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Physics · Forces

Forces and elasticity

Describe elastic and inelastic deformation, use \(F = ke\) and \(E_e = \tfrac{1}{2}ke^2\), and investigate the relationship between force and extension (Required Practical 6).

  • 6 key terms
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Teacher resources

The teacher copies: slides with the questions built in, the answers, and anything else attached to this lesson for whoever is teaching it.

Student handouts

The same files the students see, to print or hand out.

Warm-up

Answer each one, then check.

  1. 1

    What is a spring?

    Show answerHide answer

    A coiled wire that can be stretched or compressed

  2. 2

    What does proportional mean?

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    Doubling one doubles the other

  3. 3

    Convert 6 cm to m.

    Show answerHide answer

    0.06 m

  4. 4

    What is elastic potential energy?

    Show answerHide answer

    Energy stored in a stretched spring

  5. 5

    What is the unit of force?

    Show answerHide answer

    Newton

Learning Objectives

  1. 1Explain why more than one force is needed to stretch, bend or compress an object.
  2. 2Describe elastic and inelastic deformation.
  3. 3Recall and apply \(F = ke\) and \(E_e = \tfrac{1}{2}ke^2\).
  4. 4Interpret force-extension graphs and describe Required Practical 6.

HOOKE'S LAW

force \(=\) spring constant \(\times\) extension \(F = ke\)

The extension of an elastic object is directly proportional to the force applied, provided the limit of proportionality is not exceeded. The same applies to compression.

Required Practical 6: Method

Investigate force and extension.

  1. 1 Measure the original length

    With no masses on the spring.
  2. 2 Add a mass

    Record the force (weight = mg) and the new length.
  3. 3 Calculate the extension

    New length minus original length.
  4. 4 Repeat

    Add masses one at a time, keeping below the limit of proportionality at first.
  5. 5 Plot

    Force (y-axis) against extension (x-axis).
  6. 6 Gradient

    Gradient of the straight part = spring constant k.

Spring Constant

A force of 3.0 N stretches a spring by 6.0 cm (within the limit of proportionality). Calculate the spring constant.

Show the solutionHide the solution
  1. 1 Convert \(6.0\) cm \(= 0.060\) m
  2. 2 Rearrange \(k = F \div e\)
  3. 3 Substitute \(k = 3.0 \div 0.060\)
  4. 4 Answer \(k = 50\) N/m

Answer50 N/m

Elastic Potential Energy

Calculate the energy stored in the spring when the extension is 0.040 m and k = 50 N/m.

Show the solutionHide the solution
  1. 1 Write the equation \(E_e = \tfrac{1}{2}ke^2\)
  2. 2 Substitute \(E_e = 0.5 \times 50 \times 0.040^2\)
  3. 3 Answer \(E_e = 0.040\) J

Answer0.040 J

Elastic or Inelastic?

Elastic deformation

  • The object returns to its original shape when the force is removed.
  • Happens within the limit of proportionality.

Inelastic deformation

  • The object does not return to its original shape.
  • Happens beyond the limit of proportionality.

Key Ideas

Learn these.

  • Two forces

    To stretch, bend or compress a stationary object, more than one force is needed (for example pull at both ends).

  • Work done

    The work done on an elastic object equals the elastic potential energy stored, provided it is not inelastically deformed.

  • Linear

    A straight line through the origin: proportional.

  • Non-linear

    A curve: not proportional.

Spring Test

A spring stretches 4.0 cm when a 2.0 N force is applied. (a) Calculate k in N/m. (b) What force gives an extension of 10 cm if the limit is not exceeded? (c) What energy is stored at 10 cm?

1. Convert cm to m.

2. Use F = ke and Ee = ½ke².

A good answer shows: (a) 50 N/m. (b) F = 50 × 0.10 = 5.0 N. (c) E = 0.5 × 50 × 0.10² = 0.25 J.

Can I...?

  1. 1State F = ke.
  2. 2Convert cm to m.
  3. 3Calculate a spring constant.
  4. 4Calculate stored energy.
  5. 5Describe elastic and inelastic deformation.
  6. 6Read a force-extension graph.
  7. 7Describe Required Practical 6.
  8. 8Find the gradient.

Summary & Exam Focus

  • \(F = ke\).
  • \(E_e = \tfrac{1}{2}ke^2\).
  • Beyond the limit of proportionality: non-linear, may not return.
  • Spring constant = gradient of the linear part.

Exam focus

A spring has a spring constant of 50 N/m. Calculate the force needed to stretch it by 0.10 m. (2 marks) (2 marks)

Use F = ke.

Key terms

The vocabulary this lesson expects you to use. Each one is linked from the first place it appears above.

Extension
The increase in length of a spring.
Spring constant
The force needed per metre of extension (N/m).
Limit of proportionality
The point beyond which force and extension are no longer proportional.
Elastic deformation
A change of shape that is reversed when the force is removed.
Inelastic deformation
A permanent change of shape.
Linear
Following a straight line.

Questions and answers

10 questions set on this lesson, with the mark schemes and model answers open.

1. Exam question Calculate 2 marks Easier

A spring has a spring constant of 50 N/m. Calculate the force needed to stretch the spring by 0.10 m. Use the equation: force = spring constant × extension

Mark scheme — 2 marks available

  • Correct substitution — 1 mark
  • 5.0 N — 1 mark

Model answer

\(50 \times 0.10 = 5.0\) N

2. Exam question Use the graph 5 marks Core

A student investigates a spring. The graph shows how the force changes with extension. (a) State the extension at the limit of proportionality. (b) Calculate the spring constant of the spring. (c) Calculate the elastic potential energy stored when the extension is 0.040 m.

A force-extension graph that is straight to 6 centimetres then curves.

Mark scheme — 5 marks available

  • 6 cm (accept 5.5 to 6.5) — 1 mark
  • Uses 3.0 N at 0.060 m — 1 mark
  • 50 N/m — 1 mark
  • Correct substitution — 1 mark
  • 0.040 J — 1 mark

Model answer

(a) About 6 cm. (b) \(k = 3.0 \div 0.060 = 50\) N/m. (c) \(E_e = 0.5 \times 50 \times 0.040^2 = 0.040\) J

3. Exam question Describe 2 marks Easier

Describe the difference between elastic deformation and inelastic deformation of a spring.

Mark scheme — 2 marks available

  • Elastic: returns to original shape — 1 mark
  • Inelastic: does not return — 1 mark

Model answer

In elastic deformation the spring returns to its original length when the force is removed; in inelastic deformation it does not and is permanently changed.

4. Exam question Describe 6 marks Core

Describe how to investigate the relationship between the force applied to a spring and the extension of the spring. Your answer should include the apparatus, the measurements, and how you would use them.

Mark scheme — 6 marks available

  • Level 3 (5 to 6 marks): a complete method with stand, ruler and masses, original length measured, several forces (weights) applied with the new length each time, extension calculated, graph plotted and spring constant from the gradient, with a precaution (eye level, avoid overstretching) — 5 to 6 marks
  • Level 2 (3 to 4 marks): a method covering force and extension with some detail missing — 3 to 4 marks
  • Level 1 (1 to 2 marks): simple statements about adding masses and measuring length — 1 to 2 marks

Model answer

See levels-of-response scheme.

5. Exam question Explain 2 marks Easier

Explain why two forces are needed to stretch a spring that is fixed to a wall.

Mark scheme — 2 marks available

  • Forces act at both ends — 1 mark
  • Equal and opposite forces — 1 mark

Model answer

The wall applies a force in the opposite direction to the pulling force, so the spring is stretched; with only one force the object would accelerate rather than change shape.

6. Multiple choice 1 mark Easier

Extension is...

  1. A original length
  2. B new length minus original length Correct
  3. C the force
  4. D the mass

Why: It is the increase in length.

7. Multiple choice 1 mark Core

A 4 N force gives a 0.08 m extension. k =

  1. A 0.32 N/m
  2. B 5 N/m
  3. C 50 N/m Correct
  4. D 320 N/m

Why: 4 ÷ 0.08 = 50.

8. Multiple choice 1 mark Core

A straight line force-extension graph through the origin shows...

  1. A inverse proportion
  2. B no relationship
  3. C inelastic behaviour
  4. D direct proportion Correct

Why: F ∝ e.

9. Multiple choice 1 mark Core

Beyond the limit of proportionality the spring...

  1. A may not return to its original length Correct
  2. B always returns
  3. C has zero extension
  4. D stops being a spring

Why: It is inelastically deformed.

10. Multiple choice 1 mark Stretch

The gradient of the linear section is the...

  1. A extension
  2. B spring constant Correct
  3. C mass
  4. D work done

Why: F ÷ e.