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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] Both sides previous revision Previous revision 2015/10/21 09:40 mdawber [Floating ball] 2015/10/21 09:31 mdawber [Helium Balloon] 2015/10/19 16:48 mdawber [Bernoulli's principle] 2015/10/19 16:46 mdawber [Equation of continuity] 2015/10/19 16:44 mdawber [Pascal's Principle] 2015/10/19 16:42 mdawber [Sinking and Floating] 2015/10/19 16:40 mdawber [Pressure in an open container] 2015/07/22 10:58 mdawber created 2015/10/21 09:40 mdawber [Floating ball] 2015/10/21 09:31 mdawber [Helium Balloon] 2015/10/19 16:48 mdawber [Bernoulli's principle] 2015/10/19 16:46 mdawber [Equation of continuity] 2015/10/19 16:44 mdawber [Pascal's Principle] 2015/10/19 16:42 mdawber [Sinking and Floating] 2015/10/19 16:40 mdawber [Pressure in an open container] 2015/07/22 10:58 mdawber created 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 =====