Essential University Physics: Volume 1 (3rd Edition)
3rd Edition
ISBN: 9780321993724
Author: Richard Wolfson
Publisher: PEARSON
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Chapter 15, Problem 70P
Density and pressure in Earth’s atmosphere are proportional: ρ = p/h0g, where h0 = 8.2 km is a constant called the scale height 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 = p0e−h/h0, where p0 is the surface pressure. (b) At what height will the pressure have dropped to half its surface value?
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The rate of change of atmospheric pressure P with respect to altitude h is
proportional to P, provided that temperature is constant. At 15°C the pressure is
101.3 kPa at sea level and 87.14 kPa at h = 1000 m. Answer the following
questions.
a) What is the atmospheric pressure at an altitude of 4000 m? Round to three decimal
places.
b) What is the atmospheric pressure at the top of Mount Greylock in Massachusetts, at
an altitude of 1063 m? Round to three decimal places.
CHECK ANSWER
kPa
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kPa
The pressure on Earth's atmosphere as a function of height y above sea level can be determined by
assuming g to be constant and that the density of air is proportional to the pressure, i.e., px P.
Note that this assumption is not very accurate since temperature and other weather effects can
influence pressure. [Hint: Po = 1.013 × 105 N/m², po = 1.29 kg x m-³]
(1) Start by finding a relation between the pressure Po and the density of air po at 0° at sea level
(y=0) and the pressure P and density p at height y. Using this relation find an expression
for p as a function of P, i.e., p = p(P).
(2) Find the pressure as a function y.
(3) At what altitude above sea level is the atmospheric pressure equal to half the pressure at sea
level?
An airplane passenger has a volume V1 of air in his stomach just before the plane takes off from a sea-level airport.
What volume will this quantity of air have at cruising altitude at the same temprerature ( body temp. ), in terms of V1, the pressure on the ground P1, and the cabin pressure at cruising altitude P2?
What is this volume, in cubic centimeters, if the initial volume is 110 cm^3 and the cabin pressure drops to 7.5x10^4 Pa when the plane is at cruising altitude?
Chapter 15 Solutions
Essential University Physics: Volume 1 (3rd Edition)
Ch. 15.1 - What quantity of water has the same mass as 1 m3...Ch. 15.2 - Neglecting friction and other nonconservative...Ch. 15.3 - The density of a rubber ball is three-fifths that...Ch. 15.4 - The photo shows smoke particles tracing...Ch. 15.5 - A large tank is filled with liquid to the level h1...Ch. 15 - Why do your ears pop when you drive up a mountain?Ch. 15 - Commercial aircraft cabins are usually pressurized...Ch. 15 - Water pressure at the bottom of the ocean arises...Ch. 15 - The three containers in Fig. 15.22 are filled to...Ch. 15 - Why is it easier to float in the ocean than in...
Ch. 15 - Figure 15.23 shows a cork suspended from the...Ch. 15 - Meteorologists in the United States usually report...Ch. 15 - A mountain stream, frothy with entrained air...Ch. 15 - Why are dams thicker at the bottom than at the...Ch. 15 - Its not possible to breathe through a snorkel from...Ch. 15 - A helium-filled balloon stops rising long before...Ch. 15 - A barge filled with steel beams overturns in a...Ch. 15 - Why do airplanes take off into the wind?Ch. 15 - Is the flow speed behind a wind turbine greater or...Ch. 15 - The density of molasses is 1600kg/m3. Find the...Ch. 15 - Atomic nuclei have densities around 1017kg/m3,...Ch. 15 - Compressed air with mass 8.8 kg is stored in a...Ch. 15 - The pressure unit torr is defined as the pressure...Ch. 15 - Measurement of small pressure differencesfor...Ch. 15 - Whats the weight of a column of air with...Ch. 15 - A 4680-kg circus elephant balances on one foot. If...Ch. 15 - You unbend a paper clip made from 1.5-mm-diameter...Ch. 15 - Whats the density of a fluid whose pressure...Ch. 15 - A research submarine can withstand an external...Ch. 15 - Prob. 25ECh. 15 - A vertical tube open at the top contains 5.0 cm of...Ch. 15 - A child attempts to drink water through a...Ch. 15 - Barometric pressure in the eye of a hurricane is...Ch. 15 - Prob. 29ECh. 15 - A 5.4-g jewel has apparent weight 32 mN when...Ch. 15 - Styrofoams density is 160kg/m3. What percent error...Ch. 15 - A steel drum has volume 0.23 m3 and mass 16 kg....Ch. 15 - Water flows through a 2.5-cm-diameter pipe at 1.8...Ch. 15 - Show that pressure has the units of energy...Ch. 15 - A typical mass flow rate for the Mississippi River...Ch. 15 - Prob. 36ECh. 15 - A typical human aorta, the main artery from the...Ch. 15 - When a couple with total mass 120 kg lies on a...Ch. 15 - A fully loaded Volvo station wagon has mass 1950...Ch. 15 - Youre stuck in the exit row on a long flight, and...Ch. 15 - A vertical tube 1.0 cm in diameter and open at the...Ch. 15 - Dam breaks present a serious risk of widespread...Ch. 15 - A U-shaped tube open at both ends contains water...Ch. 15 - Prob. 44PCh. 15 - A garage lift has a 45-cm-diameter piston...Ch. 15 - Archimedes purportedly used his principle to...Ch. 15 - Youre testifying in a drunk-driving case for which...Ch. 15 - A glass beaker measures 14 cm high by 5.0 cm in...Ch. 15 - A typical supertanker has mass 2.0 106 kg and...Ch. 15 - A balloon contains gas of density and is to lift a...Ch. 15 - (a) How much helium (density 0.18 kg/m3) is needed...Ch. 15 - A 55-kg swimmer climbs onto a Styrofoam block of...Ch. 15 - If the blood pressure in the unobstructed artery...Ch. 15 - Youre a consultant for maple syrup producers. They...Ch. 15 - The water in a garden hose is at 140-kPa gauge...Ch. 15 - The venturi flowmeter shown in Fig. 15.26 is used...Ch. 15 - A 1.0-cm-diameter venturi flowmeter is inserted in...Ch. 15 - A balloons mass is 1.6 g when its empty. Its...Ch. 15 - Blood with density 1.06 g/cm3 and 10-kPa gauge...Ch. 15 - Prob. 60PCh. 15 - A drinking straw 20 cm long and 3.0 mm in diameter...Ch. 15 - In 2012, film producer James Cameron (Terminator,...Ch. 15 - Prob. 63PCh. 15 - Water emerges from a faucet of diameter d0 in...Ch. 15 - Assuming norm.nl atmospheric pressure, how massive...Ch. 15 - Figure 15.28 shows a simplified diagram of a Pitot...Ch. 15 - At a hearing on a proposed wind farm, a...Ch. 15 - A pencil is weighted so it floats vertically with...Ch. 15 - A can of height h and cross-sectional area A0 is...Ch. 15 - Density and pressure in Earths atmosphere are...Ch. 15 - (a) Use the result of Problem 70 to express...Ch. 15 - A circular pan of liquid with density is centered...Ch. 15 - A solid sphere of radius R and mass M has density ...Ch. 15 - The difference in air pressure between the inside...Ch. 15 - Find the torque that the water exerts about the...Ch. 15 - One vertical wall of a swimming pool is a regular...Ch. 15 - Youre a private investigator assisting a large...Ch. 15 - A plumber conies to your ancient apartment...Ch. 15 - Your class in naval architecture is working on the...Ch. 15 - Prob. 80PPCh. 15 - Prob. 81PPCh. 15 - Prob. 82PPCh. 15 - Prob. 83PP
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