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A mountain-climber friend with a mass of 74 kg ponders the idea of attaching a helium-filled balloon to himself to effectively reduce his weight by 25% when he climbs. He wonders what the approximate size of such a balloon would be. Hearing of your physics skills, he asks you. Share with him your calculations that find the volume of the balloon.

Respuesta :

davidlcastiblanco

Answer:

[tex]V=16.65 m^3[/tex]

Explanation:

The volume of the balloon can be find compared the force in each cases so:

reduce 25% from 74kg

[tex]R=\frac{25}{100}*74kg=18.5kg[/tex]

So the net force uproad on the balloon is

[tex]F_b=18.5kg*g[/tex]

Now the density of the both gases air and helium are different however the volume is the same change offcorss the mass so:

[tex]P_h=\frac{m}{V}=0.179 kg/m^3[/tex]

[tex]P_A=1.29 kg/m^3[/tex]

[tex]F_b=F_A-F_H[/tex]

[tex]F_b=m_a*g-m_h*g[/tex]

[tex]m=P/V[/tex]

[tex]18.5kg*g=(1.29kg/m^3-0.179kg/m^3*)V*g[/tex]

[tex]V=\frac{18.5kg}{(1.29-0.179)kg/m^3}[/tex]

[tex]V=16.65 m^3[/tex]

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