Calculate the buoyant force in air on a kilogram of titanium (whose density is about 4.5 grams per cubic centimeter). compare with the weight mg of this much titanium.

1) The buoyant force acting on an object immersed in a fluid is:

where  is the density of the fluid,  is the volume of displaced fluid, and  is the gravitational acceleration.

2) We must calculate the volume of displaced fluid. Since the titanium object is completely immersed in the fluid (air), this volume corresponds to the volume of 1 Kg of titanium, whose density is . Using the relationship between density, volume and mass, we find


3) Now we can recall the formula written at step 1) and calculate the buoyant force. The air density is , so we have


4) The weight of 1 Kg of titanium is instead:

So, the buoyant force is negligible compared to the weight.