The MSLC will have a booth at the Cook College Days festival

The MSLC will have a booth at the Cook College Days festival where it will give rides in hot air balloons. You, along with your physics study group, are working at the booth. The hot air balloon has a volume of 2.4 Times 10^3 m^3. The hot air has a density of 0.950 kg/m^3, whereas the surrounding air has a density of 1.29 kg/m^3. What is the maximum load the balloon can lift (including its own weight.)? Estimate how many people we can put in the balloon at any one time. (Assuming that the mass of the balloon and its cargo is 250 kg, and the average size person has a mass of 70 kg).

Solution

mass of hot air, m = 0.95*2.4*10^3 = 2280 kg

upthrust of the surrounding air, U = 1.29*2.4*10^3*9.8 = 30340.8 N

Let the maximum load be M

So, (m+M+250)*g = U

So, (2280 + M+250)*9.8 = 30340.8

So, M = 816 kg <--------answer

b)

Let the number of people be n

So, n*70 + 250 = 816

So, n = 8 <-------answer