Principles of Physics: A Calculus-Based Text
5th Edition
ISBN: 9781133104261
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 15, Problem 66P
To determine
To show: The variation of atmospheric pressure with altitude is
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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?
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 density of air is 1.3 kg/m at sea level. From your knowledge of air pressure at ground level, estimate the height of the atmosphere. As a simplifying assumption, take the atmosphere to be of
uniform density up to some height, after which the density rapidly falls to zero. (In reality, the density of the atmosphere decreases as we go up.) t
O 1 km
O 10 km
O 100 km
O 1000 km
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Chapter 15 Solutions
Principles of Physics: A Calculus-Based Text
Ch. 15.1 - Suppose you are standing directly behind someone...Ch. 15.2 - Prob. 15.2QQCh. 15.4 - An apple is held completely submerged just below...Ch. 15.4 - Prob. 15.4QQCh. 15.6 - Prob. 15.5QQCh. 15.7 - You observe two helium balloons floating next to...Ch. 15 - A wooden block floats in water, and a steel object...Ch. 15 - Prob. 2OQCh. 15 - Prob. 3OQCh. 15 - Prob. 4OQ
Ch. 15 - A solid iron sphere and a solid lead sphere of the...Ch. 15 - Prob. 6OQCh. 15 - Prob. 7OQCh. 15 - Prob. 8OQCh. 15 - An ideal fluid flows through a horizontal pipe...Ch. 15 - Prob. 10OQCh. 15 - Prob. 11OQCh. 15 - A small piece of steel is tied to a block of wood....Ch. 15 - A piece of unpainted porous wood barely floats in...Ch. 15 - Prob. 14OQCh. 15 - A water supply maintains a constant rate of flow...Ch. 15 - Prob. 1CQCh. 15 - Because atmospheric pressure is about 105 N/m2 and...Ch. 15 - Two thin-walled drinking glasses having equal base...Ch. 15 - Prob. 4CQCh. 15 - Prob. 5CQCh. 15 - Prob. 6CQCh. 15 - Prob. 7CQCh. 15 - Prob. 8CQCh. 15 - Prob. 9CQCh. 15 - Prob. 10CQCh. 15 - Prob. 11CQCh. 15 - Prob. 12CQCh. 15 - (a) Is the buoyant force a conservative force? (b)...Ch. 15 - An empty metal soap dish barely floats in water. A...Ch. 15 - Prob. 15CQCh. 15 - How would you determine the density of an...Ch. 15 - Prob. 17CQCh. 15 - Place two cans of soft drinks, one regular and one...Ch. 15 - Prob. 19CQCh. 15 - Prob. 1PCh. 15 - A 50.0-kg woman wearing high-heeled shoes is...Ch. 15 - Prob. 3PCh. 15 - Prob. 4PCh. 15 - Prob. 5PCh. 15 - The small piston of a hydraulic lift (Fig. P15.6)...Ch. 15 - A container is filled to a depth of 20.0 cm with...Ch. 15 - Prob. 8PCh. 15 - (a) Calculate the absolute pressure at an ocean...Ch. 15 - (a) A very powerful vacuum cleaner has a hose 2.86...Ch. 15 - What must be the contact area between a suction...Ch. 15 - Prob. 12PCh. 15 - Review. The tank in Figure P15.13 is filled with...Ch. 15 - Review. The tank in Figure P15.13 is filled with...Ch. 15 - Prob. 15PCh. 15 - Prob. 16PCh. 15 - Mercury is poured into a U-tube as shown in Figure...Ch. 15 - Prob. 18PCh. 15 - A backyard swimming pool with a circular base of...Ch. 15 - A tank with a flat bottom of area A and vertical...Ch. 15 - Prob. 21PCh. 15 - A Styrofoam slab has thickness h and density s....Ch. 15 - A table-tennis ball has a diameter of 3.80 cm and...Ch. 15 - The gravitational force exerted on a solid object...Ch. 15 - A 10.0-kg block of metal measuring 12.0 cm by 10.0...Ch. 15 - Prob. 26PCh. 15 - Prob. 27PCh. 15 - Prob. 28PCh. 15 - How many cubic meters of helium are required to...Ch. 15 - Prob. 30PCh. 15 - A plastic sphere floats in water with 50.0% of its...Ch. 15 - The weight of a rectangular block of low-density...Ch. 15 - Decades ago, it was thought that huge herbivorous...Ch. 15 - Prob. 34PCh. 15 - Prob. 35PCh. 15 - A light balloon is filled with 400 m3 of helium at...Ch. 15 - A horizontal pipe 10.0 cm in diameter has a smooth...Ch. 15 - Prob. 38PCh. 15 - A large storage tank with an open top is filled to...Ch. 15 - Review. Old Faithful Geyser in Yellowstone...Ch. 15 - (a) A water hose 2.00 cm in diameter is used to...Ch. 15 - Water flows through a fire hose of diameter 6.35...Ch. 15 - Prob. 43PCh. 15 - Prob. 44PCh. 15 - A village maintains a large tank with an open top,...Ch. 15 - Prob. 46PCh. 15 - Figure P15.47 shows a stream of water in steady...Ch. 15 - An airplane is cruising at altitude 10 km. The...Ch. 15 - The Bernoulli effect can have important...Ch. 15 - Prob. 50PCh. 15 - Prob. 51PCh. 15 - Prob. 52PCh. 15 - Prob. 53PCh. 15 - Prob. 54PCh. 15 - Prob. 55PCh. 15 - Prob. 56PCh. 15 - Prob. 57PCh. 15 - Prob. 58PCh. 15 - Review. A copper cylinder hangs at the bottom of a...Ch. 15 - Prob. 60PCh. 15 - An incompressible, nonviscous fluid is initially...Ch. 15 - In about 1657, Otto von Guericke, inventor of the...Ch. 15 - A 1.00-kg beaker containing 2.00 kg of oil...Ch. 15 - A beaker of mass mb containing oil of mass mo and...Ch. 15 - Prob. 65PCh. 15 - Prob. 66PCh. 15 - A U-tube open at both ends is partially filled...Ch. 15 - Prob. 68PCh. 15 - Prob. 69PCh. 15 - The spirit-in-glass thermometer, invented in...
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- How many cubic meters of helium are required to lift a light balloon with a 400-kg payload to a height of 8 000 m? Take Hc = 0.179 kg/m3. Assume the balloon maintains a constant volume and the density of air decreases with the altitude z according to the expression pair = 0e-z/8 000, where z is in meters and 0 = 1.20 kg/m3 is the density of air at sea level.arrow_forwardA horizontal pipe 10.0 cm in diameter has a smooth reduction to a pipe 5.00 cm in diameter. If the pressure of the water in the larger pipe is 8.00 104 Pa and the pressure in the smaller pipe is 6.00 104 Pa, at what rate does water flow through the pipes?arrow_forwardA manometer containing water with one end connected to a container of gas has a column height difference of 0.60 m (Fig. P15.72). If the atmospheric pressure on the right column is 1.01 105 Pa, find the absolute pressure of the gas in the container. The density of water is 1.0 103 kg/m3. FIGURE P15.72arrow_forward
- Why is the Earths atmosphere denser near sea level than it is at a high altitude? Be sure to explain why the atmospheres density is not uniform and why the air isnt all in contact with the Earths surface.arrow_forward(a) Calculate the absolute pressure at an ocean depth of 1 000 m. Assume the density of seawater is 1 030 kg/m3 and the air above exerts a pressure of 101.3 kPa. (b) At this depth, what is the buoyant force on a spherical submarine having a diameter of 5.00 m?arrow_forwardThe weight of Earths atmosphere exerts an average pressure of 1.01 105 Pa on the ground at sea level. Use the definition of pressure to estimate the Height of Earths atmosphere by approximating Earth as a sphere of radius RE = 6.38 106 m and surface area A = 4RE2.arrow_forward
- A hollow copper (Cu = 8.92 103 kg/m3) spherical shell of mass m = 0.950 kg floats on water with its entire volume below the surface. a. What is the radius of the sphere? b. What is the thickness of the shell wall?arrow_forwardThe temperature of the atmosphere is not always constant and can increase or decrease with height. In a neutral atmosphere, where there is not a significant amount of vertical mixing, the temperature decreases at a rate of approximately 6.5 K per km. The magnitude of the decrease in temperature as height increases is known as the lapse rate (Γ). (The symbol is the upper case Greek letter gamma.) Assume that the surface pressure is p0 = 1.013 × 105 Pa where T = 293 K and the lapse rate is (−Γ = 6.5 K/km). Estimate the pressure 3.0 km above the surface of Earth.arrow_forwardVariation of Pressure in the atmosphere. The pressure of the atmosphere decreases as we move higher in the atmosphere. The decrease in pressure is proportional to the decrease in density of air. р = 2|2° P P Where P = pressure at any point in the atmosphere, and p = density of air at any point in the atmosphere Po pressure at sea level = 1.013 x 105 Pa, and Po air density at sea level = 1.3 kg/m³. a) What is the density p in terms of po, P, and Po? b) Start from the formula dP = - p g dy to determine the pressure at any height y. Note: P is variable c) What is the pressure if the height is 5.0 km above sea level? d) At what height above sea level is the pressure equal to ½ Po ?arrow_forward
- The volume of an air bubble increases by a factor of 3.19 times as it rises from the bottom of a lake (density = 1000 kg/m 3). This is due to the drop of the absolute pressure by a factor of 1/3.19. Ignoring any temperature changes, What is the depth of the lake? Take g = 9.8 m/s2. One atmospheric pressure = 1.013 x 105 N/m2. Please round your answer to one decimal place. Equation: ??ℎ+??=ρgh+Pa= 3.19 ??arrow_forwardWhat would be the height of the atmosphere if the air density (a) were uniform and (b) decreased linearly to zero with height? Assume that at sea level the air pressure is 1.00 atm and the air density is 1.28 kg/m^3.arrow_forwardAt what altitude in the Earth's atmosphere is the pressure equal to ½2 of the pressure at sea levelarrow_forward
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