Weight Force: Definition & Freefall Questions

[Freddy86]

Hi, I have been looking everywhere for an answer on what weight actually is so I joined the Physics Forum as it looks very promising. I have looked in many many places for a definition of the weight force and get completely different answers so I am now very very confused. All the textbooks I read along with websites seem to say that weight is the gravitational pull on a mass and is calculated as:

W = mg (it also acts down)

That was all fine until I watched an undergraduate MIT lecture where the professor said that weight is the reaction force from the ground. If there is no ground beneath you (freefall) then "your weight is zero by definition" is the lecturers exact words and he seemed very explicit about this being the true definition of weight. Wikipedia also states there are these two conflicting views of what weight actually is. These two definitions both have flaws along with the fact they contradict each other. If weight is the reaction force from the ground then free body diagrams must be wrong as the convention for these diagrams is that the weight force is acting down. On the other hand if weight really is the product of the gravitational field and mass then the notion that scales measure your weight must be completely wrong. For example, if you are in free fall with some scales attached to your feet then they will read zero which means your weight is zero according to MIT but how can it be according to W= mg as you still have g and you still have mass! So I guess my two main questions are:

1) When you are in freefall do you have weight or not?
2) Do scales really measure your weight? I ask this because if you are in freefall then according to W = mg you still have a weight but since the scales read zero then scales must surely not measure your weight by this definition.

If anyone can kindly help with my confusion I will be eternally grateful!

 

[voko]

All scales really just measure how far off equilibrium they are. They do not measure any force directly.

Now the question boils down to how the physical quantity they measure is related to "weight", whatever definition is being used.

 

[dauto]

W = mg (it also acts down)1) When you are in freefall do you have weight or not?

That depends

Within Newtonian physics weight is just a force and is indeed present during freefall. That level of understanding is enough for the vast majority of applications.

Withing Einstein's relativity theory the weigh isn't a force at all and is indeed indistinguishable from the apparent force that you get when you are inside of a moving reference frame. - For instance, when inside of an accelerating car, you feel what seems to be a force pushing you back into your chair.

Either way, what the MIT professor was probably talking about was the more prosaic fact that scales don't really measure the weight of objects, measuring instead the contact force of the object on the scale's surface. If the object is standing at rest on a horizontal scale surface, those will be indeed numerically identical, but that will not be the case in more complex situations. Try standing on a bathroom scale on a incline.

 

[Doc Al]

Hi, I have been looking everywhere for an answer on what weight actually is so I joined the Physics Forum as it looks very promising. I have looked in many many places for a definition of the weight force and get completely different answers so I am now very very confused. All the textbooks I read along with websites seem to say that weight is the gravitational pull on a mass and is calculated as:

W = mg (it also acts down)

That's the standard definition (at least in most textbooks, as you note) and the one I recommend you use. (Especially in Newtonian physics.)

That was all fine until I watched an undergraduate MIT lecture where the professor said that weight is the reaction force from the ground. If there is no ground beneath you (freefall) then "your weight is zero by definition" is the lecturers exact words and he seemed very explicit about this being the true definition of weight.

That definition of "weight" is usually called apparent weight. And the standard definition, the Earth's gravitational force on a object, is sometimes called the true weight.

Wikipedia also states there are these two conflicting views of what weight actually is. These two definitions both have flaws along with the fact they contradict each other. If weight is the reaction force from the ground then free body diagrams must be wrong as the convention for these diagrams is that the weight force is acting down. On the other hand if weight really is the product of the gravitational field and mass then the notion that scales measure your weight must be completely wrong. For example, if you are in free fall with some scales attached to your feet then they will read zero which means your weight is zero according to MIT but how can it be according to W= mg as you still have g and you still have mass!

The two definitions refer to entirely different things--they cannot be used interchangeably.

So I guess my two main questions are:

1) When you are in freefall do you have weight or not?
2) Do scales really measure your weight? I ask this because if you are in freefall then according to W = mg you still have a weight but since the scales read zero then scales must surely not measure your weight by this definition.

I think you know the answers already!

(1) If you use the standard definition (weight = mg) then of course you have weight when in free fall--the Earth is still exerting a gravitational force on you. (Note that the term "weightless" refers to that second definition, the apparent weight not the true weight.)

(2) A scale (a spring or strain scale, such as a bathroom scale) essentially measures the force exerted on it. It does not measure the force of gravity directly. But as long as you are not accelerating, both the apparent weight measured on the scale will equal your true weight.

 

[Freddy86]

That's the standard definition (at least in most textbooks, as you note) and the one I recommend you use. (Especially in Newtonian physics.)


That definition of "weight" is usually called apparent weight. And the standard definition, the Earth's gravitational force on a object, is sometimes called the true weight.


The two definitions refer to entirely different things--they cannot be used interchangeably.


I think you know the answers already!

(1) If you use the standard definition (weight = mg) then of course you have weight when in free fall--the Earth is still exerting a gravitational force on you. (Note that the term "weightless" refers to that second definition, the apparent weight not the true weight.)

(2) A scale (a spring or strain scale, such as a bathroom scale) essentially measures the force exerted on it. It does not measure the force of gravity directly. But as long as you are not accelerating, both the apparent weight measured on the scale will equal your true weight.

Thanks to all for taking the time to reply. I understand what you mean by apparent weight and true weight. This is the approach my textbook uses and the one I think I will adopt. However, having watched the lecture again he definitely doesn't talk about apparent weight, he talks about the force exerted up on you by the scales as the definition of weight. He seems to say that whatever a scale reads is by definition your weight. In other words during free-fall you have no weight. Here's the link for anyone who is interested , he defines weight in the first couple of minutes of the lecture. I even watched some of his lectures on incline planes where he draws free-body diagrams to see if he labels the downward force mg as weight and he doesn't, he always labels it as the force of gravity. Whereas my book always labels the downward force for incline plane problems as weight (W).

 

[dauto]

It seems he is using a non standard definition of weight which is OK as long as he remains consistent. I don't like this particular choice of definition though. It's quite unconventional.

 

[jtbell]

As I recall, Paul Hewitt also uses this non-conventional definition of weight ("what the scale reads") in his textbook Conceptual Physics. If I had the power to re-make "conventional introductory classical mechanics" from scratch, I'd use this definition because I like it better than the conventional definition of "weight" as a synonym for "gravitational force." If they're synonyms, why bother with both of them?

However, I don't have the power to do this, so I when I teach introductory physics, I stick with the current convention.