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Science lesson plan · 10th grade (Year 11 in England) · 30 minutes

Energy stored in a stretched spring (E = ½ k e²)

Energy

CCSS NGSS.HS-PS3-1England: GCSE Combined Science: Energy (elastic potential energy)

Objective and success criteria

Students will: Energy stored in a stretched spring (E = ½ k e²).

  • I can answer questions on today's skill on my own, without help.
  • I can explain each step and say why it works.
  • I can check my answer and spot a mistake.

Before and after

Needs first: Stretching springs: extension and Hooke's law; Kinetic and gravitational potential energy

Leads to: the next skill in this area.

Materials: Wind-up toys or a pendulum, Energy transfer diagrams, Mini whiteboards, A diagram or short video clip of the idea, Printed student sheet (below).

Warm-up · 4 min

  • Quick retrieval from earlier learning (Stretching springs: extension and Hooke's law; Kinetic and gravitational potential energy). Students answer on mini whiteboards.
  • Show answers together and note who needs support in the main task.
  1. A spring is 12 cm long. When a weight is hung on it, it is 18 cm long. What is the extension, in cm? → 6 cmPrompt: Extension is how much longer the spring has become.
  2. What is the kinetic energy of a 50 kg object moving at 2 m/s? Use Eₖ = ½ m v². → 100 JPrompt: Square the speed first.
  3. A force of 3.75 N stretches a spring by 15 cm. What is the spring constant, in N/m? → 25 N/mPrompt: k = F ÷ e

Hook · 3 min

  • Wind up a toy or stretch an elastic band and ask where the energy goes.
  • Share the objective: Energy stored in a stretched spring (E = ½ k e²). Read the success criteria together.

I do: model it · 7 min

  • Work through the example out loud, saying why you do each step, not just what you do.
  • Example: A spring with spring constant 100 N/m is stretched by 0.05 m. How much energy is stored in it, in J?
  • Step 1: 0.5 × 100 × 0.05² = 0.125
  • Step 2: So the answer is: 0.125 J
  • Answer: 0.125 J
  • Pause after each step and ask a student to say what comes next.

We do: guided practice · 6 min

  • Do these together. Students try each step on whiteboards before you reveal it.
  • Use the hints as prompts rather than giving the answer.
  1. A spring with spring constant 50 N/m is stretched by 0.3 m. How much energy is stored in it, in J? → 2.25 JPrompt: E = ½ × k × e²
  2. A catapult band has a spring constant of 200 N/m and is pulled back 20 cm. How much elastic potential energy is stored, in J? Give 3 decimal places. → 4 JPrompt: Convert cm to m first.

You do: independent practice · 7 min

  • Students work on the student sheet. Circulate and check the first two answers of every student early.
  • Students who finish: write a question of their own for a partner, with the answer.

The 6 questions are on the student sheet below, with answers in the key.

Exit ticket · 3 min

  • Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
  1. A catapult band has a spring constant of 100 N/m and is pulled back 4 cm. How much elastic potential energy is stored, in J? Give 3 decimal places. → 0.08 JPrompt: Convert cm to m first.
  2. A stretched bow is released and the arrow flies off. Which energy transfer happens? (elastic potential store of the bow → kinetic store of the arrow / kinetic → elastic / chemical → nuclear / thermal → elastic) → elastic potential store of the bow → kinetic store of the arrowPrompt: Where is the energy stored before release?

Watch out for

  • Everyday meanings of words getting in the way of the science meaning: define key words explicitly.
  • Remembering facts without the reason: ask "why?" and "what is the evidence?"

Support and stretch

Support

  • Review first: Stretching springs: extension and Hooke's law.
  • Use concrete materials: wind-up toys or a pendulum.
  • Give the first step of each question, or a partly worked example to finish.
  • Pair with a confident partner for the guided practice.

Stretch

  • Explain a common mistake in writing and how to fix it.
  • Write a word problem that uses today's skill, then solve a partner's.

Homework and more practice

Free online practice with hints and printable worksheets for this skill: eurekami.com/science/grade-10.

Free lesson plan from eurekami.com/lesson-plan-builder

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Energy stored in a stretched spring (E = ½ k e²)

Name

Date

Score/ 6

  1. Question 1

    Why can E = ½ k e² only be used up to the limit of proportionality?

    • A. Beyond it, force is no longer proportional to extension
    • B. k becomes zero
    • C. The spring gets lighter
    • D. Springs store no energy past that point

  2. Question 2

    A spring with spring constant 200 N/m is stretched by 0.05 m. How much energy is stored in it, in J?

    AnswerJ

  3. Question 3

    A catapult band has a spring constant of 200 N/m and is pulled back 5 cm. How much elastic potential energy is stored, in J? Give 3 decimal places.

    AnswerJ

  4. Question 4

    Work is done stretching a spring that obeys Hooke's law. How can this work be found from a force–extension graph?

    • A. the length of the line
    • B. the gradient of the line
    • C. the highest force only
    • D. the area under the line

  5. Question 5

    A spring with spring constant 100 N/m is stretched by 0.2 m. How much energy is stored in it, in J?

    AnswerJ

  6. Question 6

    A catapult band has a spring constant of 50 N/m and is pulled back 2 cm. How much elastic potential energy is stored, in J? Give 3 decimal places.

    AnswerJ

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Answer key: Energy stored in a stretched spring (E = ½ k e²)

  1. 1. A. Beyond it, force is no longer proportional to extension

  2. 2. 0.25 J

  3. 3. 0.25 J

  4. 4. D. the area under the line

  5. 5. 2 J

  6. 6. 0.01 J