Question

A toy balloon, which has a mass of 2.90 g before it is inflated, is filled with helium (with a density of 0.180 kg/m^3) to a volume of 8400 cm^3. What is the minimum mass that should be hung from the balloon to prevent it from rising up into the air? Assume the air has a density of 1.29 kg/m^3.

Answer 1

`M=6.4243\ g`

Step-by-step explanation:

Given:

• mass of deflated balloon,
  `m_b=2.9\ g=0.0029\ kg`

• density of helium,
  `\rho_h=0.180\ kg.m^(-3)`

• volume of inflation,
  `V=8400\ cm^3=0.0084\ m^3`

• density of air,
  `\rho_a=1.29\ kg.m^(-3)`

To stop this balloon from rising up we need to counter the buoyant force.

mass of balloon after inflation:

`m=m_h+m_b`

`m=0.0084* 0.180+0.0029`

`m=0.004412\ kg`

Now the density of inflated balloon:

`\rho_b=(m)/(V)`

`\rho_b=(0.004412)/(0.0084)`

`\rho_b=0.5252\ kg.m^(-3)`

Now the buoyant force on balloon

`F_B=V(\rho_a-\rho_b).g`

`F_B=0.0084(1.29-0.5252)* 9.8`

`F_B=0.063\ N`

∴Mass to be hung:

`M=(F_B)/(g)`

`M=0.00642432\ kg`

`M=6.4243\ g`