Question

A scientist plans to release a weather balloon from ground level, to be used for high-altitude atmospheric measurements. The balloon is spherical, with a radius of 2.10 m, and filled with hydrogen. The total mass of the balloon (including the hydrogen within it) and the instruments it carries is 24.0 kg. The density of air at ground level is 1.29 kg/m3. (a) What is the magnitude of the buoyant force (in N) acting on the balloon, just after it is released from ground level

Answer 1

Fb = 490.4 N

Step-by-step explanation:

• According to Archimedes' principle, any object submerged in a fluid, receives a push upward (which we call buoyant force) equal to the weight of the volume of the fluid removed by the object.
• We can express this force (Fb), in terms of the density and the volume of the fluid, as follows:

`F_(b) = \rho * V * g (1)`

• The volume removed from the fluid by the balloon is just the volume of the balloon, assuming that it is a perfect sphere, as follows:

`V = (4)/(3)*\pi * R^(3) = (4)/(3) *\pi *(2.1m)^(3) = 38.8 m3 (2)`

• Replacing by the givens and (2) in (1), we get:

`F_(b) = \rho * V * g = 1.29 kg/m3* 38.8m3*9.8m/s2 = 490.4 N (3)`