Flat basketball

Classical Mechanics Level 3

Many of you may have noticed the phenomenon that basketballs get flat if the weather is cold. If a basketball was inflated to a gauge pressure of 60,000 Pa when the temperature outside was \(20^\circ\mbox{C}\), what is the gauge pressure inside the basketball in Pa when the temperature is \(10^\circ\mbox{C}\)?

Details and assumptions

  • The outside air maintains a constant pressure of 1 atm=101,325 Pa as the temperature changes.
  • The basketball always has a circumference of 0.75 m.
  • Gauge pressure is the pressure above ambient pressure.

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