1) The buoyant force acting on an object immersed in a fluid is:
[tex]B=d_f V_d g[/tex]
where [tex]d_f[/tex] is the density of the fluid, [tex]V_d[/tex] is the volume of displaced fluid, and [tex]g=9.81~m/s^2[/tex] 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 [tex]d=4.5~g/cm^3 = 4.5\cdot10^3~Kg/m^3[/tex]. Using the relationship between density, volume and mass, we find
[tex]V_d= \frac{m}{d}= \frac{1~Kg}{4.5\cdot10^3Kg/m^3}=2.22\cdot10^{-4}~m^3 [/tex]
3) Now we can recall the formula written at step 1) and calculate the buoyant force. The air density is [tex]d_f = 1~Kg/m^3[/tex], so we have
[tex]B=d_f V_d g=1~Kg/m^3 \cdot 2.22\cdot10^{-4}~m^3 \cdot 9.81~m/s^2=2.22\cdot10^{-3}~N[/tex]
4) The weight of 1 Kg of titanium is instead:
[tex]W=mg=1~Kg \cdot 9.81~m/s^2=9.81~N[/tex]
So, the buoyant force is negligible compared to the weight.
