| Lesson Plan |
| Grade: |
Date: 01/12/2025 |
| Subject: Physics |
| Lesson Topic: use ϕ = –GM / r for the gravitational potential in the field due to a point mass |
Learning Objective/s:
- Describe the relationship between the gravitational field and the gravitational potential for a point mass.
- Derive the expression ϕ = –GM / r from the definition of potential difference.
- Apply the formula to calculate gravitational potential and potential energy for given masses and distances.
- Identify and correct common sign‑ and reference‑point errors in gravitational‑potential problems.
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Materials Needed:
- Projector or interactive whiteboard
- Slide deck with derivation and examples
- Worksheet containing practice questions
- Scientific calculators
- Printed diagram of radial field lines
- Whiteboard and markers
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Introduction:
Imagine a satellite being released from “infinity” and falling toward a planet; students will see how the energy changes. They already know the gravitational field g = –GM/r² and how to integrate functions. By the end of the lesson they will be able to derive and correctly use ϕ = –GM/r, avoiding sign and zero‑level mistakes.
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Lesson Structure:
- Do‑now (5 '): Quick quiz on the gravitational field formula and its direction.
- Mini‑lecture (10 '): Derive ϕ = –GM/r step‑by‑step, highlighting the reference point at infinity.
- Guided example (10 '): Calculate the potential at Earth’s surface and near the Sun, using the derived formula.
- Paired practice (15 '): Students work through three practice questions from the source, checking each other’s work.
- Class discussion (5 '): Review common mistakes (sign error, wrong reference point, confusing ϕ with g).
- Exit ticket (5 '): Write one correct expression for ϕ and one typical error to avoid.
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Conclusion:
We recap the derivation, the meaning of the negative sign, and how the formula links to potential energy. Students hand in their exit tickets and receive a brief homework set of additional calculations to reinforce the concept.
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