Explanation Assume that the balloons are spherically shaped with radius 0.125 m and contain helium at Standard Temperature and Pressure and are immersed in air at 0 ° C 1 atm . Also assume that the rubber envelope has mass equal to 5.00 × 10 − 3 kg . Take the upward direction to be positive direction. Write the equation for the net force in the upward direction on each balloon. F up = B − F g , He − F g , env (I) Here, F up is the force in the upward direction, B is the buoyant force, F g , He is the weight of the helium balloon and F g , env is the weight of the rubber envelope. Write the equation for the buoyant force. B = ρ air V g (II) Here, ρ air is the density of the air, V is the volume of the balloon and g is the acceleration due to gravity. Write the equation for the weight of the helium balloon. F g , He = m He g (III) Here, m He is the mass of the helium balloon. Write the equation for density of the balloon. ρ He = m He V Here, ρ He is the density of helium and V is the volume of the balloon. Rewrite the above equation for m He . m He = ρ He V Put the above equation in equation (III). F g , He = ρ He V g (IV) Write the equation for the weight of the envelope. F g , env = m env g (V) Here, m env is the mass of the rubber envelope. Put equations (II), (IV) and (V) in equation (I). F up = ρ air V g − ρ He V g − m env g = ( ρ air − ρ He ) V g − m env g (VI) Write the equation for the volume of the balloon. V = 4 3 π r 3 Here, r is the radius of the balloon. Put the above equation in equation (VI). F up = ( ρ air − ρ He ) ( 4 3 π r 3 ) g − m env g (VII) Write the equation for the number of balloons required

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 34P

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The order of magnitude of the number of helium-filled balloons required to lift a person.

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Chapter 15, Problem 33P

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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. 15.2QQ Ch. 15.4 - An apple is held completely submerged just below...Ch. 15.4 - Prob. 15.4QQ Ch. 15.6 - Prob. 15.5QQ Ch. 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. 2OQ Ch. 15 - Prob. 3OQ Ch. 15 - Prob. 4OQ

Ch. 15 - A solid iron sphere and a solid lead sphere of the...Ch. 15 - Prob. 6OQ Ch. 15 - Prob. 7OQ Ch. 15 - Prob. 8OQ Ch. 15 - An ideal fluid flows through a horizontal pipe...Ch. 15 - Prob. 10OQ Ch. 15 - Prob. 11OQ Ch. 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. 14OQ Ch. 15 - A water supply maintains a constant rate of flow...Ch. 15 - Prob. 1CQ Ch. 15 - Because atmospheric pressure is about 105 N/m2 and...Ch. 15 - Two thin-walled drinking glasses having equal base...Ch. 15 - Prob. 4CQ Ch. 15 - Prob. 5CQ Ch. 15 - Prob. 6CQ Ch. 15 - Prob. 7CQ Ch. 15 - Prob. 8CQ Ch. 15 - Prob. 9CQ Ch. 15 - Prob. 10CQ Ch. 15 - Prob. 11CQ Ch. 15 - Prob. 12CQ Ch. 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. 15CQ Ch. 15 - How would you determine the density of an...Ch. 15 - Prob. 17CQ Ch. 15 - Place two cans of soft drinks, one regular and one...Ch. 15 - Prob. 19CQ Ch. 15 - Prob. 1P Ch. 15 - A 50.0-kg woman wearing high-heeled shoes is...Ch. 15 - Prob. 3P Ch. 15 - Prob. 4P Ch. 15 - Prob. 5P Ch. 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. 8P Ch. 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. 12P Ch. 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. 15P Ch. 15 - Prob. 16P Ch. 15 - Mercury is poured into a U-tube as shown in Figure...Ch. 15 - Prob. 18P Ch. 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. 21P Ch. 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. 26P Ch. 15 - Prob. 27P Ch. 15 - Prob. 28P Ch. 15 - How many cubic meters of helium are required to...Ch. 15 - Prob. 30P Ch. 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. 34P Ch. 15 - Prob. 35P Ch. 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. 38P Ch. 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. 43P Ch. 15 - Prob. 44P Ch. 15 - A village maintains a large tank with an open top,...Ch. 15 - Prob. 46P Ch. 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. 50P Ch. 15 - Prob. 51P Ch. 15 - Prob. 52P Ch. 15 - Prob. 53P Ch. 15 - Prob. 54P Ch. 15 - Prob. 55P Ch. 15 - Prob. 56P Ch. 15 - Prob. 57P Ch. 15 - Prob. 58P Ch. 15 - Review. A copper cylinder hangs at the bottom of a...Ch. 15 - Prob. 60P Ch. 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. 65P Ch. 15 - Prob. 66P Ch. 15 - A U-tube open at both ends is partially filled...Ch. 15 - Prob. 68P Ch. 15 - Prob. 69P Ch. 15 - The spirit-in-glass thermometer, invented in...

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The order of magnitude of the number of helium-filled balloons required to lift a person.

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Chapter 15 Solutions