Apparent weight

Also called Effective weight

Apparent weight is the size of the supporting force acting on a system, which is what a scale under it reads. It differs from the gravitational force whenever the system accelerates or a fluid helps hold it up.

The CED is precise about this one. Essential knowledge 2.6.C.1 states that the magnitude of the apparent weight of a system is the magnitude of the normal force exerted on the system, and 2.6.C.2 adds that an accelerating system has an apparent weight different from the gravitational force on it. So apparent weight is a reading, not a new kind of force.

Take up as positive for a person of mass $m$ on a scale in an elevator with acceleration $a$ . Newton's second law gives $F_N - mg = ma$ , so the scale reads $F_N = m(g + a)$ with $g = 9.8\ \text{m/s}^2$ . Accelerating upward the reading climbs; accelerating downward it falls; in free fall $a = -g$ and it reads zero, which is EK 2.6.C.3 on apparent weightlessness.

The fluid version is the same accounting with one more force. An object hanging from a spring scale in water is held by the scale and pushed up by the buoyant force, so at rest the scale reads $mg - F_b$ . That difference is what the standard density experiment measures.

Neither version changes the gravitational force. Only the supporting force changes.

The normal force procedure is in How to find normal force.

Back to the physics glossary