Chapter 15: Problem 1
Why do your ears "pop" when you drive up a mountain?
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
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Chapter 15: Problem 1
Why do your ears "pop" when you drive up a mountain?
These are the key concepts you need to understand to accurately answer the question.
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A balloon contains gas of density \(\rho_{\mathrm{g}}\) and is to lift a mass \(M,\) including the balloon but not the gas. Show that the minimum mass of gas required is \(m_{\mathrm{g}}=M \rho_{\mathrm{g}} /\left(\rho_{\mathrm{a}}-\rho_{\mathrm{g}}\right),\) where \(\rho_{\mathrm{a}}\) is the atmos- pheric density.
Show that pressure has the units of energy density.
A helium-filled balloon stops rising long before it reaches the "top" of the atmosphere, but a cork released from the bottom of a lake rises all the way to the surface. Why the difference?
Density and pressure in Earth's atmosphere are proportional: \(\rho=p / h_{0} g,\) where \(h_{0}=8.2 \mathrm{km}\) is a constant and \(g\) is the gravitational acceleration. (a) Integrate Equation 15.2 for this case to show that atmospheric pressure as a function of height \(h\) above the surface is given by \(p=p_{0} e^{-h / l h_{0}},\) where \(p_{0}\) is the surface pressure. (b) At what height will the pressure have dropped to half its surface value?
It's not possible to breathe through a snorkel from a depth greater than a meter or so. Why not?
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