A spherical balloon has a radius of 7.15 m and is filled with helium. How large a cargo can it lift, assuming that the skin and structure of the balloon have a mass of 930 kg? Neglect the buoyant force on the cargo volume itself.

 m = 876.71 kg

Explanation:

This is an exercise of Archimedes' principle, which states that the thrust on a body is equal to the weight of the dislodged liquid  

        B = ρ g V  

therefore the load that the balloon can lift is  

       B - W_structure - w_load = 0

       w_load = B - W_structure

The volume of the balloon is  

      v = 4/3 π r³

let's substitute  

      w_carga = rho g 4/3 π r³ - m_structure g  

the air density at T = 25ºc is ρ = 1.18 kg / m³

let's calculate  

     w_load = 1.18 9.8 4/3 π 7.15³ - 930 9.8  

     w_load = 17705,77 - 9114  

     w_ load = 8591.77 N

this corresponds to a mass of  

   w_load = m g  

   m = w_load / g  

   m = 8591.77 / 9.8  

   m = 876.71 kg

hi there!

your question asks at which segment does freezing occur.

since we're talking about water, the freezing point of water will be 32 degrees fahrenheit or below.

hope this ! ~

no. dot product   =0 when vecs at right angles