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Is the floating MacBook Air real?

Hat tip to John Burk – @occam98 (of Quantum Progress) for sending a link to the following video:

I am calling my shots here like Babe Ruth. This one is fake. I haven’t even crunched one number yet, but I will. So, what is the physics here? This is all about forces and gases. Well, gases can exert forces. Let me go ahead and start with a force diagram for the floating balloon-macbook air system:

If the balloon-MBA is in equilibrium, then the net force must be the zero vector. This means that the magnitude of the gravitational force must be the same as the magnitude of the buoyancy force. Gravity you know. The magnitude of the gravitational force for the system can be written as:

Just to be clear, mgas is the mass of the gas inside of the balloon (if there is any). It is usually helium. Oh, that can’t matter, can it? Well, maybe it won’t.

Now for the buoyancy force. This is slightly more complicated. I say ‘slightly’ because who really understands gravity anyway? Basically, the buoyancy force is a result of collisions with the air and the system (both the MacBook Air and the balloon). Why does this result in an upwards forces? The key is that the density of the air changes with height. This is basically due to collisions of the gas with itself. Ok. Enough talk. The best way to think about the buoyancy force is to play with it. Fortunately PhET has an awesome simulation for this. If you have never used or heard of PhET, go there now. This is collection of free java and flash-based simulators that are for the most part made of pure and unprocessed awesomeness. Here is a screen shot of that particular simulation.

Buoyancy simulator from PhET



This principle can be written as the following formula:

Where ρ is the density of the stuff the object is in (in this case it would be air). V is the volume of the object.

Estimation of the floating MacBook Air

Now, let me calculate how big of a balloon filled with helium you would need to make the MacBook Air float. First, what is the mass of the MacBook Air? According to Apple’s site, it has a mass of 1.06 kg – oh, this is for the 11 inch model. It is not perfectly rectangular cubic, but if I make it bigger than it is, it has dimensions of 1.7 cm x 29.95 cm x 19.2 cm. This gives it a volume of 9.8 x 10-4 m3.

How about I just look at the MacBook Air. If it had no balloon, what would be the net force needed to keep it in equilibrium? Essentially, there are two forces acting on it – gravity and buoyancy. Even though it isn’t a balloon, it still has air pushing on it. I am just trying to be fair here. So, the force the string (that is attached to the balloon or whatever) on the laptop needs to be:

I went ahead and calculated this (which is essentially just the weight) because it doesn’t change. Now, how big of a balloon? First, let me go ahead and make an assumption in Apple’s favor. Let me assume that they have invented a super balloon material that has no mass. Yes, none. Also, somehow they managed to make the balloon stay at that size with nothing inside of it. It is just completely empty. Oh, it wouldn’t float you say? Remember, the helium doesn’t make it float. The helium keeps the balloon from collapsing under the pressure of the air. The awesome engineers licked that collapsing balloon problem. They had to so they could make this awesome display.

I know how much buoyancy force the balloon needs (it has no mass). This means that:

That volume is rather difficult to picture. Let me pretend that the balloon is spherical. This would give it a radius of:

So, at a very minimum (with ultra-super-secret Apple balloon technology) the balloon would have a diameter of 1.16 meters. Let me fix that picture of the floating MacBook Air with the minimum sized balloon.

Ok. That was fun.

Oh, but how does that display work? I really don’t know. It must be magic.