What is the difference between apparent weight and true weight in elevators?

[AlexandraMarie112]

Homework Statement

Hi everyone,I just want to know if my answers are correct.

Homework Equations

The Attempt at a Solution

1. For each situation, indicate whether the normal force exerted on you will be gater tha,less than or equal to your true weight.

a) Elevator starts to move down from the top floor n<w
b)Elevator moves down between floors with a constant speed n=w
c)Elevator moving down slows down at bottom floor n>w
d) Elevator starts to move up from the bottom floor n>w
e)Elevator moves up between floors with a constant speed n=w
f)Elevator moving up slows down at the top floor n<w 2. In what direction is the elevators velocity in the case when the normal force acting on you is less than the weight force? Downwards

In what direction is the elevators acceleration in the case when the normal force is less than the weight force? Downwards

 

[Efrain Garcia]

Actually, they would always be equal. Weight is the force of gravity acting on mass, so as the elevator goes down, the normal force decreases, but so does your weight. They will always be in balance. I think what he meant was not weight, but mass. Mass doesn't change, as it is a measure of "stuff" something is made of. In that case, the work seems about right.

 

[TSny]

Weight is the force of gravity acting on mass, so as the elevator goes down, the normal force decreases, but so does your weight.

The force of gravity (weight) acting on a mass is the attractive force which the Earth exerts on the mass through gravitational interaction. The force of gravity on the mass does not depend on whether or not the mass is moving. If you throw a baseball upward, the force of gravity acting on the ball is the same whether the ball is moving upward, instantaneously at rest at the top of the flight, moving downward, or sitting on the ground after it lands.

 

[TSny]

1. For each situation, indicate whether the normal force exerted on you will be gater tha,less than or equal to your true weight.

a) Elevator starts to move down from the top floor n<w
b)Elevator moves down between floors with a constant speed n=w
c)Elevator moving down slows down at bottom floor n>w
d) Elevator starts to move up from the bottom floor n>w
e)Elevator moves up between floors with a constant speed n=w
f)Elevator moving up slows down at the top floor n<w

Your answers to 1 look good.

2. In what direction is the elevators velocity in the case when the normal force acting on you is less than the weight force? Downwards

Is this answer in agreement with all of your answers to 1?

In what direction is the elevators acceleration in the case when the normal force is less than the weight force? Downwards

Yes.

 

[Efrain Garcia]

The force of gravity (weight) acting on a mass is the attractive force which the Earth exerts on the mass through gravitational interaction. The force of gravity on the mass does not depend on whether or not the mass is moving. If you throw a baseball upward, the force of gravity acting on the ball is the same whether the ball is moving upward, instantaneously at rest at the top of the flight, moving downward, or sitting on the ground after it lands.

That can't be correct. If you step on an elevator and stand on a scale, then the elevator goes down, the scale will register LESS weight. And this is where points of reference come in. If you take the point of view of the baseball, and not that of an outside observer, the force of gravity acting upon you IS different. It decreases and increases depending on what point of the arc you are in. Similarly, if you are inside an elevator, that means the only point of reference you have is inside the elevator. That being the case, the force you feel does change.

 

[AlexandraMarie112]

Your answers to 1 look good.

Is this answer in agreement with all of your answers to 1?

Yes.

So for my question 2 , it would be upwards and downwards?

 

[TSny]

If you step on an elevator and stand on a scale, then the elevator goes down, the scale will register LESS weight.

Yes, but the scale is not measuring the force of gravity acting on you. The scale reads whatever force is pushing on the scale. This force that you are pushing on the scale is called the "normal force". Sometimes the reading of the scale is called the "apparent weight". But this is not the force of gravity.

And this is where points of reference come in. If you take the point of view of the baseball, and not that of an outside observer, the force of gravity acting upon you IS different. It decreases and increases depending on what point of the arc you are in.

This is not true. Why would the Earth attract the baseball differently while it is moving upward compared to moving downward?

Similarly, if you are inside an elevator, that means the only point of reference you have is inside the elevator. That being the case, the force you feel does change.

The force you "feel" in an elevator is not the force of gravity. You feel the force that the floor of the elevator pushes upward on you. Again, this is the "normal force".

 

[TSny]

So for my question 2 , it would be upwards and downwards?

Yes, the direction of the velocity could be upward or downward. Would it also be possible to have n < W when the elevator has zero velocity?

 

[Efrain Garcia]

Yes, but the scale is not measuring the force of gravity acting on you. The scale reads whatever force is pushing on the scale. This force that you are pushing on the scale is called the "normal force". Sometimes the reading of the scale is called the "apparent weight". But this is not the force of gravity.
This is not true. Why would the Earth attract the baseball differently while it is moving upward compared to moving downward? The force you "feel" in an elevator is not the force of gravity. You feel the force that the floor of the elevator pushes upward on you. Again, this is the "normal forcce".

What is the difference, really? To the observer in the elevator, the force of gravity does change. If you are an observer outside the elevator, then you could say the attraction of gravity is the same, but both would be correct. I guess it just comes down to Newtonian v Einsteinian definitions of "gravity". For example, if you replaced that ball with an elevator, and pretend you are in it, you will experience a greater amount of force, then you would feel a normal amount of force, then you would feel less as the ball dropped back. As your weight increases and decreases, so will the normal force. And if your weight increases and decreases, that must mean that the net forces acting on you are influencing one another. While you could say the force of gravity stays the same, and you would be factually correct, that is not what is experienced inside the elevator. As for the scale, the scale is reading weight, so it is solely influenced by "gravity". The normal force is what counteracts whatever force gravity and other factors are presenting.

 

[TSny]

Efrain,
The usual interpretation, in Newtonian mechanics, of "the force of gravity" on an object near the Earth is that it refers to the attractive action-at-a-distance force that the Earth exerts on the object. It is equal to mg where m is the mass of the object and g is the acceleration of gravity (which has a fixed value near the surface of the earth). The value of mg does not depend on the motion of the mass m. The force of gravity is also called "weight"; or, sometimes "true weight" when distinguishing it from "apparent weight" (e.g., scale reading in the elevator).

In general relativity, "force of gravity" no longer has a definite meaning. But I believe that the problem stated in post #1 is given in the context of Newtonian mechanics.

 

[vela]

So for my question 2 , it would be upwards and downwards?

According to your answers to #1, you can also have n>w when the elevator is going up or when it's going down.

So what do you suppose is the point of the questions in #2? What are they trying to get you to realize?

 

[Orodruin]

If you step on an elevator and stand on a scale, then the elevator goes down, the scale will register LESS weight.

This is true only in the accelerating phase. When the elevator decelerates in order to come to a halt the scale will register more weight and when the elevator travels at constant velocity it will register the same weight, even if the elevator is going down. The direction of acceleration is what is important, not the direction of motion.

 

[David Lewis]

The force of gravity is also called "weight"; or, sometimes "true weight" when distinguishing it from "apparent weight" (e.g., scale reading in the elevator).

That's correct. Both definitions are acceptable but may yield different answers. For example, an astronaut in orbit is weightless only under the apparent weight definition. Most problems want you to assume the force of gravity definition unless otherwise specified.