Physics Question

Question

Buoyancy and high altitude ballooning. Buoyant forces are supplied by every
fluid (liquid or gas), it’s the mechanism that sends high altitude balloons all the way
up to the stratosphere. For gases, density is given in units of grams/liter (g/L). It is
much more convenient than kg/L because gases have such low densities. Here’s a
table of the relevant densities for this problem (and the next one):
Gas Density (g/L)
Air 1.225
Hydrogen 0.08988
Helium 0.1786

 

a) If we went outside and filled a balloon with hydrogen so that it occupied a volume
of V = 1.00 m3, what would be the net force acting on the balloon (is the net force
upward or downward)?

b) repeat part a) but assume we made a Helium balloon instead

Answer 1

F_net = F_b - F_g

 

 

buoyant force: F_b = ρ_airgV_balloon

 

weight: F_g = ρ_gasgV_balloon

 

 

Substituting, F_net = (ρ_air - ρ_gas)gV_balloon

 

 

 

a) F_net = (1.225 - 0.08988)(9.8)(1) = 11.1 N

 

 

Here we divide by 1000 to convert g to kg but also multiplied by 1000 to convert L to m³.

 

 

b) F_net = (1.225 - 0.1786)(9.8)(1) = 10.2 N

 

 

Since both net forces are positive, the net forces point upwards.