how do we measure the weight & mass of a balloon filled with helium?

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My intuition leads me to believe that the balloon would have negative weight? and I have no idea how we could measure the mass

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If you have access to a vacuum chamber, you could make it so the balloon won’t float and you can weigh it on a scale. You don’t need a full vacuum to achieve this. You could even fill the chamber with hydrogen, just needs to be less dense than the balloon.

Another way is to weigh an empty balloon, weigh a helium tank, then fill the balloon and add the difference in weight to the empty balloon weight and you have the weight of the filled balloon.

It’s not going to have negative weight and the buoyant forces pushing it upward are going to be greater than the weight so you cannot use that number directly.

You measure the negative weight, and compare it to the weight of air of the same volume. So you either have to do a multi-step experiment or you have to calculate the volume from the dimensions of the balloon (and then look up the density of air at your given pressure)

Well, yeah it would more or less have a negative weight, in that when you put something on a scale you normally neglect effects of buoyancy.

Strictly speaking it does have weight. Just that weight is being applied to the ground through the air it is sitting on top of.

Measuring it’s mass is less ambiguous though. At least with respect to what mass means. One way would be to calculate it indirectly. You can get the force from buoyancy by any number of methods, one silly one would be to flip a scale upside down and put the balloon under it.

Next you can measure the local absolute air pressure with a barometer and that gives you the density of the air.

After that you measure the volume of the balloon say by sinking it in a tub and measuring the amount of displaced water, or some other more accurate method that avoids compressing the balloon.

Now you have the volume and density of air displaced by the balloon, and the volume of the balloon. Since the bouyant force upward is a result of the difference in mass of displaced air and the mass of the balloon you can then calculate the mass of the balloon.

The negative weight is a function of bouyancy, and you can determine the mass by measuring the weight directly (which ends up negative) and then adding the weight of an equivalent volume of Air to that then apply the relavent gravitational constant to convert from weight to mass.

Alternately, you can compress a kniwn volume of helium into a non-elastic container (such as a steel tank) and measure how much the mass if the container changes.

The balloon does not have negative weight. The balloon rises because it’s *buoyant* – that is, it weighs less than the air around it, so the air around it can push it out of the way in order to sink. It’s no different from floating in water: something heavier than water can push it out of the way and sink, while something lighter than water gets pushed out of the way by the water and floats.

The weight (=force from gravity on the balloon itself alone) is still positive, but there’s another force that is greater than its weight, and the *total* force on the balloon points upward.

As for how you’d measure this force, the simplest way is to just attach a string to the balloon, let it rise until the string is pulled taut, and then measure the tension in the string.