Answer:

1) The volume of helium in the ballon when is fully inflated is 492.8070 m³

2) The magnitude of the force of gravity (with no people) is 869.3119 N

Explanation:

Given:

ρair = density of air = 1.28 kg/m³

ρhelium = density of helium = 0.18 kg/m³

R = radius of balloon = 4.9 m

mtotal = 121 kg

Vtotal = 0.073 m³

mp = average mass per person = 73 kg

Vp = 0.077 m³

g = gravity = 9.8 m/s²

Questions:

1) What is the volume of helium in the balloon when fully inflated, Vhelium = ?

2) What is the magnitude of the force of gravity on the entire system (but with no people), Fg = ?

1) The volume of helium in the ballon when is fully inflated

[tex]V_{helium} =\frac{4}{3} \pi R^{3} =\frac{4}{3} \pi *4.9^{3} =492.8070m^{3}[/tex]

2) First, you need to calculate the mass of helium

[tex]m_{helium} =\rho _{helium} *V_{helium} =0.18*492.8070=88.7053kg[/tex]

The magnitude of the force of gravity (with no people)

[tex]F_{g} =m_{helium} *g=88.7053*9.8=869.3119N[/tex]