---
title: "Apparent Weight — AP Physics C Mechanics Definition"
description: "Apparent weight is the normal force a scale reads, which differs from mg when you accelerate. Master elevator, incline, and orbit problems for AP Physics C."
canonical: "https://fiveable.me/ap-physics-c-mechanics/key-terms/apparent-weight"
type: "key-term"
subject: "AP Physics C: Mechanics"
unit: "Unit 2"
---

# Apparent Weight — AP Physics C Mechanics Definition

## Definition

Apparent weight is the magnitude of the normal force supporting an object, which equals the scale reading. It matches true weight (mg) only when the object isn't accelerating vertically; in an accelerating elevator or in orbit, apparent weight differs from gravitational force.

## What It Is

Apparent weight is what a scale actually reads, and a scale doesn't measure gravity. It measures the [normal force](/ap-physics-c-mechanics/key-terms/normal-force "fv-autolink") pushing back on whatever is standing on it. When you're at rest, [Newton's second law](/ap-physics-c-mechanics/unit-2/5-newtons-second-law/study-guide/c4OMxeY505zPKE78 "fv-autolink") forces the normal force to equal mg, so the scale reading matches your true weight. But the moment you accelerate, those two numbers split apart.

The whole concept comes from one move you'll make constantly in [AP Physics C](/ap-physics-c-mechanics "fv-autolink"). Draw a free-body diagram, write N - mg = ma (taking up as positive), and solve for N. Accelerate upward and N = m(g + a), so you feel heavier. Accelerate downward and N = m(g - a), so you feel lighter. If you're in free fall, a = -g, the normal force vanishes, and your apparent weight is zero even though gravity is still pulling on you at full strength. That's exactly what's happening to an orbiting astronaut. Gravity hasn't turned off; there's just nothing pushing back.

## Why It Matters

Apparent weight lives in Topic 2.6 (Gravitational Force), where the CED distinguishes the gravitational force on a system from the support force the system actually experiences. It matters because it's the cleanest test of whether you really understand Newton's second law versus just memorizing W = mg. Every apparent-weight problem is secretly a free-body-diagram problem, so it bridges [Unit 2](/ap-physics-c-mechanics/unit-2 "fv-autolink")'s force analysis with Unit 3's circular motion and orbits. It also explains [weightlessness](/ap-physics-c-mechanics/key-terms/weightlessness "fv-autolink") correctly, which is a classic misconception trap. Astronauts aren't weightless because they escaped gravity (at orbital altitude, g is still roughly 90% of its surface value). They're weightless because they and their spacecraft are both in free fall, so nothing exerts a normal force on them.

## Connections

### [Weight (Unit 2)](/ap-physics-c-mechanics/key-terms/weight)

True [weight](/ap-physics-c-mechanics/key-terms/weight "fv-autolink") is the gravitational force mg, and it doesn't care what you're doing. Apparent weight is the normal force, and it changes the instant you accelerate. The gap between them, N - mg, equals ma, so the difference between the two literally measures your acceleration.

### [Weightlessness (Unit 2)](/ap-physics-c-mechanics/key-terms/weightlessness)

Weightlessness is just the special case where apparent weight hits zero. It happens whenever the only [force](/ap-physics-c-mechanics/unit-2/2-forces-and-free-body-diagrams/study-guide/2LH73zRqxtRXtAKH "fv-autolink") acting on you is gravity, like free fall or orbit. Your true weight is still there; there's just no surface pushing back to make you feel it.

### Uniform Circular Motion (Unit 3)

At the top of a vertical loop or in orbit, gravity supplies some or all of the [centripetal force](/ap-physics-c-mechanics/key-terms/centripetal-force "fv-autolink"), so the normal force shrinks. Solve N + mg = mv²/r at the top of a loop and you'll see apparent weight drop, hitting zero at the minimum speed where gravity alone provides the centripetal force.

### [Gravitational Field (Unit 2)](/ap-physics-c-mechanics/key-terms/gravitational-field)

The field g tells you the gravitational force per unit mass at a location, which sets your true weight there. Apparent weight then depends on how you're moving through that field. Same g, totally different scale readings depending on your acceleration.

## On the AP Exam

Apparent weight shows up most often in multiple-choice questions built around an accelerating elevator. A standard stem gives you a passenger on a scale with the elevator accelerating upward, then asks for the scale reading or the ratio of apparent weight to true weight. For a 70 kg passenger accelerating up at 3.0 m/s², that ratio is (g + a)/g ≈ 1.3. Your job is always the same: draw the free-body diagram, write N - mg = ma along the vertical axis, and solve for N.

Watch for the less obvious versions too. On a frictionless incline, the apparent weight perpendicular to the surface is N = mg cos θ, not mg. In orbit problems, an astronaut moving under gravity alone has an apparent weight of exactly zero, and in an elliptical orbit the satellite's apparent weight stays zero everywhere because gravity is the only force acting. No released FRQ has used the phrase verbatim, but FRQs regularly require the underlying skill, which is correctly separating the gravitational force from the normal force in a second-law equation.

## apparent weight vs weight

Weight is the gravitational force mg, fixed by your mass and the local field. Apparent weight is the normal force from whatever supports you, and it's what a scale reads. They're equal only when your vertical acceleration is zero. Accelerate upward and apparent weight exceeds mg; fall freely and apparent weight drops to zero while your true weight never changes.

## Key Takeaways

- Apparent weight is the magnitude of the normal force on a system, which is exactly what a bathroom scale measures.
- Apparent weight equals true weight (mg) only when vertical acceleration is zero; otherwise N = m(g + a) for upward acceleration and N = m(g - a) for downward.
- Weightlessness means apparent weight is zero because the object is in free fall, not because gravity has disappeared.
- An orbiting astronaut has zero apparent weight even though Earth's gravity at orbital altitude is still close to its surface value.
- On an incline, the apparent weight perpendicular to the surface is mg cos θ, since the normal force only balances the perpendicular component of gravity.
- Every apparent-weight problem is solved the same way: draw the free-body diagram, apply Newton's second law, and solve for the normal force.

## FAQs

### What is apparent weight in AP Physics C?

Apparent weight is the magnitude of the normal force supporting an object, which is what a scale reads. It equals mg when the object isn't accelerating but differs from mg whenever there's vertical acceleration, like in an elevator or in orbit.

### Is an astronaut in orbit actually weightless?

No, not in the true sense. Earth's gravity at typical orbital altitude is still about 90% of its surface value, so the astronaut's true weight is nearly normal. Their apparent weight is zero because they and the spacecraft are in continuous free fall, so no normal force acts on them.

### What's the difference between apparent weight and true weight?

True weight is the gravitational force mg, set by mass and the gravitational field. Apparent weight is the normal force from a supporting surface. They split apart whenever you accelerate: N = m(g + a) accelerating upward, N = m(g - a) accelerating downward, and N = 0 in free fall.

### How do you calculate apparent weight in an elevator?

Apply Newton's second law to the person: N - mg = ma with up as positive, then solve for N. For a 70 kg passenger accelerating upward at 3.0 m/s², the apparent weight is m(g + a) ≈ 70(9.8 + 3.0) ≈ 896 N, about 1.3 times their true weight.

### Can apparent weight ever be greater than real weight?

Yes. Any time you accelerate upward (an elevator starting up, the bottom of a vertical loop, a rocket launch), the normal force must exceed mg to produce that acceleration, so your apparent weight is greater than your true weight.

## Related Study Guides

- [2.6 Gravitational Force](/ap-physics-c-mechanics/unit-2/6-gravitational-force/study-guide/CzrVgTyZ4BKEJNfh)

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