an empty rubber balloon has mass 0.0120kg, the balloon is filled with helium of density 0.181 kg/m^3. the balloon is spherical w/ radius 0.500m. if the balloon is ties to a vertical string, what is thw tension in the string?

density of air 1.29 kg/m^3

3 answers

Volume of air in the balloon = V =(4/3)*PI*r^3 = (4/3)*PI*0.5^3

mass of air displaced is 1.29 * V
mass of helium is 0.181*V

Upward force due to pressure difference between helium and air is (1.29 - 0.181)*V

Sum of forces in the y direction is 0:

(1.29 - 0.181)*V - T - 0.0120 = 0

Solve for T, The tension in the balloon's string

thank you!