Question

On October 21, 2001, Ian Ashpole of the United Kingdom achieved a record altitude of 3.35 km (11 000 ft) powered by 600 toy balloons filled with helium. Each filled balloon had a radius of about 0.50 m and an estimated mass of 0.30 kg. (a) Estimate the total buoyant force on the 600 balloons. (b) Estimate the net upward force on all 600 balloons. (c) Ashpole parachuted to the Earth after the balloons began to burst at the high altitude and the buoyant force decreased. Why did the balloons burst?

Answer 1

3698.28287 N

1932.48287 N

Step-by-step explanation:

`\rho` = Density of air = 1.2 kg/m³

g = Acceleration due to gravity = 9.81 m/s²

v = Volume of air in balloon =
`(4)/(3)\pi r^3`

r = Radius of balloon = 0.5 m

The buoyant force is given by

`B=600* \rho vg\\\Rightarrow B=600* 1.2* (4)/(3)\pi 0.5^3* 9.81\\\Rightarrow B=3698.28287\ N`

The buoyant force generated by the balloons is 3975.65408 N

The net force would be

`F=B-mg\\\Rightarrow F=3698.28287-0.3* 600* 9.81\\\Rightarrow F=1932.48287\ N`

The net upward force on the balloon is 2209.85408 N

As the balloons gain altitude the outside pressure starts decreasing and the pressure difference between the inside and outside of the balloon becomes significant. This causes the balloon to burst.