Chapter 15: Problem 13
Why do airplanes take off into the wind?
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Chapter 15: Problem 13
Why do airplanes take off into the wind?
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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 atmospheric density.
Water flows through a 2.5 -cm-diameter pipe at \(1.8 \mathrm{m} / \mathrm{s}\). If the pipe narrows to 2.0 -cm diameter, what's the flow speed in the constriction?
A can of height \(h\) and cross-sectional area \(A_{0}\) is initially full of water. A small hole of area \(A_{1} \ll A_{0}\) is cut in the bottom of the can. Find an expression for the time it takes all the water to drain from the can. (Hint: Call the water depth \(y\), use the continuity equation, and integrate.)
A vertical tube \(1.0 \mathrm{cm}\) in diameter and open at the top contains \(\left.5.0 \mathrm{g} \text { of oil (density } 0.82 \mathrm{g} / \mathrm{cm}^{3}\right)\) floating on \(5.0 \mathrm{g}\) of water. Find the gauge pressure (a) at the oil-water interface and (b) at the bottom.
Arterial stenosis is a constriction of an artery, often due to plaque buildup on the artery's inner walls. Serious medical conditions can result, depending on the affected artery. Stenosis of the carotid arteries that supply blood to the brain is a leading cause of stroke, while stenosis of the renal arteries can lead to kidney failure. Pulmonary artery stenosis results from birth defects, and can result in insufficient oxygen supply. Because the heart has to work harder to get blood through a constricted artery, stenosis can contribute to high blood pressure. In answering the questions below, assume steady flow (which is true in arteries only on short timescales). How does the blood flow speed at a stenosis compare with the speed in the surrounding artery? a. lower b. the same c. higher
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