What does an elevator scale measure?
You will be able to: Use a force equation to distinguish gravitational weight from the scale’s normal force.
Can you feel weightless while gravity is still acting?
A 60 kg rider stands on an elevator scale. At rest it reads 600 N using g = 10 m/s². While accelerating upward at 2 m/s² it reads 720 N, although gravity is nearly unchanged.
A useful starting point: Gravitational force and field strength →
Words and symbols before equations
- Apparent weight
- Support force magnitude measured by an ideal scale, in N.
- Normal force N
- Upward contact force exerted by the scale on the rider.
- Weight mg
- Downward gravitational force.
- Local equivalence idea
- In a small enclosed region, support effects from acceleration can mimic those of gravity; large-scale field variation requires more information.
What this picture assumes
Ideal floor scale with maintained contact or the free-fall limit. Up is positive; g = 10 m/s². Controls exclude accelerations requiring a negative floor normal force.
Read the picture in three steps
- Locate the labeled sources, system boundary or graph axes. Read the units before comparing values.
- Upward acceleration 2 m/s²; weight 600 N; scale reading 720 N. Velocity direction does not enter this force equation.
- Check what the picture assumes below. Use the Explore task to predict one change before moving a control.
Connect the picture to the physics
With up positive, N − mg = ma. Thus N = m(g + a) while contact is maintained. The sign of acceleration matters, not whether the elevator is currently travelling up or down.
During ideal free fall, a = −g and N = 0. Rider and scale accelerate together, so the scale does not need to push. Gravity is still present. Apparent weightlessness also occurs in orbital free fall.
A laboratory accelerating in otherwise force-free space can produce a support force resembling a gravitational weight. This local connection motivates the equivalence principle. It does not say the gravitational field literally changes whenever a lift changes acceleration, and force measurements alone do not erase field gradients over large regions.
A worked example, step by step
A 50 kg rider moves upward but slows with acceleration −3 m/s². Find the scale reading.
- Take up positive; motion is upward, but acceleration is downward.
- Use N − 500 = 50(−3).
- N = 500 − 150 = 350 N.
- The reading is smaller than gravitational weight because the rider accelerates downward; the upward velocity does not determine the reading.
A scale measures support force, not mass directly. A display in kilograms assumes a calibration value of g.
An elevator moves downward at constant velocity. Is the scale reading smaller than mg?
Compare with an explanation
No. Acceleration is zero, so the reading is mg.
Predict. Change one thing. Explain.
Hold mass fixed. Move acceleration from positive to zero to −g. Explain each scale reading while imagining either upward or downward velocity.
On narrow screens, swipe or scroll diagrams sideways to read all labels.
Upward acceleration 2 m/s²; weight 600 N; scale reading 720 N. Velocity direction does not enter this force equation.
Ideal floor scale with maintained contact or the free-fall limit. Up is positive; g = 10 m/s². Controls exclude accelerations requiring a negative floor normal force.
Explain what you noticed: Which quantity changed? Which stayed fixed? Use the relevant force, system boundary, acceleration 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 questionFor a 40 kg rider, calculate normal force at a = +2, 0 and −10 m/s². Explain which case is weightless and whether gravity has disappeared.
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Compare with the answer and four-point rubric
- 1 point: At +2 m/s², N = 40(12) = 480 N.
- 1 point: At zero acceleration, N = 400 N.
- 1 point: At −10 m/s², N = 0.
- 1 point: The last case is apparent weightlessness; gravity still exerts 400 N downward.
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 quantity controls an elevator scale reading?
Acceleration together with mass and gravity, not velocity alone.
RECALL 2Why does a falling scale read zero?
It and the rider fall together without a support force.
RECALL 3Does apparent weightlessness mean g = 0?
No.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
What does an elevator scale measure?
- N = m(g + a) with upward-positive a and maintained contact.
- Free fall: a = −g ⇒ N = 0 while mg remains nonzero.
- For a floor scale, a negative computed N signals loss of the assumed contact.
Remember: A scale measures support force, not mass directly. A display in kilograms assumes a calibration value of g.
Conditions: Ideal floor scale with maintained contact or the free-fall limit. Up is positive; g = 10 m/s². Controls exclude accelerations requiring a negative floor normal force.
Refresh Kid · AP Physics C: Mechanics Unit 2 (official Unit 2) · Objectives 2.6.C; 2.6.D · Review edition
Framework, scope and review status
Mapped to College Board CED, Topic 2.6, objectives 2.6.C; 2.6.D. CED effective Fall 2024, current PDF ©2026; checked September 16, 2026 alongside the Fall 2026 clarifications. This is Mechanics Unit 2: Force and Translational Dynamics. The unit covers Topics 2.1–2.10. Calculus is introduced where it is needed for continuous mass and velocity-dependent forces. Shell theorem is applied without requiring a proof; spring combinations are purely series or purely parallel. 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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