The problem is as follows: An empty rubber balloon has a mass of 0.012 kg. The b

Question

The problem is as follows:

An empty rubber balloon has a mass of 0.012 kg. The balloon is filled with helium at a density of 0.181 kg/m^3. At this density, the balloon has a radius of 0.500 m. If the filled balloon is fastened to a vertical line, what is the tension in the line?

I understand that there is a system that comprises of the balloon and helium. I know that I must compute the mass of the helium and the density of the system, which I did and got 0.095kg of helium and 0.204 kg/m^3 for the density of the system. My question is how do I find the tension using what I already found? I understand I must apply Newton's 2nd law, but how?

Thank you for your time.

Explanation / Answer

The balloon is in equilibrium under three forces which are buyont force , total weight of the balloon and helium and tension in the stirng

   F =  B - (m_balloon + m_helium )g -T   

     T =  B - (m_balloon + m_helium )g

T = ( _air - _helium ) g ( 4/3 r^3 ) - m_balloon * g

       = ( 1.29 - 0.181 ) * 9.8 m/s^2 ( 4/3 * ( 0.500 m)^3 - ( 0.0120 kg * 9.8 )

        = 5.57 N

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