Question

A child holds a helium-filled rubber balloon with a volume of 0.01 m³ in air at 0 degrees C. Neglect the weight of the rubber and string and the buoyant force of the air on the child.

(a) How great a force must she exert to keep the balloon from rising?

(b) How many such balloons would it take to lift a 20-keg child?

Some useful data: At 0 degrees C, the density of the helium is 0.178 kg/m³ and the density of air is 1.29 kg/m³.

Answer 1

Gravitational acceleration = g = 9.81 m/s²

Density of air = _a = 1.29 kg/m³

Density of helium = _h = 0.178 kg/m³

Volume of the balloon = V = 0.01 m³

Force exerted by the child to keep the balloon from rising = F

The buoyancy force on the balloon supports the weight of the helium and the force exerted by the child.

_aVg = _hVg + F

F = (_a - _h)Vg

F = (1.29 - 0.178)(0.01)(9.81)

F = 0.109 N

Number of balloons needed to lift a 20 kg child = n

Mass of the child = m = 20 kg

_anVg = _hnVg + mg

_anV = _hnV + m

m = nV(_a - _h)

20 = n(0.01)(1.29 - 0.178)

n = 1798.56

a) Force exerted to keep the balloon from rising = 0.109 N

b) Number of balloons needed to to lift a 20 kg child = 1798.56