A 600-kg weather ballon is designed to lift a 4000-kg package. What volume should the ballon have after being inflated with helium at standard temperature and pressure so the total load can be lifted up?
The problem asks for volume. Take it a step further...
assume the ballon is spherical, and find it's radius.
Let V be the balloon volume.
Let rho1 = air density and
rho2 = helium density. Look them up or use the gas law to compute them. Helium weighs 4/29 as much as air at the same T and p.
For the balloon and its weight to be lifted,
rho1*V = 4000 + 600 + rho2*V
V = 4600/(rho1-rho2)
ok what is rho? I know the answer to this problem is 9.96 m because our teacher gave us the answer
Ok nvm i will do the math. Sorry didn't read what they stood for. Thx for the help =)
To solve this problem, we need to understand the concept of buoyancy. Buoyancy is the upward force exerted by a fluid on a submerged object that opposes the force of gravity. In this case, the fluid is helium, and the submerged object is the weather balloon.
The buoyant force can be calculated using Archimedes' principle, which states that the buoyant force is equal to the weight of the fluid displaced by the object. Since the buoyant force must be equal to the weight of the total load (weather balloon + package), we can set up the following equation:
Buoyant force = weight of total load
The weight of the total load can be calculated using the equation:
Weight = mass x gravity
Where mass is the total mass of the load (weather balloon mass + package mass), and gravity is the acceleration due to gravity.
Let's substitute the given values into the equation:
Total mass of load = weather balloon mass + package mass = 600 kg + 4000 kg = 4600 kg
Gravity, g = 9.8 m/s^2 (standard value)
Weight of load = 4600 kg x 9.8 m/s^2 = 45,080 N
Now, let's calculate the buoyant force. The buoyant force is equal to the weight of the displaced helium, which is also equal to the weight of the total load:
Buoyant force = 45,080 N
The buoyant force can be calculated using the equation:
Buoyant force = density of fluid x volume of fluid x gravity
Since the fluid in this case is helium, we need to know the density of helium. At standard temperature and pressure (STP), the density of helium is approximately 0.179 kg/m^3.
Let's substitute the values into the equation:
Buoyant force = 0.179 kg/m^3 x volume of fluid x 9.8 m/s^2
Now, we can solve for the volume of the fluid (helium):
Volume of fluid = Buoyant force / (density of fluid x gravity)
Volume of fluid = 45,080 N / (0.179 kg/m^3 x 9.8 m/s^2)
Calculating this value will give us the volume of the fluid required to generate enough buoyant force to lift the total load.
To find the radius of the spherical balloon, we can use the formula for the volume of a sphere:
Volume of sphere = (4/3) x π x radius^3
Since we have the volume of the fluid, we can equate it to the volume of the sphere equation and solve for the radius:
Volume of sphere = Volume of fluid
(4/3) x π x radius^3 = Volume of fluid
Solving this equation will give us the required radius of the spherical balloon.