# Why Isn't Weight Negative?

1. Sep 26, 2014

### logan3

I don't understand why the force of weight is always positive. Doesn't gravity point down, so isn't a = g = -9.8 m/s2? I understand that people always say it's because you can choose the positive and negative directions, but why change g to be positive in these weight situations and not in others?

Also, I'm really having trouble understanding this in elevator/scale problems, like when an elevator is moving up, but slowing down.

2. Sep 26, 2014

### A.T.

Force is a vector. It's magnitude is always positive. The sign of it's components depends on the chosen coordinates.

What don't you understand about a elevator moving up while slowing down?

3. Sep 26, 2014

### sweet springs

Hi.
Bubbles in water have negative mass in contrast to environment, the filled water. Bubble go upward inverse to gravity. It is a funny interpretation, isn't it?

4. Sep 26, 2014

### SteamKing

Staff Emeritus
No, it's sadly an incorrect one.

What do you mean by "Bubbles in water have a negative mass in contrast to environment, the filled water."?

A bubble is a bit of gas which has become trapped temporarily in a surrounding mass of fluid. The bubble rises because its mass is less than that of the volume of water which is displaced by the bubble. Ever hear of this guy Archimedes? It's the principle of buoyancy at work here, not some unicorn called 'negative mass'.

5. Sep 26, 2014

### FactChecker

You are making a good point. There is a choice of coordinate systems but they should all be right hand rule coordinate systems.

Example 1: There are a lot of cases where people use a "North, West, Up" coordinate system to identify positions. There are other cases where "North, East, Down" is used. So "Up" can be either positive or negative, depending on what the coordinate system is.

Example 2: In airplane flight dynamics, the usual body coordinate system is "nose, right wing, down". So "down" is positive. On the other hand, positions on the airplane are usually "tail, right wing, up" (the terminology is "fuselage station, butt line, water line"). In those coordinates, "up" is positive.

The value of 'g' is always stated as positive, but a negative sign must appear somewhere in the equations when needed. So the force of weight can be positive or negative, depending on the coordinate system being used. When you are working on a project, half the work is in keeping track of what mixture of coordinate systems is being used and converting from one to another.

Last edited: Sep 26, 2014
6. Sep 26, 2014

### DrDu

I don't think the example is so bad. E.g. in solid state physics it is customary to consider the holes as particles on it's own which obviously have an effective mass opposite to that of the particles that are missing.

7. Sep 26, 2014

### Staff: Mentor

It's a terrible example in the context of OP's question. The people who use this trick in solid state physics are already years past learning basic Newtonian mechanics; bringing it up in a thread in started by someone asking why weight is always positive can only lead to confusion.

8. Sep 26, 2014

### vanhees71

In addition, the holes in a Fermi sea treated as quasi particles in many-body quantum theory (which is quantum field theory in fact) have a positive mass as it should be ;-)).

9. Sep 26, 2014

### Philip Wood

When you answer questions about projectiles and so on, you should always state in which direction you are taking components. If you choose upwards for one of the components, then g is negative; if you choose downwards, g is positive. If you wish to work with the vector rather than its component, then you use a special symbol like g or $\vec{g}$.

Let's deal with upward components of vectors. Then the lift's velocity (component), v, is positive but $\frac{dv}{dt}$ is negative if the lift is slowing down. Thus the upward acceleration component is negative. In fact we could deal directly with the vectors themselves and say that the velocity is upwards but the acceleration is downwards. The latter is true because the change in velocity (final velocity – initial velocity) is downwards.

Last edited: Sep 26, 2014
10. Sep 26, 2014

### logan3

Ok, so I am correct in thinking that if I do the normal thing and have down be negative direction and up be positive, then g in weight problems would be negative, and thus weight would be given as a negative force? But the only reason the force of weight is positive in so many problems is because they choose down to be positive and thus g becomes positive?

11. Sep 26, 2014

### FactChecker

It's interesting, but I have to disagree for this reason: There is a clear way to set the value of 0 weight. When there are no other massive bodies around, that is 0 weight. In most usage on earth, weight is directly associated with mass. Breaking that relationship would be confusing. A gallon bucket of water under water would "weigh" nothing. Pulled half way out, it would "weigh" 4.17 lb. Pulled completely out of water, it would weigh 8.34 lb. That is one of the signs of the Apocalypse. oo)

12. Sep 26, 2014

### Philip Wood

But the only reason the force of weight is positive in so many problems is because they choose down to be positive and thus g becomes positive?

Exactly so.

Though, as pointed out earlier, to be strictly correct, weight itself is a vector so has a direction, but is neither positive nor negative. It's the upward component of weight which is negative, and/or the downward component which is positive.

13. Sep 26, 2014

### Staff: Mentor

I think that you have to be careful about what the variable "g" is referring to in a given context. More specifically, you need to know the type of mathematical object: vector, magnitude, or component.

If g is a magnitude, specifically the constant 9.8 m/s^2, then it is always positive. I think that this is the most common meaning.

If g is a vector then there is no such thing as positive or negative. It points down, but vectors don't have a "greater than" operation, so you cannot say that a vector is greater than 0 or not, so pointing down does not imply that it is negative.

If g is the component of a vector then it can be positive or negative depending on your coordinate system.

14. Sep 26, 2014

### logan3

Sorry, I don't understand this. A vector has magnitude and direction. The direction denotes whether it is positive or negative.

15. Sep 26, 2014

### A.T.

No, the direction determines which components of the vector are positive or negative. The vector as a whole doesn't have a sign.

16. Sep 26, 2014

### sweet springs

Force $$\mathbf{F}$$ is equal to product of weight or mass m and gravity acceleration $$\mathbf{g}$$. So $$\mathbf{F}=m \mathbf{g}$$. This relation holds for any axis you choose, upward, downward, even perpendicular, etc. When you choose upward axis $$\mathbf{g}$$ is expressed as negative coordinate. When you choose downward axis $$\mathbf{g}$$ is expressed as positive coordinate. When you choose perpendicular axis, it is expressed as a pair of coordinates. Vectors $$\mathbf{F}$$ and $$\mathbf{g}$$
have same direction because m is positive number.

Last edited: Sep 26, 2014
17. Sep 26, 2014

### logan3

I think I'm just getting more confused from this thread. People are all saying different things. Thanks anyways.

18. Sep 26, 2014

### Staff: Mentor

No, it doesn't. Is southeast positive or negative?

Vector spaces are not ordered sets.

19. Sep 26, 2014

### FactChecker

Sorry. I hope you have not given up. Maybe we can start back at the beginning.
It isn't. Always put things in terms of the coordinate system you are using. If the coordinate system you are using says that the direction down is positive, then the downward force of weight is positive. If the coordinate system you are using says that the direction up is positive, then the downward force of weight is negative.
Most people will define g as the positive number 9.8 m/s2. Then, when acceleration is calculated, the equation depends on whether positive direction is down or up. If the coordinate system says that down is positive then downward acceleration from gravity is positive and a = g. But if the coordinate system says that direction up is positive then the downward acceleration from gravity is negative and a = -g.
I would think of g as always being a positive number 9.8m/s2. It is used with or without a negative sign, as appropriate.for the coordinate system you are using. Either a=g or a=-g, depending on if you are using a coordinate system where down is positive or down is negative, respectively.

Always put things in terms of the coordinate system that you are using.
Suppose you are using a coordinate system where the direction down is positive. The elevator moving up means that its velocity is negative. The fact that it is slowing down means that its acceleration is positive.

Alternatively, suppose you are using a coordinate system where the direction up is positive. The elevator moving up means that its velocity is positive. The fact that it is slowing down means that its acceleration is negative.