Question

A helium balloon ride lifts up passengers in a basket. Assume the density of air is 1.28 kg/m³ and the density of helium in the balloon is 0.18 kg/m³. The radius of the balloon (when filled) is R = 5.3 m. The total mass of the empty balloon and basket is m_b = 120 kg and the total volume is V_b = 0.059 m³. Assume the average person that gets into the balloon has a mass m_p = 71 kg and volume V_p = 0.078 m³.

ONLY NEED THE ONES WITH BOLD AND ????

a volume of helium in the balloon when fully inflated =623.6145193

b magnitude of the force of gravity on the entire system (but with no people= 2278.378518

c What is the magnitude of the buoyant force on the entire system (but with no people)? Include the volume of the balloon, basket, and helium. = ?????????

d magnitude of the force of gravity on each person= 696.51

e What is the magnitude of the buoyant force on each person?= ?????????

f How many FULL people can the balloon lift up? (Your answer must be an integer. = ?????????

Answer 1

c)
The magnitude of the buoyant force on the entire system,
Fb = a * Vh * g + a * Vb * g
Where a is the density of air, Vh is the volume of the balloon, and Vb is the volume of the basket.
Vh = 4/3 * * R³
= 4/3 * * 5.3³ = 623.6 m³

Substituting values,
Fb = 1.28 * 9.81 [623.6 + 0.059]
= 7831.34 N

e)
Buoyant force on each person, Fbp = a * Vp * g
Where Vp is the volume of each person.
Fbp = 1.28 * 0.078 * 9.81
= 0.979 N

f)
Force of gravity on the entire system without people, Fg = h * Vh * g + mb * g
Where h is the density of helium.
Fg = 0.18 * 623.6 * 9.81 + 120 * 9.81
= 2278.48 N

Force of gravity of each person, Fgp = mp * g
= 71 * 9.81
= 696.51 N

Total buoyant force = Total force of gravity.
Consider that there are n number of persons in the basket.
Fb + Fbp = Fg + n * Fgp
7831.34 + 0.979 = 2278.48 + n * 696.51
696.51 * n = 5553.84
n = 7.97
= 8