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

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r-ruslan

3 months ago

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

th the weight mg of this much titanium.

Physics

1 answer:

ValentinkaMS [3.4K] · Answer 1 · 2026-02-23T13:50:10+03:00

1) The buoyant force acting on an object submerged in a fluid can be described as:
$B=d_f V_d g$
where $d_f$ indicates the fluid's density, $V_d$ represents the volume of the fluid displaced, and $g=9.81~m/s^2$ signifies the gravitational acceleration.

2) To determine the volume of the displaced fluid, we note that the titanium object is entirely submerged in the fluid (air), thus this volume matches the volume of 1 Kg of titanium, which has a density of $d=4.5~g/cm^3 = 4.5\cdot10^3~Kg/m^3$ . Using the correlation between density, volume, and mass, we derive
$V_d= \frac{m}{d}= \frac{1~Kg}{4.5\cdot10^3Kg/m^3}=2.22\cdot10^{-4}~m^3$

3) We can now revisit the equation in step 1) to compute the buoyant force. Given that the air density is $d_f = 1~Kg/m^3$ , this provides us with
$B=d_f V_d g=1~Kg/m^3 \cdot 2.22\cdot10^{-4}~m^3 \cdot 9.81~m/s^2=2.22\cdot10^{-3}~N$

4) The weight of 1 Kg of titanium is:
$W=mg=1~Kg \cdot 9.81~m/s^2=9.81~N$
Therefore, the buoyant force is negligible when compared to the weight.