I know I’m wrong, but I can’t figure out why. Mind you, it’s been quite a few years since I took any form of science classes.
Take empty mylar balloon B. It has a mass, which multiplied by the “g” constant, gives us it’s weight.
Now fill balloon B with helium. The helium has mass, and the total of balloon+helium > balloon. Ergo, it weighs more. So why does the balloon float?
Well, if you don’t put enough helium in, it doesn’t.
It’s not like the stuff’s magic and put any amount into a balloon and it will float.
What you have to do is put enough of it in to counteract the weight you mentioned.
Think of it this way. If helium gas was visible and you just opened up the valve on that helium tank, you’d see all that gas heading straight up. Now all by itself those helium molecules have weight, so why are they going up?
Because air has more weight/density than helium does. So helium floats upwards till it reaches a balance point between gravity’s pull on its weight and the density of the other gases around it.
Ok… back to the balloon. You’ve captured this gas in an envelope of mylar, this ads considerable weight to the same volume of helium, but if you put enough helium into that envelope, it still wants to float upwards because the weight of the balloon is nothing near the weight of the big old tank of gas that you filled the balloon from. So if allowed to, the balloon would float up to a similar (if much lower due to the weight of the mylar) balance point.
Think of this in a similar manner to ordinary air in water. If you take that same mylar envelope, does it float if it’s totally empty? I’m not sure, maybe it settles to the bottom of the tub, but take a deep breath and exhale into that mylar envelope, and it will float right up to the surface.
-Doug
(I’m sure someone more versed in chemistry & physics will clarify the slight muddle I’ve made of density & weight)
From http://www.howstuffworks.com :
The law of buoyancy is more commonly called The Principle of Archimedes, in honor of the famous Siracusan, his discoverer. According to the anecdote, as he got inside the bathtub, the water overflew, and from this he inferred that his body had displaced an amount of volume equal to his submerged bodily parts, which, by virtue of its mass, was pushing him upwards. His higher density with respect to water summoned him downwards while forcing the fluid up and out of the tub. Overjoyed by this most exciting of analytic assessments, he stormed away and began shouting on the streets, clothes still off, Eureka! I have found it!).
Just to clarify a bit, the effect of weight and density on an object being submerged in a fluid are equivalent. The relevant criterion here is mass. For example, when the density of the submerged object surpasses that of the fluid it is displacing, it must be more massive since its volume is equal to that of the displaced fluid. From this it follows that the denser object will weigh more (W=mg), and thus the force of gravity will not only counteract but exceed the buoyancy force (equal to the weight of the displaced fluid) intending to drive the object upwards. Ergo, the submerged entity sinks. Invert roles, as in the case of helium, and the object goes up.
Thanks God for making farts lighter than air! 
The weight of the volume contained by the balloon+helium is less than the weight of the displaced volume of air. Therefore, the balloon floats. Buoyancy in action.
Just to throw a wrench in the works, remember that a helium balloon on the space shuttle doesn’t float to the “ceiling”- it just hovers, weightless, along with the astronauts. (This is assuming the shuttle is actually in orbit, of course).
Arjuna34
We had a thread on this several months ago. I pointed out that the force that pushes the balloon up is actually due to the pressure gradient induced by gravity (more pressure at bottom of balloon pushing up than the smaller pressure at the top pushing down, so the balloon goes up). Buoyancy IS due to the different densities of the filled balloon and the surrounding air, but it’s important to identify the origin of the force that pushes the balloon up.
In the space shuttle there’s no pressure gradient, since everything is in “free fall”, so there’s no force to push the balloon up, so it just floats.
It ocurred to me some years ago that you could make a balloon out of steel, if you evacuated all the air in it. Assuming you make it a centimeter thick, you can calculate how big it must be to displace its own weight in air. I seem to remember getting a diameter of a few meters, which was pretty neat. But then, you would need to support it from collapsing, which will add a considerable amount of weight.