A helium-filled balloon (whose envelope has a mass of mb=0.250kg ) is tied to a uniform string of length ℓ= 2.00 m and mass m=0.0500kg . The balloon is spherical with a radius of r=0.400m. When released in air of temperature 20°C and density rho air =1.20kg/m³, it lifts a length h of string and then remains stationary as shown in Figure P14.56. We wish to find the length of string lifted by the balloon. (a) When the balloon remains stationary, what is the appropriate analysis model to describe it? (b) Write a force equation for the balloon from this model in terms of the buoyant force B , the weight Fb of the balloon, the weight FHe of the helium, and the weight Fs of the segment of string of length h . (c) Make an appropriate substitution for each of these forces and solve symbolically for the mass msms of the segment of string of length hh in terms of mb,r,rho air , and the density of helium rhoHc. (d) Find the numerical value of the mass ms. (e) Find the length h numerically.
