A balloon has a volume of 1000 m3 and a mass of 500 kg when empty. When full of helium, what is the maximum mass it can lift off the ground? The density of helium is 0.18 kg/m3 and the density of air is 1.29kg/m3.
Mass of helium=0.18x1000=180kg
Mass of displaced air=1.29x1000=1290kg
Net difference=1290-180=1180kg=total mass it can lift.
Net payload=1180-500=680kg
It says that the correct answer is 610 kg. How did they get 610 kg as the answer?
It was a typo. :)
Net difference=1290-180=1110kg=total mass it can lift.
Net payload=1110-500=610kg
To find the maximum mass the balloon can lift off the ground when full of helium, we need to calculate the buoyant force acting on the balloon.
The buoyant force is the force exerted on an object immersed in a fluid (in this case, the balloon in the air or atmosphere). It is calculated by subtracting the weight of the fluid displaced by the object from the weight of the object itself.
The weight of the fluid displaced by the balloon depends on the difference in density between the fluid and the balloon. The density of helium is 0.18 kg/m3, and the density of air is 1.29 kg/m3. This means that the density of helium is less than the density of air, so the balloon filled with helium will be buoyant in the air.
To calculate the buoyant force, we first need to find the weight of the fluid displaced by the balloon:
Weight of air displaced = density of air * volume of balloon
Weight of air displaced = 1.29 kg/m3 * 1000 m3
Weight of air displaced = 1290 kg
Now we can calculate the buoyant force:
Buoyant force = Weight of air displaced - Weight of balloon
Buoyant force = 1290 kg - 500 kg
Buoyant force = 790 kg
Therefore, the maximum mass the balloon can lift off the ground when full of helium is 790 kg.