Question

A 2.8kg balloon is filled with helium ( density = 0.179 kg/m 3 ).

Part A

If the balloon is a sphere with a radius of 5.1m , what is the maximum weight it can lift? (N)

Answer 1

Volume of the balloon is

V = 4?r³/3

   = (4)(?)(5.1 m)³ / 3

   = 555.36552 m³
The density of helium,?_helium = 0.179 kg/m³
The density of airm, ?_air = 1.29 kg/m³
The mass of the balloon, m = 2.8 kg

The air's weight equal to mg
   W_air = ?_air V g
           = (1.29 kg/m³)(555.36552 m³)(9.8 m/s²)
           = 7020.93 N

The weight of balloon including helium is
   W_helium = mg+?_helium V g         
              = (2.8 kg)(9.8 m/s²) + (0.179 kg/m³)(555.36552 m³)(9.8 m/s²)
                = 1001.66 N

Therefore maximum weight it can lift is

maximum weight lift = W_air -W_helium
            = 7020.93 N - 1001.66 N
          = 6019.27 N