This is valid for any shaped object where V is the volume. Notice that the total force from the air only one depends on the collision between the air molecules and the surface. It doesn’t matter what the ball is made of or what substance it is filled with. Only the volume is the problem.
Then why does a party balloon float but a basketball of the same size fall? It is concerned with whether the upward force is sufficient to overcome the force of gravity that is pulling the object downwards.
Let’s put some numbers. Assume both a basketball and a balloon have a diameter of 20 cm. Calculate mass and plug in Fair equation, I get an upward thrust of 0.049 Newton. That is Tiny.
But the rubber shell of the airship is thin, so the gravitational force is not very great. And if you fill it with helium, a gas with a lower density than air, you can compensate for the mass of the thin surface of the balloon and achieve equilibrium. If you can take the mass of the rubber plus the helium by the upward force, the balloon will float.
It doesn’t matter what you put in basketball; it will still fall. The rubber shell of a basketball is much thicker and heavier than the wall of the ball. The microscopic buoyancy force is essentially insignificant compared to the pull of gravity on an object of this mass, and it cannot overcome it. So the ball drops.
Build your floating hideout
Now let’s work on your super criminal lair. Ryan North claims that if you make a hollow metal sphere large enough, you can turn it into a secret floating base to use while trying to take over the world. Or maybe you just want to hang out there, I don’t know.
Is that really possible?
Let’s make a spherical object and see if it floats. Remember that for an object to float, its weight must be equal to the weight of the displaced air. For this object, it will have two parts — an outer shell and an inner gaseous part. The gas inside will have radius R and density & rho; ~ 1 ~. The shell has a thickness t with a density .2.
The first (and simple) thing to calculate is the buoyancy force. This depends only on the volume of the entire sphere, which has radius R + t. But if we get this super villain base, it will only work with a thin shell. That means we can say the radius of the whole thing is the same as the radius of the inner part(R).
