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
![V_{helium} =\frac{4}{3} \pi R^{3} =\frac{4}{3} \pi *4.9^{3} =492.8070m^{3}](https://tex.z-dn.net/?f=V_%7Bhelium%7D%20%3D%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20R%5E%7B3%7D%20%3D%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20%2A4.9%5E%7B3%7D%20%3D492.8070m%5E%7B3%7D)
2) First, you need to calculate the mass of helium
![m_{helium} =\rho _{helium} *V_{helium} =0.18*492.8070=88.7053kg](https://tex.z-dn.net/?f=m_%7Bhelium%7D%20%3D%5Crho%20_%7Bhelium%7D%20%2AV_%7Bhelium%7D%20%3D0.18%2A492.8070%3D88.7053kg)
The magnitude of the force of gravity (with no people)
![F_{g} =m_{helium} *g=88.7053*9.8=869.3119N](https://tex.z-dn.net/?f=F_%7Bg%7D%20%3Dm_%7Bhelium%7D%20%2Ag%3D88.7053%2A9.8%3D869.3119N)