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Textbook Expert
Textbook ExpertVerified Tutor
26 Dec 2021

Given information

The mass of the person is .

The diameter of the spherical balloon is .

Step-by-step explanation

Step 1.

When an object is fully or partially in a fluid it exerts an upward force on the object which opposes the weight of the object. This upward force is called buoyant force.

The upward buoyant force is equal to the combined force due to the weight of the balloon and the weight of the person.

The formula to calculate the buoyant force is

 

Here, is the buoyant force, is the density of the air, is the volume of the balloon and is the acceleration due to gravity.

The volume of the balloon is

   

Here, is the radius and is the number of balloons.

The formula to calculate the mass of the balloon is

 

Here, is the mass and is the density of the balloon.

The formula to calculate the total downward force is

 

Here, is the mass of the person.

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