College Physics II – Mechanics, Sound, Oscillations, and Waves
Definition
Apparent weight is the normal force exerted by a surface on an object, which can differ from the object's true weight due to acceleration. It may be perceived differently in scenarios like elevators or free-fall.
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Apparent weight equals true weight when an object is at rest or moving with constant velocity.
In an elevator accelerating upwards, apparent weight increases because the normal force must counteract both gravity and the additional upward force.
In free fall, apparent weight is zero because there is no normal force acting on the object.
Apparent weight can be calculated using $F_N = m(g + a)$ for upward acceleration and $F_N = m(g - a)$ for downward acceleration, where $F_N$ is the normal force, $m$ is mass, $g$ is gravitational acceleration, and $a$ is the acceleration of the system.
Changes in apparent weight are due to non-inertial reference frames where Newton’s laws need to be modified by including fictitious forces.
Review Questions
How does apparent weight change when an elevator accelerates downwards?
What happens to apparent weight during free fall?
How do you calculate apparent weight in an accelerating system?
Related terms
True Weight: The gravitational force exerted on an object, equal to mass times gravitational acceleration ($mg$).
Normal Force: The perpendicular contact force exerted by a surface on an object in response to its weight.
Free Fall: The motion of an object under the influence of gravitational force only, experiencing zero apparent weight.