Question

A spherical helium filled balloon (B) with a hanging passenger cage being held by a single vertical cable (C) attached to Earth (Cable is going from the cage to ground). If the total mass of the balloon and the cage is 200 kg and the radius of the balloon is 5 m, how much tension (at least), the cable could be able to support in order to keep the balloon from breaking away. (Density of air is approximately 1.225 kg/m3 .)

Answer 1

The tension is
`T = 4326.7 \ N`

Step-by-step explanation:

From the question we are told that

The total mass is
`m = 200 \ kg`

The radius is
`r = 5 \ m`

The density of air is
`\rho_a = 1.225 \ kg/m^3`

Generally the upward force acting on the balloon is mathematically represented as

`F_N = T + mg`

=>
`(\rho_a * V * g ) = T + mg`

=>
`T = (\rho_a * V * g ) - mg`

Here V is the volume of the spherical helium filled balloon which is mathematically represented as

`V = (4)/(3) * \pi r^3`

=>
`V = (4)/(3) * 3.142 *(5)^3`

=>
`V = 523.67\ m^3`

So

`T = (1.225 * 523.67* 9.8 ) - 200 * 9.8`

`T = 4326.7 \ N`