an empty rubber balloon has 0.0120 kg it filled of helium. the density of helium is 0.179 kg/m^3 of and the radius of the balloon is 0.500 what is the buoyant force over the balloon
To calculate the buoyant force acting on the balloon, we need to first determine the volume of the balloon, and then use the formula for buoyant force.
1. Calculate the volume of the balloon:
The volume of a balloon can be calculated using the formula for the volume of a sphere: V = (4/3) * pi * r^3, where r is the radius.
Given that the radius of the balloon is 0.500 m:
V = (4/3) * pi * (0.500)^3
V = (4/3) * 3.14159 * 0.125
V = 0.523599 m^3
2. Calculate the mass of the displaced air:
The density of helium is given as 0.179 kg/m^3. Since the balloon is filled with helium, the mass of the displaced air is equal to the volume of the balloon (calculated in step 1) multiplied by the density of helium.
Mass of displaced air = volume of balloon * density of helium
Mass of displaced air = 0.523599 m^3 * 0.179 kg/m^3
Mass of displaced air = 0.0937 kg
3. Calculate the buoyant force:
The buoyant force acting on the balloon can be calculated using the formula: Buoyant force = mass of displaced air * acceleration due to gravity.
Given that the mass of the displaced air is 0.0937 kg, and the acceleration due to gravity is approximately 9.8 m/s^2:
Buoyant force = 0.0937 kg * 9.8 m/s^2
Buoyant force = 0.9172 N
Therefore, the buoyant force acting on the balloon is approximately 0.9172 Newtons.