An empty rubber balloon has a mass of 0.0120 kg. The balloon is filled with helium at 0°C, 1 atm pressure, and a density of 0.179 kg/m3. The filled balloon has a radius of 0.500 m. a) What is the magnitude of the buoyant force acting on the balloon? b) What is the magnitude of the net force acting on the balloon?

a) F_b = 6.62 N

b) F_net = 5.583 N

Explanation:

Given:

- Conditions of He gas: T = 0 C, P = 1 atm, ρ = 0.179 kg/m^3

- The mass of balloon m = 0.012 kg

- The radius of balloon r = 0.5 m

Find:

a) What is the magnitude of the buoyant force acting on the balloon?

b) What is the magnitude of the net force acting on the balloon?

Solution:

- The buoyant force F_b acting on the balloon is equal to the weight of the air it displaces. The mass of the displaced air ρ*V is the volume of the balloon times the density of the. Multiplying that by acceleration due to gravity gives its weight.

F_b = ρ*V*g

F_b = 4*ρ*g*pi*r^3 / 3

F_b = 4*1.29*9.81*pi*.5^3 / 3

F_b = 6.62 N

- The net force will be the difference between the balloon's weight and the buoyant force. The weight of the balloon is the density of the helium times the volume of the balloon added to the mass of the empty balloon.

F_g = ρ*V*g + m*g

F_g = 4*ρ*g*pi*r^3 / 3 + 0.012*9.81

F_g = 4*0.179*9.81*pi*.5^3 / 3 + 0.012*9.81

F_g = 1.037 N

- The net force is the difference between weight and buoyant force

F_net = F_g - F_b

F_net = 6.62 - 1.037

F_net = 5.583 N