This topic separates what gravity does from what a surface or scale measures. That distinction explains heavier or lighter feelings in elevators, floating in orbit, and why acceleration can imitate gravity.

Apparent Weight

Apparent weight is the quantity associated with what a person feels and what a scale reads. It is not automatically the same as the gravitational force.

In ordinary conditions on Earth, a person standing still has zero vertical acceleration, so the upward normal force equals the downward gravitational force. In that special case, apparent weight and gravitational force have the same magnitude, which is why they are often confused.

Apparent Weight in an Accelerating System

To find apparent weight, apply Newton’s second law to the object being supported, not to the floor or elevator around it.

This equation shows that the scale reading depends on acceleration. If the system accelerates upward, then $N>mg$ and the object feels heavier. If it accelerates downward, then $N<mg$ and the object feels lighter. If $a_y=0$, then $N=mg$, which includes both rest and constant-velocity motion.

A useful way to interpret common situations is:

Free-body diagrams comparing the gravitational force ($F_{grav}$) to the support force ($F_{support}$) across four cases, including perfectly weightless motion where $F_{support}=0$. The figure makes the key AP point explicit: the “heavier/lighter” feeling tracks changes in the contact/support force, not changes in gravity. Source

• Upward acceleration: apparent weight increases.

• Downward acceleration: apparent weight decreases.

• No acceleration: apparent weight equals gravitational force.

• Free fall: apparent weight becomes zero.

The sensation of heaviness or lightness comes from changes in the support force, not from gravity suddenly changing.

Weightlessness

Students often think weightlessness means there is no gravity. In AP Physics C, that is usually incorrect.

A system appears weightless when no force acts or when gravity is the only force acting. In both cases, there is no supporting contact force, so nothing pushes up on the object. As a result, a scale reads zero.

When Weightlessness Occurs

Several important cases produce weightlessness:

• Deep space with negligible forces: if no significant force acts, there is no normal force and no apparent weight.

• Free fall near Earth: gravity still acts, but the object and its surroundings accelerate together, so no support force is needed.

• Orbit: a spacecraft, astronaut, and loose objects inside all fall together under gravity, so they can float relative to one another.

In orbit, gravity is not absent. It is usually strong enough to keep the spacecraft moving in its curved path. The key idea is that gravity alone does not create a scale reading; a scale reading requires a contact force.

A common AP mistake is to say that astronauts are weightless because they are “beyond gravity.” The correct statement is that they are weightless because their apparent weight is zero.

Apparent Weight Versus Gravitational Force

The gravitational force on an object near Earth is $mg$. That force is exerted by Earth. Apparent weight, by contrast, is exerted by a surface or support. These are different interactions, even when they happen to have equal magnitudes.

This distinction matters whenever acceleration is present. In a falling elevator, the gravitational force remains essentially $mg$, but the floor no longer pushes up with the same force. If the elevator and person are in free fall together, the floor exerts no normal force at all, so the person’s apparent weight is zero even though Earth still pulls downward.

Illustration of the “falling elevator” thought experiment: when the elevator and passenger accelerate together in free fall, the floor does not need to push on the passenger. The absence of a support (normal) force corresponds to zero apparent weight even though gravity still acts. Source

Bathroom scales and spring scales respond to compression or tension caused by support forces. They therefore measure apparent weight, not gravitational force directly.

The Equivalence Principle

The equivalence principle links the physics of gravity and the physics of acceleration.

Imagine being inside a closed elevator with no view outside.

Schematic of a windowless elevator cabin resting in a gravitational field, representing the baseline scenario where objects fall “down” and a scale can read nonzero due to a support force. In the equivalence-principle comparison, this situation can be locally indistinguishable from a gravity-free cabin undergoing constant upward acceleration. Source

If the elevator is in deep space but accelerating upward, objects fall to the floor and a scale gives a nonzero reading. Those observations can match what would happen if the elevator were standing still in a gravitational field. Locally, acceleration can mimic gravity.

The reverse idea is equally important. If the elevator is in free fall near Earth, objects float relative to the elevator, and scales read zero. That local behavior matches what would happen in a gravity-free inertial environment. This is why free fall is the essential physical picture behind apparent weightlessness.

The word local is crucial. Over large regions, gravity can vary from place to place, producing effects that a uniformly accelerating frame does not reproduce exactly. For AP Physics C Mechanics, the key takeaway is that a person inside a small laboratory cannot always distinguish gravity from acceleration using only local mechanical experiments.

Solving Questions Efficiently

• Identify the object of interest.

• Draw only the external forces on that object.

• Recognize a scale reading as the normal force.

• Decide whether the system is supported, accelerating, or in free fall.

• Then use Newton’s second law to relate $N$ and $mg$.