Why Does a Balloon Only Expand at a Certain Air Pressure?

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Notice that when we blow up a balloon, or held up a balloon outside a car and accellerate, the balloon doesn't expand constantly. It seems like there is a critical air pressure for the balloon to start expanding. Is that true and how can we calculate this?
 
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I'd hazard a guess that the critical pressure for expansion is the atmospheric pressure plus the pressure created from the elastic tension in of the rubber acting to compress the air inside. If you can overcome the sum of these pressures when you blow into the balloon, it will expand.
 
The thicker the skin of the balloon of the balloon, the more force it takes to stretch it. But as the balloon expands, its skin gets thinner, so less pressure is required to further expand it. So a balloon is hardest to expand when it's completely uninflated, and once you get it going it keeps getting easier.
 
Thank you so much the explanation is so good:)