A 650 kg weather balloon is designed to lift a 4600 kg package. What volume should the balloon have after being inflated with helium at 0 degrees celcius and 1 atm pressure to lift the total load?
The buoyancy force must equal the weight lifted. Let V be the volume.
g*[(He density)* V + 650 kg] = (Air density)*V*g
Cancel out the g's. Assume the outside air density correesponds to the same 1 atm and 0 C. He density is 4 kg/22.4 m^3 and the air density is 29/22.4 kg/m^3
0.179 V + 650 = 1.295 V
Solve for V (in cubic meters)
Lifted weight= Bouyant force
g*[(He density)*V+650+4600]=Air density *V*g
g= gravity= 9.8 N/Kg
Air Density= 1.29 Kg/m^3
He Density= 0.179 Kg/ m^3
Ballon Voulme= Gas Volume= Air volume approximately
Solving the equation
V= 4227 m^3
funny how you helped me a decade later
Well, to calculate the volume, we need to solve the equation 0.179V + 650 = 1.295V. Let's do some math!
Subtracting 0.179V from both sides, we get 650 = 1.295V - 0.179V.
Combining like terms, we have 650 = 1.116V.
Now, let's divide both sides by 1.116 to isolate V. Doing that, we end up with V ≈ 582.16 cubic meters.
So, the balloon should have a volume of approximately 582.16 cubic meters after being inflated with helium. That's quite a large balloon! Just hope it doesn't float away like my sense of dignity at a clown convention!
To solve for V, we need to set up the equation and isolate V.
0.179 V + 650 = 1.295 V
First, let's subtract 0.179 V from both sides of the equation:
650 = 1.295 V - 0.179 V
Simplifying this equation, we get:
650 = 1.116 V
Now, let's divide both sides of the equation by 1.116 to solve for V:
650 / 1.116 = V
V ≈ 583.67 cubic meters
Therefore, the volume of the balloon should be approximately 583.67 cubic meters.
To find the volume of the balloon needed to lift the total load, we can use the equation provided:
g * [(He density) * V + 650 kg] = (Air density) * V * g
Before proceeding, let's simplify the equation by canceling out the g's. We can assume that the outside air density corresponds to the same 1 atm and 0 degrees Celsius conditions. He density is given as 4 kg/22.4 m^3, and the air density is given as 29/22.4 kg/m^3.
After canceling out the g's, the equation becomes:
(He density * V + 650 kg) = (Air density * V)
Substituting the given densities:
(4 kg/22.4 m^3) * V + 650 kg = (29/22.4 kg/m^3) * V
Next, let's solve for V:
0.179 V + 650 = 1.295 V
Rearranging the equation:
1.295 V - 0.179 V = 650
0.179 V = 650
Dividing both sides by 0.179:
V = 650 / 0.179
V ≈ 3631.28 cubic meters
Therefore, the volume of the balloon needed to lift the total load is approximately 3631.28 cubic meters.