Question

A spherical helium filled balloon is attached to a string that is fixed to the ground. the balloon has a volume of .30/4m^3 and helium has a density of .20 kg/m^3. What is the weight of the balloon and helium if the tension on the string is .8N?

Answer 1

V=0.3/4 m³
Helium ρ₁=0.2 kg/m³
Air ρ₂=1.33 kg/m³
the buoyant force F = ρ₂Vg
mg+T =F
W=mg = F-T = ρ₂Vg-T=
=9.8•1.33•0.3/4 – 0.8=0.978-0.8=0.178 N

Answer 2

But do I have to include He density in this equation at all?

Answer 3

If W₁ is the weight of helium and W₀ is the weight of balloon,
W=W₁+W₀
W₁ =m₁g= ρ₁Vg=9.8•0.2• 0.3/4 =0.147 N
Then
W₀=W-W₁ = 0.178-0.147=0.031 N