proportional to force
3 Gradient of graph of F against x
4 Area under the graph of F against x
 

Keywords

Elasticity Force Spring Extension Original length Hooke’s law Spring constant Elastic potential energy Elastic limit Series arrangement Parallel arrangement Plasticine
The views expressed in the notes here are those of the contributor and don’t necessarily represent the views of Pandai.

1.4 Elasticity

PHYSICS • Form 5 • Chapter 1: Force and Motion II

1.4 Elasticity

Learn how elastic materials return to their original shape and size, how force affects the extension of a spring, and how elastic potential energy is stored in a stretched spring.

Learning Objectives

  • State the meaning of elasticity.
  • Explain the relationship between force and extension of a spring.
  • Use Hooke’s law, F = kx.
  • Determine spring constant and elastic potential energy.
  • Compare spring arrangements in series and in parallel.

How a Spring Stretches and Stores Energy

See how force changes the extension of a spring, how Hooke’s law is used, and how the graph shows spring constant and elastic potential energy.

Elasticity infographic showing extension of a spring, Hooke's law, force against extension graph, spring constant and elastic potential energy

Stretch the Spring

Move the force slider. Compare the spring and graph side by side.

Spring setup Original length l₀ Extended length l 10 N Extension x F
F against x graph F / Nx / m current point area = Eₚ Gradient = spring constant, k
10 N
small forcelarge force

Fixed values: k = 100 N m⁻¹, l₀ = 0.20 m.

Original length, l₀0.20 m
Extended length, l0.30 m
Extension, x0.10 m
 

Safe elastic region

More force makes the spring extend more. The spring can still return to its original length.

FormulaF = kx
Eₚ0.50 J
x = l − l₀0.10 m

Short Explanation

What is Elasticity?

Elasticity is the property of a material that enables an object to return to its original shape and size after the force applied on it is removed.

Elastic and Non-Elastic Examples

A spring, sponge and elastic cord can return to their original shape or length. Plasticine changes shape but does not return to its original shape.

Hooke’s Law

The extension of a spring is directly proportional to the force applied on the spring, provided that the elastic limit is not exceeded. F = kx

Elastic Potential Energy

Elastic potential energy is the work done to stretch the spring. It is equal to the area under the graph of force against extension.

Factor Change in Factor Effect on Spring Constant
Material of spring Different material Changes according to the type of material
Length of spring Shorter spring Higher spring constant
Length of spring Longer spring Lower spring constant
Diameter of spring Smaller diameter Higher spring constant
Diameter of spring Larger diameter Lower spring constant
Thickness of spring wire Wire with smaller diameter Lower spring constant
Thickness of spring wire Wire with larger diameter Higher spring constant

Try to Answer First

Answer in your mind, then press “Check Answer”.

1

What is the meaning of elasticity?

Check Answer
Answer: Elasticity is the property of a material that enables an object to return to its original shape and size after the force applied on it is removed.
2

State Hooke’s law.

Check Answer
Answer: The extension of a spring is directly proportional to the force applied on the spring, provided that the elastic limit is not exceeded.
3

A spring extends by 6 mm when stretched by a force of 12 N. Calculate the spring constant.

Check Answer
Answer: \(k = \dfrac{F}{x}\), so \(k = \dfrac{12}{6} = 2\ \mathrm{N\,mm^{-1}}\).

Common Mistakes

  • !Thinking that all materials are elastic.
  • !Saying that plasticine is elastic because its shape can be changed.
  • !Mixing up original length, extended length and extension.
  • !Forgetting that the gradient of the F against x graph gives the spring constant.
  • !Thinking that elastic potential energy is the gradient of the graph instead of the area under the graph.

Concept Misunderstandings

Misunderstanding

Any object that changes shape is elastic.

Correct Concept

An object is elastic only if it returns to its original shape and size after the force is removed.

Misunderstanding

Spring constant is the area under the graph.

Correct Concept

Spring constant is the gradient of the graph of force, F, against extension, x.

Misunderstanding

Elastic potential energy is the gradient of the graph.

Correct Concept

Elastic potential energy is the area under the graph of force, F, against extension, x.

Summary

  • Elasticity is the ability of a material to return to its original shape and size after the force is removed.
  • Hooke’s law states that extension is directly proportional to force if the elastic limit is not exceeded.
  • The spring constant can be calculated using \(k = \dfrac{F}{x}\) or from the gradient of the graph of F against x.
  • Elastic potential energy is the area under the graph of F against x.
  • The spring constant is affected by material, spring length, spring diameter and thickness of spring wire.

Short Activity

Objective: Identify elasticity, Hooke’s law, spring constant and elastic potential energy.

A. Objective Quiz

1 Which material does not return to its original shape after the force is removed?

2 Hooke’s law can be written as:

B. Fill in the Blanks

3 The extension of a spring is the increase in of the spring.

4 Elastic potential energy is equal to the under the graph of F against x.

C. Matching / Drag and Drop

Drag each term to the correct meaning. If using a phone, tap the answer first, then tap the matching box.

Choices
Hooke’s law
Elasticity
Spring constant
Elastic potential energy
Meanings
1 Returns to original shape and size
2 Extension is directly proportional to force
3 Gradient of graph of F against x
4 Area under the graph of F against x
 

Keywords

Elasticity Force Spring Extension Original length Hooke’s law Spring constant Elastic potential energy Elastic limit Series arrangement Parallel arrangement Plasticine
The views expressed in the notes here are those of the contributor and don’t necessarily represent the views of Pandai.
Chapter : Force and Motion II
Topic : Elasticity
Form 5 Physics
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