Elevators, scales & apparent weight
You will be able to: Distinguish gravitational weight from the support force measured by a scale.
Why does a scale change when an elevator accelerates?
Standing on a bathroom scale in an elevator, you feel a stronger push from the floor as the elevator starts accelerating upward. Earth’s pull has barely changed; the support force has.
A useful starting point: Gravity and weight →
Words and symbols before equations
- Apparent weight
- Magnitude of the support normal force, the force a scale senses.
- Gravitational weight mg
- Earth’s pull; approximately constant near the surface.
- Free fall
- Motion under gravity alone, with no supporting contact force.
What this picture assumes
g=10 m/s². The scale senses normal force. Velocity is not specified. At a=−10 m/s², contact force is zero.
Connect the picture to the physics
Take upward as positive. The two vertical forces on a standing person are normal force N up and mg down. Newton’s law gives N−mg=ma, so N=m(g+a).
The sign of acceleration matters, not the sign of velocity. An elevator moving up while slowing has downward acceleration and a lower scale reading. Constant upward or downward velocity gives N=mg.
In free fall a=−g, so N=0: apparent weightlessness despite nonzero gravity. A floor cannot pull downward, so a calculated negative N means the assumed contact has failed. Locally, a support-force sensation alone cannot tell an observer whether it comes from gravity or acceleration; this motivates the equivalence principle.
| Quantity | Gravitational weight | Apparent weight |
|---|---|---|
| Interaction | Earth pulls the rider | Scale pushes the rider |
| Near-surface formula | mg | N=m(g+a_y) |
| Ideal free fall | Still mg | Zero |
A worked example, step by step
A 50 kg rider is in an elevator accelerating upward at 2 m/s². Then it moves upward at constant speed. Find the scale force in each stage, using g=10 m/s².
- Gravitational weight is 50×10=500 N in both stages.
- Accelerating upward: N−500=50×2, so N=600 N.
- Constant speed: a=0, so N=500 N.
- The first reading is larger because the net force must point upward. Upward motion by itself does not demand a larger reading.
A zero scale reading does not prove that gravity has disappeared.
The elevator moves downward and slows. Does the reading rise or fall?
Compare with an explanation
It rises above mg: slowing downward motion requires upward acceleration.
Predict. Change one thing. Explain.
Keep mass fixed. Change upward-signed acceleration through −10, −2, 0 and +2 m/s². Explain the scale force at each value without assuming a velocity direction.
Scale force 600 N; gravitational weight 500 N. Acceleration 2 m/s², upward positive. Common arrow scale 0.17 drawing units/N.
g=10 m/s². The scale senses normal force. Velocity is not specified. At a=−10 m/s², contact force is zero.
Explain what you noticed: Which quantity changed? Which stayed fixed? Use a force or motion 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 60 kg rider has upward-signed acceleration −2 m/s². (a) Draw forces, (b) write Newton’s law, (c) find N, and (d) give two possible motion descriptions.
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Compare with the answer and four-point rubric
- 1 point: N upward and mg downward.
- 1 point: N−600=60(−2).
- 1 point: N=480 N.
- 1 point: Moving up and slowing, or moving down and speeding up; both have downward acceleration.
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 does a scale sense?
Support force, often displayed after calibration as a mass equivalent.
RECALL 2Which controls the reading: velocity or acceleration?
Vertical acceleration in this setup.
RECALL 3Why can orbiting astronauts feel weightless?
They and their surroundings are in free fall while gravity still acts.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
Elevators, scales & apparent weight
- N=m(g+a_y), upward positive and contact maintained.
- Free fall: a_y=−g and N=0.
Remember: A zero scale reading does not prove that gravity has disappeared.
Conditions: g=10 m/s². The scale senses normal force. Velocity is not specified. At a=−10 m/s², contact force is zero.
Refresh Kid · Unit 2 · Objectives 2.6.C · Review edition
Framework, scope and review status
Mapped to College Board CED, Topic 2.6, objectives 2.6.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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