FYKOS Year 30 Series 5 Problem 5 — balloon · FYKOS 30 #30.5.5

Physics · mechanics · thermodynamics

Problem

Consider a balloon with mass

m

(blown up) and volume

V

filled with helium. An infinite string of length density

τ=10gm^{−1}

is tied to the balloon. Assuming the atmosphere is isothermal, in which the pressure depends on height

z

p=p_0e^{-z/z_0}

,, (

z_{0}

is a parameter of the atmosphere), what is the maximum height the balloon will reach?