A helium balloon has a volume of 0.003m^3. What is the force on the balloon if it’s surrounded by air? (

Question

note: density of helium is 0.2 kg/m^3, and the density of air is 1.2 kg/m^3.

i used 9.8 for gravity, and i got the Fnet to be 3.92x10^-3 N, but i’m not sure!

Answer 1

I'm coming up with a different answer: F_net = 2.94 × 10^–2 N (see below)

The buoyant force (F_B) on the balloon is the the weight of the displaced air:

F_B = (ρ_air)(V)(g) where

ρ_air = the density of air given to be 1.2 kg/m³

V = the volume of the balloon given to be 0.003 m³

g = 9.8 m/s²

The weight of the balloon (W_b) is the weight of the helium inside (this is the usual approximation):

W_b = (ρ_He)(V)(g) where

ρ_He = the density of helium given to be 0.2 kg/m³ (and V and g are the same as given above)

The net force (F_net) on the balloon is obtained by subtracting W_b from F_B:

F_net = F_B – W_b = (ρ_air)(V)(g) – (ρ_He)(V)(g) = (ρ_air –ρ_He)(V)(g)

Plugging in values for ρ_air, ρ_He, V, and g gives

F_net = (1.2 –0.2)(0.003)(9.8) = 2.94 × 10^–2 N

Answer 2

F = v(ρ - ρ_He)g = 0.003m³·9.8m/s²(1.274kg/m³ - 0.1761kg/m³) = 0.0323 N