Height, gravity and the choice of zero
You will be able to: Calculate near-surface gravitational potential-energy changes and connect them to gravity’s work.
Does choosing a different zero change the energy needed to lift a book?
Lift a 2 kg backpack from the floor to a shelf 1 m higher. The backpack–Earth system gains 20 J of gravitational potential energy when g=10 N/kg. Calling the floor or the table “zero height” will not change that gain.
A useful starting point: Gravity and mass →
Words and symbols before equations
- Potential energy U
- Energy associated with a system’s configuration; measured in J.
- Height y
- Vertical coordinate in m, increasing upward here.
- Reference zero
- An arbitrary level where gravitational potential energy is assigned zero.
- Conservative force
- A force whose work depends only on the initial and final configurations.
What this picture assumes
Object mass 2 kg; initial height 1 m in fixed physical coordinates; g=10 N/kg. The zero control changes the potential-energy reference, not the physical motion.
Connect the picture to the physics
Gravitational potential energy belongs to the interacting backpack–Earth system. Near Earth’s surface, where g changes negligibly, U_g=mgy relative to a chosen zero. The change is ΔU_g=mg(y_f−y_i).
Gravity pulls downward. When the object rises, gravity does negative work and U_g increases: W_g=−ΔU_g. During a descent, the signs reverse. A slow lift requires positive work by the lifting force as gravity does negative work.
For the same starting and ending heights, gravity’s work is the same along a straight lift or a longer ramp. Friction along those paths need not do the same work. Negative U relative to a chosen zero is allowed; only energy differences enter predictions.
A worked example, step by step
A 3 kg bag moves from y=1 m to y=3 m. Use g=10 N/kg. Calculate ΔU and gravity’s work, then shift the height zero upward by 2 m.
- Original coordinates: Δy=3−1=2 m, so ΔU=3×10×2=+60 J.
- Gravity’s work is −60 J.
- New coordinates are −1 m and +1 m. New potentials are −30 J and +30 J.
- Their difference is still +60 J. The reference changes values, not the required energy transfer.
The object alone does not own gravitational potential energy independently of Earth.
If you carry the bag back to its starting height, what is gravity’s total work?
Compare with an explanation
Zero. Gravity is conservative and the final height equals the initial height.
Predict. Change one thing. Explain.
Keep a 2 kg object’s initial height 1 m. Change its final height and then the reference-zero height. Notice which energy values shift and which difference stays fixed.
U_i=20 J; U_f=60 J; ΔU=40 J; gravity work=-40 J. Reference zero at coordinate 0 m.
Object mass 2 kg; initial height 1 m in fixed physical coordinates; g=10 N/kg. The zero control changes the potential-energy reference, not the physical motion.
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 4 kg object descends from 5 m to 2 m. Use g=10. (a) Calculate ΔU. (b) Find gravity’s work. (c) Repeat ΔU with the zero at 2 m. (d) Compare a straight drop and a frictionless curved path between the same heights.
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Compare with the answer and four-point rubric
- 1 point: −120 J.
- 1 point: +120 J.
- 1 point: Initial height 3 m and final 0 m gives the same −120 J.
- 1 point: Gravity’s work is +120 J for either path; it depends on endpoints.
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 1Which system stores gravitational U?
The interacting object and Earth.
RECALL 2What is gravity’s work in terms of U?
W_g=−ΔU_g.
RECALL 3When does mgΔy apply?
When g is approximately uniform over the height range.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
Height, gravity and the choice of zero
- ΔU_g=mgΔy and W_g=−ΔU_g for uniform g.
- U_g=mgy after choosing a zero; only differences affect predictions.
Remember: The object alone does not own gravitational potential energy independently of Earth.
Conditions: Object mass 2 kg; initial height 1 m in fixed physical coordinates; g=10 N/kg. The zero control changes the potential-energy reference, not the physical motion.
Refresh Kid · Unit 3 · Objectives 3.3.A · Review edition
Framework, scope and review status
Mapped to College Board CED, Topic 3.3, objectives 3.3.A. 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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