Choose the system before writing energy terms
You will be able to: Describe the same process with two consistent system boundaries.
Is gravity an energy transfer or an internal energy change?
A 2 kg ball falls 1 m from rest. In an object-only description, gravity does 20 J of external work. In a ball–Earth description, gravitational U decreases by 20 J while K increases by 20 J. Both predict the same speed.
A useful starting point: Count each interacting pair once →
Words and symbols before equations
- System boundary
- The line separating the objects included in your calculation from their surroundings.
- External work
- Energy transferred by a force whose source is outside the chosen system.
- Mechanical energy E_mech
- The sum K + U; it excludes thermal energy and other internal forms.
- Energy balance
- Change of stored energy equals net transfer into the chosen system.
What this picture assumes
Release from rest, no air resistance, g = 10 m/s² and negligible Earth recoil. Object-only balance uses external gravity work; object + Earth balance uses internal gravitational U. Both describe the same fall.
Read the picture in three steps
- Locate the labeled sources, system boundary or graph axes. Read the units before comparing values.
- System: object only. ΔK = 20 J; external gravity work = 20 J. Final speed 4.472 m/s in either description.
- Check what the picture assumes below. Use the Explore task to predict one change before moving a control.
Connect the picture to the physics
Begin by naming the objects inside the system and the energy forms you will track. In this point-object mechanical model, a lone ball has translational K; the ball–Earth pair also has gravitational U. Real objects can store internal thermal energy, but that is not the K term.
For the ball alone, W_g = ΔK. For ball + Earth, gravity is internal and ΔK + ΔU_g = 0 when no energy crosses the boundary and losses are negligible. Earth’s recoil energy is negligible in the usual near-Earth approximation; the stated K is the ball’s.
Do not count both gravity’s work and the corresponding decrease in U as separate energy sources in one equation. The same interaction has been represented twice. Likewise, total energy conservation does not guarantee mechanical energy conservation if friction converts mechanical energy to thermal energy.
| Question | Object only | Object + Earth |
|---|---|---|
| Stored mechanical energy | Kinetic energy K | Kinetic K and gravitational U |
| Gravity | External force does work | Internal conservative interaction |
| Energy statement | ΔK = W_gravity | ΔK + ΔU = 0, with no other transfers |
A worked example, step by step
A 1 kg ball drops from rest through 5 m, with g = 10 m/s² and no air resistance. Solve for speed using both system choices.
- Object only: gravity is external and does W_g = (1)(10)(5) = 50 J.
- Set ΔK = 50 J: ½(1)v² = 50, so v = 10 m/s.
- Ball + Earth: choose final height as U = 0, so U_i = 50 J and U_f = 0.
- Set K_i + U_i = K_f + U_f. The same equation 50 = ½v² gives 10 m/s; no extra W_g term belongs on the right.
Write either the work of an external conservative force or its internal potential-energy change, according to the boundary. Avoid counting the same interaction twice.
Does a stationary support guarantee zero work on every imaginable system?
Compare with an explanation
No. Check the force’s application-point displacement and the system. In our fixed-track particle models, the normal is perpendicular to the motion and does zero work.
Predict. Change one thing. Explain.
Change the drop height, then switch the boundary between object only and object + Earth. Observe that speed and ΔK agree while the energy-transfer labels change.
On narrow screens, swipe or scroll diagrams sideways to read all labels.
System: object only. ΔK = 20 J; external gravity work = 20 J. Final speed 4.472 m/s in either description.
Release from rest, no air resistance, g = 10 m/s² and negligible Earth recoil. Object-only balance uses external gravity work; object + Earth balance uses internal gravitational U. Both describe the same fall.
Explain what you noticed: Which quantity changed? Which stayed fixed? Use the relevant work, system boundary, energy or calculus 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 3 kg object falls 2 m from rest with g = 10 m/s². Give the object-only and object–Earth balances, final K, and speed. Explain why adding 60 J of work to a 60 J loss of U would be incorrect.
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Compare with the answer and four-point rubric
- 1 point: Object-only balance: ΔK = W_g = 60 J.
- 1 point: Object + Earth balance: ΔK + ΔU = 0, with ΔU = −60 J.
- 1 point: K_f = 60 J and v = √(120/3) = √40 = 6.32 m/s.
- 1 point: The work and potential-energy change describe the same gravitational interaction; adding both as inputs double counts it.
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 the first step in an energy problem?
Name the system and decide which interactions are internal.
RECALL 2When is mechanical energy constant?
When the chosen K + U balance has no net external transfer and no conversion to untracked forms.
RECALL 3Does “energy conserved” mean K stays constant?
No. Energy can move between K, U and other forms.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
Choose the system before writing energy terms
- Object only in free fall: ΔK = W_g.
- Object + Earth with negligible losses: ΔK + ΔU_g = 0.
- General bookkeeping: change of stored energy = net energy transferred in.
Remember: Write either the work of an external conservative force or its internal potential-energy change, according to the boundary. Avoid counting the same interaction twice.
Conditions: Release from rest, no air resistance, g = 10 m/s² and negligible Earth recoil. Object-only balance uses external gravity work; object + Earth balance uses internal gravitational U. Both describe the same fall.
Refresh Kid · AP Physics C: Mechanics Unit 3 (official Unit 3) · Objectives 3.4.A; 3.4.B; 3.4.C · Review edition
Framework, scope and review status
Mapped to College Board CED, Topic 3.4, objectives 3.4.A; 3.4.B; 3.4.C. CED effective Fall 2024, current PDF ©2026; checked September 16, 2026 alongside the Fall 2026 clarifications. This is Mechanics Unit 3: Work, Energy, and Power. The unit covers Topics 3.1–3.5. Calculus connects work to force integrals, force to potential-energy derivatives, and power to the rate of energy transfer. Models distinguish object-only and multi-object systems; translational models exclude rotational energy unless explicitly noted. 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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