Explanation Given info: The iron pile is in the shape of cone, the radius of the cone is r and equal to the central height of h . The barge is square in shape, with vertical sides of length 2 r . Assume the top of the barge without the pile of iron has height H o above the surface of the water. When the mass of the iron M Fe is added to the barge, the barge sinks a distance Δ H until the buoyant force from the water equals to the additional weight of the iron and supporting the extra weight is, B = ρ w ( 2 r ) 2 Δ H × g = M Fe g (1) Here, ρ w is the density of the water. g is the acceleration due to gravity. M Fe is the mass of the iron pile. Formula to calculate the mass of the iron pile is, M Fe = ρ Fe π 3 r 2 H Here, ρ Fe is the density of the iron pile. H is the height of the cone. r is the radius of the cone. Substitute ρ Fe π 3 r 2 H for M Fe in equation (1). ρ w ( 2 r ) 2 Δ H × g = ( ρ Fe π 3 r 2 H ) g Δ H = ( ρ Fe ρ w ) ( π 3 ) ( r 2 ( 2 r ) 2 ) H = ( ρ Fe ρ w ) ( π 12 ) H If the iron is piled to height H , the barge will sink by distance Δ H , so the distance from the water level to the top of the iron pile is, D top = H o − Δ H + H Substitute ( ρ Fe ρ w ) ( π 12 ) H for Δ H in above expression. D top = H o − ( ρ Fe ρ w ) ( π 12 ) H + H The radius of the cone is equal to the height. H = r Substitute r for H in above expression. D top = H o − ( ρ Fe ρ w ) ( π 12 ) r + r Substitute 1000 kg / m 3 for ρ w and 7

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 68P

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Chapter 15, Problem 67P

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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 reason for the following situation is impossible.

Solution Summary: The author explains that lowering the height of the iron pile on the barge while keeping the base radius the same results in the top rising higher above the water level.

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The reason for the following situation is impossible.

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Chapter 15 Solutions