Choose the system before tracking energy
You will be able to: Explain the same event using two consistent choices of system boundary.
Is gravity transferring energy or changing energy inside the system?
Drop a ball. If you study the ball alone, Earth is outside and gravity does positive work on it. If you study ball plus Earth, gravity is an internal interaction and gravitational potential energy converts into kinetic energy.
A useful starting point: Choosing a system →
Words and symbols before equations
- System boundary
- The line separating the selected objects from their surroundings.
- Internal conversion
- Energy changes form within the chosen system.
- External transfer
- Energy crosses the boundary, for example through work.
- Mechanical energy
- Sum of kinetic and relevant potential energies, K+U.
What this picture assumes
A 2 kg ball falls 3 m from rest with g=10, no air resistance and negligible Earth recoil. The two settings describe the same physical event.
Connect the picture to the physics
The same motion can have more than one valid energy description. List the system’s members first. Include gravitational potential energy when the interacting object and Earth are in the system.
For the ball alone modeled as a particle, W_g=ΔK. For ball plus Earth, negligible external transfer gives ΔK+ΔU_g=0. Earth’s recoil kinetic energy is negligible in the usual near-surface approximation.
Do not count the same gravitational interaction twice by including both W_g as an external input and ΔU_g internally in one balance. Real objects can have internal energies; the particle model tracks translational kinetic energy and deliberately leaves those details out.
| Feature | Ball alone | Ball + Earth |
|---|---|---|
| Gravity | External force doing work | Internal interaction |
| Energy statement | W_g = ΔK | ΔK + ΔU_g = 0 |
| Prediction | Same final speed | Same final speed |
A worked example, step by step
A 2 kg ball starts from rest and falls 3 m without air resistance. Use g=10. Account for its final kinetic energy with two system choices.
- Ball alone: Earth exerts an external force. W_g=mgd=60 J, so ΔK=60 J.
- Ball plus Earth: U_g falls by 60 J, so K rises by 60 J while total mechanical energy stays constant.
- Both descriptions give K_f=60 J and v=√(60)≈7.75 m/s.
- The chosen boundary changes the accounting, not the predicted motion.
Never count gravity as both external work and an internal potential-energy change in the same energy equation.
If your system includes a block and its spring, is the spring’s work an external input?
Compare with an explanation
No. The spring interaction is internal; account for its elastic potential-energy change.
Predict. Change one thing. Explain.
Switch between ball-only and ball-plus-Earth for a 2 kg ball falling 3 m from rest. Keep the motion fixed. Explain why the transfer label changes while the final 60 J of kinetic energy does not.
Gravity does +60 J external work; ball K increases from 0 to 60 J. Gravitational potential energy is not an internal term for the ball alone.
A 2 kg ball falls 3 m from rest with g=10, no air resistance and negligible Earth recoil. The two settings describe the same physical event.
Explain what you noticed: Which quantity changed? Which stayed fixed? Use a work, energy or power relationship to justify your prediction.
Apply the idea to a fresh problem Practice →Show what you understand.
Two original questions are a starting check, not proof of mastery. Explain your choice before revealing the answer.
Original written challenge
4 points · self-check · not an official AP questionA 1 kg object falls 2 m from rest without air resistance. (a) Find gravity’s work for the object-only system. (b) Find ΔU for object+Earth. (c) Find final K. (d) Explain why adding gravity’s work and the potential decrease as two separate inputs would be wrong.
This response is not submitted or saved. Copy it before leaving.
Compare with the answer and four-point rubric
- 1 point: +20 J.
- 1 point: −20 J.
- 1 point: 20 J.
- 1 point: It counts one gravitational interaction twice. Choose one consistent system account.
Accept equivalent correct methods and explanations. This is a Refresh Kid teaching rubric, not an official AP scoring guideline.
Retrieve it before you reveal it.
RECALL 1What is your first step in an energy problem?
Name the objects inside the system.
RECALL 2Is internal conversion a transfer across the boundary?
No.
RECALL 3Does a larger system always conserve mechanical energy?
No; internal dissipative processes can convert mechanical energy to other forms.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
Choose the system before tracking energy
- Ball alone: W_g=ΔK.
- Ball + Earth, isolated ideal mechanical model: ΔK+ΔU_g=0.
- Identify the boundary before assigning energy terms.
Remember: Never count gravity as both external work and an internal potential-energy change in the same energy equation.
Conditions: A 2 kg ball falls 3 m from rest with g=10, no air resistance and negligible Earth recoil. The two settings describe the same physical event.
Refresh Kid · Unit 3 · Objectives 3.4.A, 3.4.C · Review edition
Framework, scope and review status
Mapped to College Board CED, Topic 3.4, objectives 3.4.A, 3.4.C. CED effective Fall 2024, current PDF ©2026; checked September 16, 2026. Fall-2026 corrections also checked. The lesson breakdown and questions are original Refresh Kid work, not official topic subdivisions.
Implementation and automated checks are separate from independent teacher review and observation of students. Both human review stages remain pending. This is a review edition, not a certified or validated assessment.
Optional further resource: College Board’s released questions and scoring guides. Papers can combine units; this link is an archive, not an assignment of every question to this lesson.
Our learn, explore, practice and recall sequence is informed by the IES learning guide. The exact Refresh Kid implementation has not been evaluated for learning effectiveness.
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