# helium balloons

I think a helium-filled balloon has negative weight; my coworkers disagree. We consulted a dictionary which stated that weight is a function of force directed towards earth due to gravity. I believe this confirms my theory. Any physicists or know-it-alls out there?

A helium baloon does not have negative weight, it is just that the air around the balloon weighs more. If you put a helium balloon in a vacuum chamber (you’d need a fairly rigid baloon so it didn’t pop when introduced to the vacuum) you would indeed get a positive weight. Helium has a positive weight, it’s just that the air around the helium has a more positive weight, making the balloon rise. There is a downward force on the balloon caused by gravity, which is all that qualifies for something to have “weight.” Your coworkers are correct. Sorry to break the news to you.

Your balloon still has weight, only the atmosphere it displaces weighs more. Weigh it in a vacuum - very tricky as Jayron said - or in a helium atmosphere and you have a different basis for measurement. Is an aircraft carrier weightless because it floats on water?

i thought i remember reading that mass remains constant but weight varies with the medium and gravitational force. you weigh less in water or on the moon. again, my physics is sketchy so i could be confusing my terms and definitions.

Well, you can define weight as the net foce on an object due to weight and buoyancy combined, as long as you’re consistent with it. The problem with this is that by this definition, any surface ship has exactly zero weight, which most folks don’t like. If you want a consistent definition, and you want the USS Eisenhower to weigh anything, you’ve got to ignore buoyancy.
On the other hand, weight does depend on the local graviational field, so objects truly do weigh less on the Moon than on the Earth. You can also choose whether to include fictitious forces due to acceleration, so, for instance, you might say that a pilot in a fighter jet undergoing maneuvers can weigh up to ten times normal.

You people gotta be kidding! So any body that is not falling has no weight? A balloon is supported by the air, a ship (including submarines) is supported by the water and my butt is supported by the chair. What difference does it make? Weight is defined as the force with which the Earth attracts the body (regardless of how or even if the body is supported).

again, the definintion of weight that i had read was specifically a force directed towards earth. sailor’s argument seems logical but i’d like to know the source of that weight definition. the difference between the chair and the water/air is that you can put a scale under the chair and measure the increase in weight due to the person sitting on top of it. adding objects to a body of water or air increases the pressure if the medium is in an enclosed container or else it displaces the medium. you can do the math and determine the mass of the object in question, but not the weight.

Zwaldd, your argument that things do not have weight unless you can measure it is similar to the question of weather a tree that falls makes a noise if there’s no one there to hear it. Let’s get real. You can not put a scale under my house to see how much it weighs. You can weigh my small boat very easily. Are you telling me it no longer weighs after it’s afloat? Don’t be silly. When it is on land it is the ground that supports the weight and when it is in the water, it is the water that supports the weight.

The definition of weight as the force with which the earth attracts a body is from any elementary book of physics. Your definition of weight would only be acceptable in a very colloquial sense and is, strictly speaking, wrong.

Websters:
the force with which a body is attracted toward the earth or a celestial body by gravitation and which is equal to the product of the mass and the local gravitational acceleration.

As for the OP, negative weight is WRONG. Anything else is playing with words.

consider the following: two closed cardboard boxes, one is empty, one contains a large helium filled balloon. put them on a scale. which box weighs more? forget about the scale. pick them up - which one is lighter? what if you didn’t know what was inside? if you said that one box weighed less than the other, then all other things equal, the contents of the box would have to have negative weight. again, i’m just throwing out arguments that don’t quite jibe with what i’m hearing. any physicists out there?

The contents of the box do not have to have negative weight. The contents of the “empty” box weigh more than the contents of the box with the balloon in it. The air that fills the “empty” box weighs more than the air and the helium balloon in the other box. That explains why the box with the balloon weighs less without resorting to negative weight for an explanation.

Weight is normally defined as in any other mechanical force:
F=ma, or weight = mass x acceleration. In the normal case, the mass is the mass of the object, and the acceleration is the acceleration due to gravity (32ft/s^2 on earth). This lets you figure out useful stuff such as how fast something will fall when dropped. Naturally, ideal conditions are assumed: negligible air (or other fluid) resistance, no buoyancy effects, etc.

This isn’t a very useful definition where buoyancy take place- underwater, or with lighter-than-air materials. Obviously the MASS stays the same, and so does the weight if you still call it mass x 32ft/s^2. If you were underwater all the time I could see where a new weight definition would be more useful.

I can see a use for negative weights for helium balloons also. Lets say I have a 6’ helium balloon that can just barely suspend a 30lb weight. I’d call the weight of the balloon -30lbs. If I add a 40lb weight and put the whole thing in a box, the box will act like a 10lb weight (with 40lbs of inertia (ignoring the fact that pounds are not a unit of mass).

The bottom line is that the weight of an object depends on the surroundings (on earth, the moon, in space, underwater), while the mass stays the same.

Arjuna34

Whoa! Hold on… I said that you could define weight as including buoyancy, not that you should. You can define anything any which way you want, as long as you’re consistent. Some definitions, however, are a lot more useful than others.

On the other hand, I’m sticking by my guns in including fictitious inertial forces with the gravitational field. After all, as any relativist knows, gravity is a fictitious force, itself

gravity is a fictitious force

Yeah, it was invented by the elevator industrial complex to force us to buy their products which are totally unnecessary.

>> You can define anything any which way you want

Sure you can. Next time you pay a bill hand them a \$1 and tell them you have “defined” it as \$20.

Look this is getting to be kind of silly. Would you say an airplane in flight has no weight? I mean you can say it if you like and you can define things whichever way you want but in the world the rest of us live in that is just wrong.

A balloon, an airplane, a nuclear sub, my boat and my butt all have weight and they are supported by upwards forces. Whether these forces are caused by solids or by static fluids or by dynamic forces of accelerating fluids is immaterial. Those bodies do not lose weight.

If you want to lose weight you must (A) get a few million miles away from Earth or (B) work out more and eat less.

And defining the bill with George’s face on it as a twenty would be a good example of a definition with very litte usefulness. I wouldn’t use that definition, nor would I use a definition of “weight” by which an airplane or battleship is weightless, because, as you rightly point out, to do so would be silly.

I didn’t suggest that airplanes or battleships have a more useful definition of “weight” than the normal one, but I do believe there are situations imaginable where the mass x 32ft/s^2 definition could be discarded for something else.

Do we all agree that “weight” is the force from gravity that pulls an object towards the center of the earth? (And I DON’T want to start the “which way is down” thread again!)
If so, weight is defined by F=ma. Obviously, mass remains constant no matter what the situation is, for a given object. Since you’re trying to figure out F (the weight), all you can do is measure a by dropping something and measuring the acceleration (using an appropriately shaped object to minimize drag, etc., especially underwater). If you do that, you’ll a different number underwater for most things, due to buoyancy. What’s wrong with that? If I know the object’s mass, and measure its acceleration, I know the force acting on it, which IS the weight. The net force acting on the object really is what you measure this way, so who cares what the “weight” would be if you assume 32ft/s^2?

I’m not saying the mass is different- a submarine at neutral buoyancy underwater could have zero weight by the above definition, but thousands of tons of mass, so you’d still need large forces to move it.

Of course, as others have said, you can define weight anyway you want. There are problems with just blindly measuring acceleration and computing the weight- for example, underwater, you’d get different weights for two objects with the same mass, if they had different densities. Is that a feature or a bug?

Arjuna34

Arjuna34:

No, no, no, no, no, no and no! My goodness this is tenth grade stuff! Ask your children for goodness sakes!

A submarine (like anything else) falling freely in a vacuum would accelerate with 1g

If it does not move it is because the buoyancy exactly compensates the weight force. The resulting force is zero. If the resulting force is other than zero the body will move.

How many times do we need to repeat this? If a body is not falling it is because there is a force counteracting the force of it’s weight.

My weight pulls me down, the chair pushes me up, result: I don’t move.

Well, I’ve done my best to explain it. At this point I think I should probably give up.

sailor, I don’t disagree with anything you said, and I don’t see how what I said contradicts you.

Of course if a body isn’t falling, it’s because a force is counteracting the force of gravity. Where in my posts did I suggest otherwise?

All I was suggesting is that there could be a more useful definition of “weight” in some enviroments, such as underwater. We’re not disagreeing on what is physically happening (fortunately, I’ve made it through 10th grade physics, so I don’t need to consult a 10th grader). I didn’t say the neutral-buoyant sub doesn’t sink because it has zero weight, I said that because it doesn’t sink, perhaps it should be labeled “zero weight”. I still claim that it can be useful to distinguish these two cases:

1. You sit on a chair- you’re not falling because the chair is exerting a force equal and opposite to the force of gravity on you. Note for future reference in #2 that the weight of the chair (the object exterting the counteracting force) doesn’t matter here.

2. You are suspended in the water, with a weight belt. You don’t move in the water because the water is exterting a force equal and opposite to the force of gravity on you and the weight belt. Here, I claim an argument can be made for calling this “zero weight”. I’m NOT saying you have zero mass, or that the “one and only true weight of mass x 32ft/s^2” is zero, just that I could define a potentially useful quantity analogous to “weight” that would be zero in this case. Maybe I should call it “local weight”, or “relative weight”, to distinguish it from the “true weight”.
One difference between this case and #1 is that the weight of the water (caused by gravity) is what’s exerting the opposing force, as distinguished from #1. This may help you in discovering the difference between a submarine at neutral buoyancy and a submarine sitting on land.

I think we’re starting to get hung up in semantics here, since we obviously know what is actually happening in each case- it’s just a matter of definitions.

Well as long as we are playing with words and making up definitions let me ask you these questions:

Any body at rest, let’s concentrate on the vertical forces and ignore the other two axis.

My definition of weight is the force with which the earth attracts the mass of the body which, since the body is at rest, must be exactly balanced by other forces. These other forces can be of three types: solid (tension or compression), static fluid forces or reaction (eg: jet)

Your definition of “weight” would be the force with which the earth attracts an object minus the vertical force provided by static fluid forces. How about the reaction forces? Do we include or exclude those?

Now, a ship that is in a drydock which is being pumped dry… is it gaining weight as the support is transferred from the water to the dock? I don’t think so

Yes you can make your own definition of weight but that is not the commonly accepted definition of weight. I do not think you will find any science text that will support your definitions. Or can you cite one?

The OP asked if a balloon can be said to have “negative” weight and the answer is NO. If your answer is “yes if you want to define it that way” then it is meaningless. Of course you can never lose a bet like that because you just make up your own definitions.

That definition is, of course, wrong.

Oops, forgot the smiley

Your definition is in opposition to the dictionary definition of weight that you gave earlier.