How Large Must a Helium Balloon Be to Achieve Neutral Buoyancy?

[TR1]

Homework Statement

What diameter must a helium filled balloon have to float with neutral buoyancy? The mass of the empty balloon is 2 g.

Homework Equations

FB = (density)(gravity)(Volume)
Volume of balloon = 4/3(4.13)r^2
Density = mass/Volume

The Attempt at a Solution

I know that the balloon will float when its weight is equal to the weight of the air displaced.
Weight of balloon = Weight of air displaced
Weight of empty balloon = 0.002kg x 9.81 = 0.01962N
Thus weight of air displaced = 0.01962N
But this is a far as I am getting as I am very confused with where the density plays a roles since no densities is given in this problem.

 

[haruspex]

You've overlooked a contributor to the weight of the balloon.
You do need facts concerning gas densities. Assume atmospheric pressure.

 

[Chestermiller]

Homework Statement

What diameter must a helium filled balloon have to float with neutral buoyancy? The mass of the empty balloon is 2 g.

Homework Equations

FB = (density)(gravity)(Volume)
Volume of balloon = 4/3(4.13)r^2
Density = mass/Volume

The Attempt at a Solution

I know that the balloon will float when its weight is equal to the weight of the air displaced.
Weight of balloon = Weight of air displaced
Weight of empty balloon = 0.002kg x 9.81 = 0.01962N
Thus weight of air displaced = 0.01962N
But this is a far as I am getting as I am very confused with where the density plays a roles since no densities is given in this problem.

Use the ideal gas law to get the density of air (and helium if you think that will be significant compared to the balloon weight).

Chet

 

[SteamKing]

Homework Statement

What diameter must a helium filled balloon have to float with neutral buoyancy? The mass of the empty balloon is 2 g.

Homework Equations

FB = (density)(gravity)(Volume)
Volume of balloon = 4/3(4.13)r^2
Density = mass/Volume

The Attempt at a Solution

I know that the balloon will float when its weight is equal to the weight of the air displaced.
Weight of balloon = Weight of air displaced
Weight of empty balloon = 0.002kg x 9.81 = 0.01962N
Thus weight of air displaced = 0.01962N
But this is a far as I am getting as I am very confused with where the density plays a roles since no densities is given in this problem.

Your formula for the volume of the balloon is incorrect.

V = (4/3)π r³ (yes, r cubed, not r squared)

and π ≈ 3.14159 ..., not 4.13