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phy131studiof15:lectures:chapter15 [2015/10/21 09:31]
mdawber [Helium Balloon]
phy131studiof15:lectures:chapter15 [2015/10/21 09:40] (current)
mdawber [Floating ball]
Line 197: Line 197:
 I want to inflate a ball so that it will float in water  with exactly half of the ball above the surface and the other half below when the temperature is 20$\mathrm{^{o}C}$. The ball will be 20 cm in diameter and made from rubber which is 1 cm thick and has density 1800 $\mathrm{kg\,​ m^{-3}}$. The density of air at  20$\mathrm{^{o}C}$ under normal conditions, such as those that exist above the surface of the water, is 1.2 $\mathrm{kg\,​ m^{-3}}$. The density of water is 1000 $\mathrm{kg\,​ m^{-3}}$. The inside of the ball is to be filled with pressurized air, which will have a higher mass density than that outside the ball. What should the mass density of air inside the ball be so that ball floats as desired? ​   I want to inflate a ball so that it will float in water  with exactly half of the ball above the surface and the other half below when the temperature is 20$\mathrm{^{o}C}$. The ball will be 20 cm in diameter and made from rubber which is 1 cm thick and has density 1800 $\mathrm{kg\,​ m^{-3}}$. The density of air at  20$\mathrm{^{o}C}$ under normal conditions, such as those that exist above the surface of the water, is 1.2 $\mathrm{kg\,​ m^{-3}}$. The density of water is 1000 $\mathrm{kg\,​ m^{-3}}$. The inside of the ball is to be filled with pressurized air, which will have a higher mass density than that outside the ball. What should the mass density of air inside the ball be so that ball floats as desired? ​  
  
 +Weight of displaced fluid
  
 +$(\frac{1}{2}1000+\frac{1}{2}1.2)\frac{4}{3}\pi0.1^{3}$
 +
 +Weight of ball including dense air
 +
 +$1800\frac{4}{3}\pi(0.1^{3}-0.09^{3})+\rho_{air}\frac{4}{3}\pi0.09^{3}$
 +
 +At equilibrium these two are equal, so
 +
 +$\rho_{air}=\frac{(\frac{1}{2}1000+\frac{1}{2}1.2)\frac{4}{3}\pi0.1^{3}-1800\frac{4}{3}\pi(0.1^{3}-0.09^{3})}{\frac{4}{3}\pi0.09^{3}}$
 +
 +$\rho_{air}=17.55\mathrm{kg\,​m^{-3}}$
 ===== Helium Balloon ===== ===== Helium Balloon =====
  
phy131studiof15/lectures/chapter15.txt ยท Last modified: 2015/10/21 09:40 by mdawber
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