Why does a balloon burst if you keep on blowing blowing?
2 answers
How far do you suppose the rubber will stretch??
As you increase the pressure the rubber stretches.
However although elastic the rubber is not very compressible and its volume of rubber material in the wall remains about the same as the balloon expands.
The total force on a semicircle of the balloon rubber is p*pi r^2 where p is the gage pressure or pressure above one atm inside. That is spread over the balloon circle and thickness t
sigma = tensile stress = p * pi r^2 / 2 pi r t = p r / 2t
now the volume of rubber = (4/3) pi r^2 t = constant k
t = k (3/4)/(pi r^2)
so
sigma = p r / 2[ k (3/4)/(pi r^2)] = p r^3/constant
In other words the stress in the rubber goes up fast, much faster than the pressure, with the radius for a given amount of rubber in the balloon skin.
When you reach the maximum tensile stress of the rubber, it breaks.
However although elastic the rubber is not very compressible and its volume of rubber material in the wall remains about the same as the balloon expands.
The total force on a semicircle of the balloon rubber is p*pi r^2 where p is the gage pressure or pressure above one atm inside. That is spread over the balloon circle and thickness t
sigma = tensile stress = p * pi r^2 / 2 pi r t = p r / 2t
now the volume of rubber = (4/3) pi r^2 t = constant k
t = k (3/4)/(pi r^2)
so
sigma = p r / 2[ k (3/4)/(pi r^2)] = p r^3/constant
In other words the stress in the rubber goes up fast, much faster than the pressure, with the radius for a given amount of rubber in the balloon skin.
When you reach the maximum tensile stress of the rubber, it breaks.