Apparent Weight

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Apparent Weight: Person on Scale in Elevator
A person with mass, m, who is located at or near the surface of the Earth will always have some weight W=mg. When a person stands on a scale, the reading (the number of pounds or newtons) on the scale is actually the Normal Force that the scale exerts back towards the person to support the person's weight. (Note that the person and the scale are stationary relative to each other, in other words they are always in contact with each other, so they always have equal and opposite action and reaction forces acting between them.) Things get complicated, though, when the scale and the person experience acceleration. This will change the contact force (the Normal Force) between the person and the scale. Let's look at several cases. We will assume that Up is the positive direction and Down is the negative direction. Case 1: No acceleration of elevator If the acceleration of the elevator is zero, then there are two possible scenarios; the elevator can be at rest (stationary, zero velocity) or moving with a constant speed (no acceleration if velocity does not change). In this case, the action and reaction force pair between the person and the scale is just the weight. The person pushes down on the scale with a force of -W=-mg (negative direction) and the scale pushes back up against the man with a Normal Force of FN = +W = +mg. Because the reading on the scale is the magnitude of the normal force, the scale will read the true weight when the elevator is NOT accelerating. Case 2: going up & speeding up (acceleration a is positive (up)) In this case, the elevator and the person are starting from rest at a lower floor. The elevator accelerates upward. The inertia of the person would prefer to stay stationary, so the elevator floor and scale must push up on the person to accelerate him upward along with the elevator. (The person doesn't sink into the floor when the elevator accelerates up. The elevator and the scale and the person...
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