A large balloon of mass 237 kg is filled with helium gas until its volume is 318 m3. Assume the density of air is 1.29 kg/m3 and the density of helium is 0.179 kg/m3.
(b) Calculate the buoyant force acting on the balloon.
____________N
(c) Find the net force on the balloon and determine whether the balloon will rise or fall after it is released.
______________ N
(d) What maximum additional mass can the balloon support in equilibrium?
_______________kg
To calculate the buoyant force acting on the balloon, we first need to determine the volume of the balloon that is filled with helium gas. Since the total volume of the balloon is given as 318 m^3, we can subtract the volume of the air from the total volume to find the volume of the helium gas.
The mass of the helium gas can be calculated by multiplying the density of helium by the volume of the helium gas.
(a) Volume of the air in the balloon:
Volume of balloon = 318 m^3
Mass of air = Density of air * Volume of air
= 1.29 kg/m^3 * (318 m^3)
= 409.62 kg
Volume of the helium gas:
Volume of helium = Volume of balloon - Volume of air
= 318 m^3 - 318 m^3
= 0 m^3
Mass of the helium gas:
Mass of helium = Density of helium * Volume of helium gas
= 0.179 kg/m^3 * 0 m^3
= 0 kg
(b) Buoyant force:
The buoyant force acting on the balloon is equal to the weight of the air displaced by the balloon, which is given by Archimedes' principle:
Buoyant force = Weight of air displaced = Mass of air displaced * gravitational acceleration
Buoyant force = (Density of air * Volume of balloon) * gravitational acceleration
= (1.29 kg/m^3 * 318 m^3) * 9.8 m/s^2
= 4012.08 N
Therefore, the buoyant force acting on the balloon is 4012.08 N.
(c) Net force:
The net force on the balloon is the difference between the buoyant force and the weight of the balloon.
Weight of balloon = Mass of balloon * gravitational acceleration
= 237 kg * 9.8 m/s^2
= 2328.6 N
Net force = Buoyant force - Weight of balloon
= 4012.08 N - 2328.6 N
= 1683.48 N
Since the net force is positive, the balloon will experience an upward force and will rise when released.
(d) Maximum additional mass:
The maximum additional mass that the balloon can support in equilibrium is equal to the weight of the balloon, which is balanced by the buoyant force.
Maximum additional mass = Weight of balloon / gravitational acceleration
= 2328.6 N / 9.8 m/s^2
= 237.55 kg
Therefore, the balloon can support a maximum additional mass of approximately 237.55 kg in equilibrium.