posted by Taylor on .
An empty rubber balloon has a mass of 0.012kg. the balloon is filled with helium at 0 degrees celcius, 1 atm pressure, and a density of 0.179 kg/m3. the filled balloon has a radius of 0.5 m.
a)what is the magnitude of the buoyant force acting on the balloon?
b)what is the magnitude of the net force acting on the balloon?
(a) air density x volume
(If you want it in Newtons, also multiply by g)
(b)net force = balloon weight (empty) + helium weight - buoyant force
= balloon weight (empty) -(air density - helim density)*Volume
The net force on balloon = the buoyant force (acts upward) minus the weight (downward)
The weight of helium filled balloon is:
volume of a sphere of radius = 0.5 m = 4/3πR³ = (4/3)(3.14)(0.5)³ = 0.523 m³
density of helium (at 0° and 1 atm) = 0.179 kg/m³
mass of helium in balloon = (0.179)(0.523) = 0.0937 kg
mass of rubber in balloon = 0.0120 kg
total mass of helium filled balloon = 0.0937 + 0.0120 = 0.1057 kg
total weight of helium filled balloon = (0.1057)(9.81) = 1.04 N
Accepting UR value of 6.62 for the buoyant force, the Net force is:
Net force acting on balloon = 6.62 (upward) - 1.04 (downward) = 5.58 N (upward) ANS