An empty weather balloon with a mass of 5kg has a radius of 2.879m when fully inflated with helium. It is supposed to carry a small load of instruments having a mass of 10kg. Taking air and helium to have the densities of 1.16kg/m³ and 0.160kg/m³ respectively will the balloon get off the ground? Acceleration due to gravity=9.81m/s², Volume of a sphere=(4/3)pi r³
To determine if the balloon will get off the ground, we need to compare the weight of the balloon with the weight it can support.
The weight of the balloon is given by the formula: weight = mass * acceleration due to gravity
The weight of the fully inflated balloon (with helium) can be calculated using the density of helium:
weight_balloon = (volume_balloon * density_helium) * acceleration due to gravity
The volume of a sphere (balloon) can be calculated using the radius:
volume_balloon = (4/3) * pi * r^3
Given that the radius of the balloon is 2.879m, the volume of the balloon is:
volume_balloon = (4/3) * pi * (2.879)^3
The weight of the fully inflated balloon can therefore be calculated as:
weight_balloon = ((4/3) * pi * (2.879)^3 * density_helium) * acceleration due to gravity
The weight of the load (instruments) is given by: weight_load = mass_load * acceleration due to gravity
Given that the mass of the load is 10kg, the weight of the load is:
weight_load = 10kg * acceleration due to gravity
Now, let's calculate the weights of the balloon and load:
To find out whether the balloon will get off the ground, we need to compare the buoyant force exerted by the helium with the weight of the system (balloon + instruments).
1. Find the volume of the balloon:
The volume of a sphere can be calculated using the formula: (4/3) * π * r^3.
Given that the radius (r) of the balloon is 2.879m, we can calculate its volume as follows:
Volume of the balloon = (4/3) * π * (2.879m)^3
2. Find the weight of the system:
The weight of the system is the sum of the mass of the balloon and the instruments, multiplied by the acceleration due to gravity (g):
Weight of the system = (mass of the balloon + mass of the instruments) * g
Given that the mass of the balloon is 5kg and the mass of the instruments is 10kg, and the acceleration due to gravity is 9.81m/s^2, we can calculate the weight of the system as follows:
Weight of the system = (5kg + 10kg) * 9.81m/s^2
3. Calculate the buoyant force:
The buoyant force is equal to the weight of the fluid displaced by the balloon. In this case, the fluid is helium. The buoyant force can be calculated using the formula:
Buoyant force = Volume of the balloon * density of helium * g
Given that the density of helium is 0.160kg/m^3 and the acceleration due to gravity is 9.81m/s^2, we can calculate the buoyant force as follows:
Buoyant force = Volume of the balloon * 0.160kg/m^3 * 9.81m/s^2
4. Compare the buoyant force with the weight of the system:
If the buoyant force is greater than or equal to the weight of the system, then the balloon will get off the ground. Otherwise, it will not.
Compare the buoyant force with the weight of the system:
If Buoyant force >= Weight of the system:
The balloon will get off the ground.
Else:
The balloon will not get off the ground.
Now you can plug in the values and calculate whether the balloon will get off the ground.