Then last night I had a dream about buoyancy that my students and I had discussed recently while reviewing. It could have been just a coincidence, one of the brain’s memory-housekeeping functions twinkling in our sleep.
If you tie a bunch of grapes to a helium balloon, one of three things can happen: if they’re light enough, the balloon will still rise. Too heavy, and they’ll sink. But if their combined weight(with that of the balloon and string) is equal to the buoyant force, the assembly will just be suspended in midair.
In my dream I was suspended from a balloon like grapes. (Ironically, my surname means grapes in Italian.) Along with a newspaper reporter we were floating above traffic. In reality the tension in the straps around by torso would have to counter the weight of my body, but in the dream they weren’t perceptible. Besides, the floating reporter was far prettier than the balloon, so I never noticed it. But being a married teacher, instead of dwelling on her, I should calculate the volume of the balloon.
Fbuoyant = Fgravity
mair*g = mload*g + mHe*g
The g which equals gravitational acceleration cancels:
mair= mload + mHe
If we express mass as the product of volume and density, then:
V*dair = mload + V*dHe , where V= balloon’s volume + load’s volume.
Rearranging the equation, we get:
V = mload/(dair-dHe).