PHYSICS DOUBT - When we are in an elevator, then..

Question

It is said that when we move up in an elevator, then our weight increases, but acc. to this - F=GMm/r^2, Our distance or r would be increasing, and F is inversely proportional to r, so shouldn't it be decreasing rather than increasing??

Answer 1

If you are going up at constant velocity, then you are in an inertial frame and all the physics will be the same - in which case you are correct. When people say you "weigh more" in an upwardly accelerating elevator, it is because you are in a non-inertial (not const v) frame and inside this frame you will feel a force = ma in the opposite direction to the acceleration. You actually can't tell that this force isn't just due to the gravitation increasing to a new value of g+a. You can look at it from the point of view of an observer: Normal force -mg = ma which means the normal force = mg + ma. A scale underneath the person measures the normal force. The Universal law of gravitation is unnecessary if you are near the earth's surface and the acceleration can easily overcome the 1/r² dependence of the force.