Buoyant Force of a Balloon
(9 points possible)
Helium balloons are used regularly in scientific research. A typical balloon would reach an altitude of 35.0 km with an air density of kg/m . At this altitude the helium in the balloon would expand to 540000.0 m . Find the buoyant force on the ballon.
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To find the buoyant force on the balloon, we can use Archimedes' principle, which states that the buoyant force on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.
The buoyant force can be calculated using the following formula:
Buoyant force = Weight of fluid displaced
To determine the weight of the fluid displaced, we need to know the volume of the fluid displaced and the density of the fluid.
1. Determine the volume of the fluid displaced:
At an altitude of 35.0 km, the helium in the balloon expands to a volume of 540,000.0 m^3.
2. Find the density of the fluid:
Given that the air density at the same altitude is given as kg/m^3, we can assume that the density of the fluid being displaced by the balloon is equal to the air density at that altitude.
3. Calculate the weight of fluid displaced:
The weight of fluid displaced is equal to the density of the fluid times the volume of the fluid displaced.
Weight of fluid displaced = Density of fluid x Volume of fluid displaced
4. Calculate the buoyant force:
The buoyant force is equal to the weight of fluid displaced.
Buoyant force = Weight of fluid displaced
By following these steps and plugging in the values for the density of the fluid and the volume of fluid displaced, you can calculate the buoyant force on the balloon.