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True weight is the gravitational force acting on an object, measured when the object is at rest. Apparent weight is the normal force the scale reads, which changes when the object accelerates. In an accelerating elevator, apparent weight differs from true weight because the net force on the object is no longer zero.

When an elevator accelerates upward, the normal force from the scale must overcome both the gravitational force and provide the net upward force for acceleration. The scale reads this increased normal force as apparent weight, which is greater than the true weight of the object.

During downward acceleration, the normal force decreases because it only needs to partially support the object against gravity. The scale reads a lower apparent weight than the true weight. The net force on the object becomes negative, pointing downward as the elevator decelerates.

During free fall, both the object and the scale accelerate downward at gravitational acceleration. The normal force becomes zero because no support is needed. The scale reads zero, and the object experiences apparent weightlessness, even though gravitational force still acts on it.

According to newton's third law introduction, the force the object exerts downward on the scale equals the normal force the scale exerts upward on the object. At rest, these forces are equal in magnitude and opposite in direction, so the scale reading equals the true weight.

Yes, both involve apparent weightlessness. Astronauts in orbit and objects in a free-falling elevator experience the same phenomenon: they and their surroundings accelerate together under gravity. Although gravitational force acts on them, they feel weightless because they are in continuous free fall.

An object's apparent weight in water equals the difference between its true weight and the buoyant force acting upward. The buoyant force reduces the net downward force, making the object appear lighter than its true weight, similar to how downward acceleration reduces apparent weight.