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Science lesson plan · 12th grade (Year 13 in England) · 45 minutes

Newton's law of gravitation and field strength

Forces and motion

CCSS NGSS.HS-PS2-4England: A level Physics: Gravitational fields (extension)

Objective and success criteria

Students will: Newton's law of gravitation and field strength.

  • 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: Mass and weight (W = mg); Orbits and orbital speed (v = 2πr / T)

Leads to: Coulomb's law: force between charges

Materials: Force meters, Toy cars and ramps, Mini whiteboards, A diagram or short video clip of the idea, Printed student sheet (below).

Warm-up · 5 min

  • Quick retrieval from earlier learning (Mass and weight (W = mg); Orbits and orbital speed (v = 2πr / T)). Students answer on mini whiteboards.
  • Show answers together and note who needs support in the main task.
  1. What is the weight of a 35 kg object on Earth? Use g = 9.8 N/kg. → 343 NPrompt: weight = mass × gravitational field strength (W = m g)
  2. The International Space Station orbits at a radius of about 6780 km from Earth's centre, taking 92 minutes per orbit. What is its orbital speed, in km/s? (v = 2πr ÷ T; give 1 decimal place) → 7.7 km/sPrompt: Convert the period to seconds.
  3. An astronaut's mass is 80 kg. Gravitational field strength on Mars is 3.7 N/kg. What would their weight be there, in N? → 296 NPrompt: Mass stays the same everywhere; weight changes.

Hook · 5 min

  • Drop a sheet of paper and a scrunched-up sheet together and ask why one falls faster.
  • Share the objective: Newton's law of gravitation and field strength. Read the success criteria together.

I do: model it · 10 min

  • Work through the example out loud, saying why you do each step, not just what you do.
  • Example: One of two masses is multiplied by 2 and the distance stays the same. By what factor does the gravitational force change? (F = G m₁ m₂ ÷ r²)
  • Step 1: × 2
  • Step 2: So the answer is: 2
  • Answer: 2
  • Pause after each step and ask a student to say what comes next.

We do: guided practice · 10 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. One of two masses is multiplied by 4 and the distance stays the same. By what factor does the gravitational force change? (F = G m₁ m₂ ÷ r²) → 4Prompt: Force is proportional to each mass.
  2. Calculate the gravitational field strength at the surface of Mars, in N/kg. Mass = 6.42 × 10²³ kg, radius = 3.39 × 10⁶ m, G = 6.67 × 10⁻¹¹ N m²/kg². (g = G M ÷ r²; give 1 decimal place) → 3.7 N/kgPrompt: Square the radius first.

You do: independent practice · 10 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 8 questions are on the student sheet below, with answers in the key.

Exit ticket · 5 min

  • Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
  1. Gravitational force follows an "inverse square law". What does this mean? (Distance has no effect / Doubling the distance halves the force / Doubling the distance doubles the force / Doubling the distance makes the force one quarter as strong) → Doubling the distance makes the force one quarter as strongPrompt: F ∝ 1/r²
  2. The distance between two masses is multiplied by 3. By what factor does the gravitational force between them change? (F = G m₁ m₂ ÷ r²; give 4 decimal places if needed) → 0.1111Prompt: Force is proportional to each mass.

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: Mass and weight (W = mg).
  • Use concrete materials: force meters.
  • Give the first step of each question, or a partly worked example to finish.
  • Pair with a confident partner for the guided practice.

Stretch

  • Move on to: Coulomb's law: force between charges.
  • 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-12.

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

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Newton's law of gravitation and field strength

Name

Date

Score/ 8

  1. Question 1

    Why is the value of g slightly smaller at the top of a high mountain?

    • A. Mountains have less mass
    • B. You are slightly further from Earth's centre
    • C. It is colder
    • D. There is less air

  2. Question 2

    Calculate the gravitational field strength at the surface of the Moon, in N/kg. Mass = 7.35 × 10²² kg, radius = 1.74 × 10⁶ m, G = 6.67 × 10⁻¹¹ N m²/kg². (g = G M ÷ r²; give 1 decimal place)

    AnswerN/kg

  3. Question 3

    One of two masses is multiplied by 2 and the distance stays the same. By what factor does the gravitational force change? (F = G m₁ m₂ ÷ r²)

    Answer

  4. Question 4

    Why do all objects near Earth's surface fall with the same acceleration (ignoring air)?

    • A. Gravity does not depend on mass
    • B. Light objects are pulled harder
    • C. A larger mass feels a larger force, but also needs more force to accelerate, so a = g for all
    • D. Heavier objects feel no extra force

  5. Question 5

    Calculate the gravitational field strength at the surface of Mars, in N/kg. Mass = 6.42 × 10²³ kg, radius = 3.39 × 10⁶ m, G = 6.67 × 10⁻¹¹ N m²/kg². (g = G M ÷ r²; give 1 decimal place)

    AnswerN/kg

  6. Question 6

    The distance between two masses is multiplied by 0.5. By what factor does the gravitational force between them change? (F = G m₁ m₂ ÷ r²; give 4 decimal places if needed)

    Answer

  7. Question 7

    The distance between two masses is multiplied by 3. By what factor does the gravitational force between them change? (F = G m₁ m₂ ÷ r²; give 4 decimal places if needed)

    Answer

  8. Question 8

    Who first published the law of universal gravitation?

    • A. Galileo Galilei
    • B. Isaac Newton
    • C. Albert Einstein
    • D. Johannes Kepler

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Answer key: Newton's law of gravitation and field strength

  1. 1. B. You are slightly further from Earth's centre

  2. 2. 1.6 N/kg

  3. 3. 2

  4. 4. C. A larger mass feels a larger force, but also needs more force to accelerate, so a = g for all

  5. 5. 3.7 N/kg

  6. 6. 4

  7. 7. 0.1111

  8. 8. B. Isaac Newton