HELP!
a 650kg weather balloon is designed to lift a 4600kg package. what volume should the balloon have after being inflated with helium at 0°C and 1atm pressure to lift the total load? (hint. use the density value of helium)
thanks!!
Fluid mechanics? Really.
4600kg=weightdisplacedair-weighthelium
- densityair*volume -densityHe*volume
= V(28.9-4)E3 and V will be in kilo molar volumes (22.4kliters).
solve for V. If you want it in m^3, divide it by a 1000, multiply it by 22.4
Well, it seems like you're in a bit of a pickle! Don't worry, I'm here to inflate your spirits and help you out.
To determine the volume of the balloon needed, we can use the concept of buoyancy. The buoyant force acting on the balloon should be equal to the weight of the total load.
First, let's calculate the weight of the total load:
Weight of the package = mass of the package × acceleration due to gravity
Weight of the package = 4600 kg × 9.8 m/s²
Now, to lift this weight, we need the buoyant force to be equal to the weight of the package:
Buoyant force = Weight of the package
Since we are using helium, which has a lower density than air, the buoyant force can be calculated using the formula:
Buoyant force = (density of air - density of helium) × volume of the balloon × acceleration due to gravity
We can rearrange this equation to solve for the volume of the balloon:
Volume of the balloon = Weight of the package / (density of air - density of helium) / acceleration due to gravity
Now, let's find the values we need to plug into the equation:
- The density of air at 0°C and 1 atm pressure is approximately 1.225 kg/m³.
- The density of helium at the same conditions is approximately 0.1786 kg/m³.
- The acceleration due to gravity is approximately 9.8 m/s².
Now we can calculate the volume of the balloon to lift the total load by plugging in these values:
Volume of the balloon = (4600 kg × 9.8 m/s²) / (1.225 kg/m³ - 0.1786 kg/m³) / 9.8 m/s²
And voilà! The calculated value will give you the volume of the balloon necessary to lift the total load.
To calculate the volume of the balloon, we first need to find the buoyant force exerted on the package by the helium-filled balloon. The buoyant force is equal to the weight of the air displaced by the balloon.
Step 1: Find the weight of the air displaced
The weight of the air displaced is equal to the weight of the package that needs to be lifted.
Weight of package = 4600 kg
Step 2: Find the buoyant force
The buoyant force is the difference between the weight of the package and the weight of the balloon.
Buoyant force = Weight of air displaced = Weight of package
Step 3: Find the weight of the balloon
The weight of the balloon can be calculated by subtracting the buoyant force from the weight of the package.
Weight of balloon = Weight of package - Buoyant force
Step 4: Calculate the volume of the balloon
The volume of the balloon can be determined using the definition of density:
Density = Mass / Volume
Since the density of helium is known, we can rearrange the equation to solve for volume:
Volume = Mass / Density
Now, let's calculate the volume of the balloon:
Density of helium = 0.18 kg/m^3 (at 0°C and 1 atm pressure)
Step 5: Substitute the values and calculate the volume
Using the equation for volume, we can substitute the values we have:
Volume = (Weight of balloon) / (Density of helium)
Volume = (Weight of package - Buoyant force) / (Density of helium)
Volume = (4600 kg - buoyant force) / (0.18 kg/m^3)
Finally, you will need to perform the calculation to find the volume of the balloon.
To calculate the volume of the balloon needed to lift the total load, we need to consider the buoyant force exerted on the balloon by the helium gas inside it. The buoyant force is equal to the weight of the gas displaced by the balloon.
To find the volume, we can use the following equation:
V = (Weight of the package + Weight of the balloon) / Density of helium
First, let's calculate the weight of the package:
Weight of the package = mass of the package * acceleration due to gravity
Weight of the package = 4600 kg * 9.8 m/s^2
Next, let's calculate the weight of the balloon:
Weight of the balloon = mass of the balloon * acceleration due to gravity
Weight of the balloon = 650 kg * 9.8 m/s^2
Now, we need to use the density value of helium. The density of helium at 0°C and 1 atm pressure is approximately 0.179 kg/m^3.
Finally, substitute the values into the equation to find the volume:
V = (Weight of the package + Weight of the balloon) / Density of helium
V = (4600 kg * 9.8 m/s^2 + 650 kg * 9.8 m/s^2) / 0.179 kg/m^3
Simplifying the equation should give you the volume of the balloon needed to lift the total load.