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
(e) What happens to the balloon if the mass of the load is less than the value calculated in part (d)?
(X) The balloon and its load will accelerate downward.
(x)The balloon and its load will remain stationary.
(x)The balloon and its load will accelerate upward.
(f) What limits the height to which the balloon can rise?
a) 1
d
d
d
To answer these questions, we need to calculate the buoyant force, net force, maximum additional mass, and understand the factors that limit the height to which the balloon can rise.
(b) To calculate the buoyant force, you can use Archimedes' principle, which states that the buoyant force is equal to the weight of the fluid displaced by the object. In this case, the fluid is air, and the weight of the fluid displaced by the balloon is equal to the weight of the air that would occupy the volume of the balloon.
The weight of the air displaced by the balloon can be calculated using the formula:
Weight of air displaced = density of air x volume of the balloon x acceleration due to gravity
Substituting the given values, we get:
Weight of air displaced = (1.29 kg/m3) x (318 m3) x (9.8 m/s2)
Calculate this to find the buoyant force acting on the balloon.
(c) To find the net force on the balloon, we need to consider the gravitational force acting on the balloon and the buoyant force. The net force is the difference between these two forces. If the buoyant force is greater than the gravitational force, the balloon will rise; otherwise, it will fall.
The gravitational force can be calculated by multiplying the mass of the balloon by the acceleration due to gravity:
Gravitational force = mass of the balloon x acceleration due to gravity
Compare the buoyant force and the gravitational force to determine whether the balloon will rise or fall.
(d) To calculate the maximum additional mass the balloon can support in equilibrium, we need to consider the net force on the balloon. In equilibrium, the net force should be zero. So, set the net force equation from part (c) equal to zero, and solve for the additional mass.
(e) If the mass of the load is less than the value calculated in part (d), the net force on the balloon will be non-zero and downward. This means the balloon and its load will accelerate downward.
(f) The height to which the balloon can rise is limited by various factors, including the buoyant force, weight of the balloon and load, and atmospheric conditions such as air density and temperature. As the balloon rises, the air density decreases, reducing the buoyant force. Additionally, the weight of the balloon and load may increase if the balloon ascends to higher altitudes due to a decrease in the gravitational pull. These factors, along with drag forces, ultimately limit the height to which the balloon can rise.