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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.

Respuesta :

Answer:

[tex]M=6.4243\ g[/tex]

Explanation:

Given:

  • mass of deflated balloon, [tex]m_b=2.9\ g=0.0029\ kg[/tex]
  • density of helium, [tex]\rho_h=0.180\ kg.m^{-3}[/tex]
  • volume of inflation, [tex]V=8400\ cm^3=0.0084\ m^3[/tex]
  • density of air, [tex]\rho_a=1.29\ kg.m^{-3}[/tex]

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

mass of balloon after inflation:

[tex]m=m_h+m_b[/tex]

[tex]m=0.0084\times 0.180+0.0029[/tex]

[tex]m=0.004412\ kg[/tex]

Now the density of inflated balloon:

[tex]\rho_b=\frac{m}{V}[/tex]

[tex]\rho_b=\frac{0.004412}{0.0084}[/tex]

[tex]\rho_b=0.5252\ kg.m^{-3}[/tex]

Now the buoyant force on balloon

[tex]F_B=V(\rho_a-\rho_b).g[/tex]

[tex]F_B=0.0084(1.29-0.5252)\times 9.8[/tex]

[tex]F_B=0.063\ N[/tex]

∴Mass to be hung:

[tex]M=\frac{F_B}{g}[/tex]

[tex]M=0.00642432\ kg[/tex]

[tex]M=6.4243\ g[/tex]

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