# Fluid Mechanics of helium-filled balloon

vmind
Hi,

I would really appreciate help in solving the following problem.

A helium-filled balloon is tied to a 2.00 m long, 0.050 kg uniform

string. The balloon is spherical with a radius of 0.400 m. When

released, the balloon lifts a length h of string and then remains in

equilibrium. The envelope of the balloon has a mass of 0.250 kg.

What is the value of h?

HallsofIvy
Homework Helper
Since 2 meters of the uniform string as mass 0.05 kg, h meters of the string will have mass (h/2)(0.05)= 0.025h kg and so weight 0.025 gh= 0.245h Newtons. The balloon itself has mass 0.25 kg and so
weight 0.25*g= 2.45 Newtons so the balloon is lifting 2.45+ 0.245h Newtons. You will need to use the bouyancy of helium (the baloon contains (4/3)(pi)(0.43= 0.268 m3 of helium) to determine how much weight the balloon can lift and so what h is.

vmind
Hello again,

Is the following formula the one I should use to find the buyoancy of helium?

B_helium = p_helium * V_helium * g

Also will the combined weight of string and balloon equal the buyoancy of helium at height h?