Physics A spherical balloon has a radius of 6.95 m and is filled with helium. The density of helium is 0.179 kg/m3, and the density of air is 1.29 kg/m3. The skin and structure of the balloon has a mass of 930 kg . Neglect the buoyant force on the cargo volume itself. Determine the largest mass of cargo the balloon can lift.

Explanation:

volume of balloon

= 4/3 π R³

= 4/3 x 3.14 x 6.95³

= 1405.47  m³

uplift force

= volume of balloon x density of air x 9.8

= 1405.47 x 1.29 x 9.8

= 1813.05 x 9.8  N  

weight of helium gas

= volume of balloon x density of helium x 9.8

= 1405.47 x .179  x 9.8

= 251.58 x 9.8 N

Weight of other mass = 930 x 9.8 N

Total weight acting downwards

=  251.58 x 9.8 +930 x 9.8

= 1181.58 x 9.8 N

If W be extra weight the uplift can balance

1181.58 x 9.8 + W x 9.8 = 1813.05 x 9.8

1181.58  + W  = 1813.05

W= 631.47 kg

the answer to this question is 60 n

i think it because equal matrices have equal dimensions, only square matrices can be symmetric. for all indices and . every square diagonal matrix is symmetric, since all off-diagonal elements are zero. in linear algebra, a real symmetric matrix represents a self-adjoint operator over a real inner product space.