\"A) What is the buoyant force in air on a spherical rigid balloon of radius 0.9
ID: 2206427 • Letter: #
Question
"A) What is the buoyant force in air on a spherical rigid balloon of radius 0.90 m filled with helium if density of air = 1.29 kg/m^3?
B) What is the buoyant force on the balloon in water if kept submerged?
C) What is the buoyant force on the balloon in water if it were filled with mercury?"
I know the volume of a sphere is 4/3piR^3 and you multiply by density to find mass of the fluid then use Fb = mfg, but is this done the same for different densities in questions B and C? Thanks for the help, I'll certainly rate the answer.
Explanation / Answer
a) Buoyant force = weight of fluid displaced. you know the radius of the balloon. With this you are able to calculate the volume of the balloon. Since it is spherical, the volume = 4/3 x pi x r^3 The volume of the balloon = the volume of air that was displaced. Using the volume of air you can calculate the mass of the air by taking the volume x density. This gives you mass of the air displaced. The weight of the air displaced = mass x gravitational acceleration (9.8 m/s^2) This weight = buoyant force. b) To find the net force you must find the weight of the balloon that is the force pulling down to the ground. The volume of helium in the balloon = the volume of the balloon. Use the volume of helium x density of helium to find the mass of helium. Add this mass to the mass of the balloon and now you have the total mass of the balloon. Multiply this with gravity and you have the weight of the balloon. In a) you calculated the buoyant force that pushes the balloon up and now you have to weight that pulls the balloon down. The net force is the sum of these two forces. *Remember that one of the forces has to be a negative value because they are in opposite directions and force is a vector.
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