Find the buoyant force on a helium balloon in air (Standard Pressure and Temperature) if the balloon is spherical with diameter 12.0 cm.
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To find the buoyant force on a helium balloon in air, we need to 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.
Here's how you can calculate the buoyant force on the helium balloon:
1. Determine the volume of the helium balloon:
The volume of a sphere can be calculated using the formula V = (4/3) * π * r^3, where r is the radius. Since we are given the diameter, which is 12.0 cm, we can find the radius by dividing the diameter by 2. So the radius (r) is 6.0 cm or 0.06 m.
Therefore, the volume of the sphere (V) is:
V = (4/3) * π * (0.06)^3
2. Calculate the weight of the displaced air:
Since the balloon is filled with helium, it displaces an equivalent volume of air. To find the weight of the displaced air, we need to know the density of air at standard pressure and temperature.
The density of air at standard pressure and temperature is approximately 1.2 kg/m^3. Therefore, the weight of the displaced air (W_air) is given by:
W_air = V * ρ_air
where ρ_air is the density of air.
3. Find the weight of the helium in the balloon:
Helium is less dense than air, so the weight of the helium is less than the weight of the displaced air. The density of helium at standard pressure and temperature is approximately 0.18 kg/m^3. Therefore, the weight of the helium (W_helium) is given by:
W_helium = V * ρ_helium
where ρ_helium is the density of helium.
4. Calculate the buoyant force:
The buoyant force (F_buoyant) is equal to the weight of the displaced air minus the weight of the helium, as the buoyant force acts in the opposite direction to the weight.
F_buoyant = W_air - W_helium
Now you can plug in the values to calculate the buoyant force on the helium balloon.