Physics for Scientists and Engineers, Technology Update (No access codes included)
Physics for Scientists and Engineers, Technology Update (No access codes included)
9th Edition
ISBN: 9781305116399
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 14, Problem 14.85CP

An ice cube whose edges measure 20.0 mm is floating in a glass of ice-cold water, and one of the ice cube's faces is parallel to the water’s surface, (a) How far below the water surface is the bottom face of the block? (b) Ice-cold ethyl alcohol is gently poured onto the water surface to form a layer 5.00 mm thick above the water. The alcohol does not mix with the water. When the ice cube again attains hydrostatic equilibrium, what is the distance from the top of the water to the bottom face of the block? (c) Additional cold ethyl alcohol is poured onto the water’s surface until the top surface of the alcohol coincides with the top surface of the ice cube (in hydrostatic equilibrium). How thick is the required layer of ethyl alcohol?

(a)

Expert Solution
Check Mark
To determine

The distance between the water surface and the bottom face of the ice block.

Answer to Problem 14.85CP

The distance between the water surface and the bottom face of the ice block is 18.3mm .

Explanation of Solution

Given info: The edge of the ice cube is 20.0mm .

Formula to calculate the weight of the ice is,

Wc=ρigs3

Here,

Wc is the weight of the ice cube.

ρi is the density of ice.

s is the side of the edge of ice.

g is the acceleration due to gravity.

Formula to calculate the buoyant force is,

FB=ρwghs2

Here,

FB is the buoyant force.

ρw is the density of water.

h is the distance between the water surface and the bottom face of the ice block.

By the Archimedes’s principle the buoyant force is equal to the weight of the ice cube.

FB=Wc

Substitute ρwghs2 for FB and ρigs3 for Wc in the above equation.

ρwghs2=ρigs3

Rearrange the above expression for h .

h=ρiρws

Substitute 1000kg/m3 for ρw , 917kg/m3 for ρi and 20.0mm for s in the above equation to find the value of h .

h=917kg/m31000kg/m3(20.0mm)=18.3mm

Conclusion:

Therefore, the distance between the water surface and the bottom face of the ice block is 18.3mm .

(b)

Expert Solution
Check Mark
To determine

The distance between the top of the water and the bottom face of the block.

Answer to Problem 14.85CP

The distance between the top of the water and the bottom face of the block is 14.3mm .

Explanation of Solution

Given info: The edge of the ice cube is 20.0mm and the thickness of alcohol layer is 5.00mm .

Formula to calculate the buoyant force due to water is,

(FB)1=ρwghws2

Here,

(FB)1 is the buoyant force due to the water.

ρw is the density of water.

h is the distance between the top of the water and the bottom face of the block.

Formula to calculate the buoyant force due to alcohol is,

(FB)2=ρaghas2

Here,

(FB)2 is the buoyant force due to the alcohol.

ρa is the density of alcohol.

ha is the thickness of alcohol.

By the Archimedes’s principle the buoyant force is equal to the weight of the ice cube.

(FB)1+(FB)2=Wc

Substitute ρwghws2 for (FB)1 , ρaghas2 for (FB)2 and ρigs3 for Wc in the above equation.

ρwghws2+ρaghas2=ρigs3

Rearrange the above expression for hw .

hw=sρihaρaρw

Substitute 1000kg/m3 for ρw , 917kg/m3 for ρi , 806kg/m3 for ρa , 5.00mm for ha and 20.0mm for s  in the above equation to find the value of hw .

hw=(20.0mm)(917kg/m3)(5.00mm)(806kg/m3)1000kg/m3=14.3mm

Conclusion:

Therefore, the distance between the top of the water and the bottom face of the block is 14.3mm .

(c)

Expert Solution
Check Mark
To determine

The thickness of the layer of ethyl alcohol.

Answer to Problem 14.85CP

The thickness of the layer of ethyl alcohol is 8.56mm .

Explanation of Solution

Given info: The edge of the ice cube is 20.0mm .

Formula to calculate the buoyant force due to alcohol is,

(FB)3=ρaghas2

Here,

(FB)3 is the buoyant force due to the alcohol.

ρa is the density of alcohol.

ha is the thickness of alcohol.

Formula to calculate the buoyant force due to water is,

(FB)4=ρwg(sha)s2

Here,

(FB)4 is the buoyant force due to the water.

ρw is the density of water.

By the Archimedes’s principle the buoyant force is equal to the weight of the ice cube.

(FB)3+(FB)4=Wc

Substitute ρaghas2 for (FB)3 , ρwg(sha)s2 for (FB)4 and ρigs3 for Wc in the above equation.

ρaghas2+ρwg(sha)s2=ρigs3

Rearrange the above expression for ha .

ha=s(ρwρi)(ρwρa)

Substitute 1000kg/m3 for ρw , 917kg/m3 for ρi , 806kg/m3 for ρa , and 20.0mm for s in the above equation to find the value of ha .

ha=(20.0mm)[(1000kg/m3)(917kg/m3)][(1000kg/m3)(806kg/m3)]=8.56mm

Conclusion:

Therefore, the thickness of the layer of ethyl alcohol is 8.56mm .

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Chapter 14 Solutions

Physics for Scientists and Engineers, Technology Update (No access codes included)

Ch. 14 - A solid iron sphere and a solid lead sphere of the...Ch. 14 - Prob. 14.7OQCh. 14 - One of the predicted problems due to global...Ch. 14 - A boat develops a leak and, after its passengers...Ch. 14 - A small piece of steel is tied to a block of wood....Ch. 14 - A piece of unpainted porous wood barely floats in...Ch. 14 - A person in a boat floating in a small pond throws...Ch. 14 - Rank the buoyant forces exerted on the following...Ch. 14 - A water supply maintains a constant rate of flow...Ch. 14 - A glass of water contains floating ice cubes. When...Ch. 14 - An ideal fluid flows through a horizontal pipe...Ch. 14 - When an object is immersed in a liquid at rest,...Ch. 14 - Two thin-walled drinking glasses having equal base...Ch. 14 - Because atmospheric pressure is about 105 N/m2 and...Ch. 14 - A fish rests on the bottom of a bucket of water...Ch. 14 - You are a passenger on a spacecraft. For your...Ch. 14 - Prob. 14.6CQCh. 14 - Prob. 14.7CQCh. 14 - If you release a ball while inside a freely...Ch. 14 - (a) Is the buoyant force a conservative force? (b)...Ch. 14 - All empty metal soap dish barely floats in water....Ch. 14 - Prob. 14.11CQCh. 14 - Prob. 14.12CQCh. 14 - Prob. 14.13CQCh. 14 - Does a ship float higher in the water of an inland...Ch. 14 - Prob. 14.15CQCh. 14 - Prob. 14.16CQCh. 14 - Prairie dogs ventilate their burrows by building a...Ch. 14 - Prob. 14.18CQCh. 14 - Prob. 14.19CQCh. 14 - A large man sits on a four-legged chair with his...Ch. 14 - Prob. 14.2PCh. 14 - A 50.0-kg woman wearing high-heeled shoes is...Ch. 14 - Estimate the total mass of the Earths atmosphere....Ch. 14 - Calculate the mass of a solid gold rectangular bar...Ch. 14 - (a) A wry powerful vacuum cleaner has a hose 2.86...Ch. 14 - The spring of the pressure gauge shown in Figure...Ch. 14 - The small piston of a hydraulic lift (Fig. P14.8)...Ch. 14 - What must be the contact area between a suction...Ch. 14 - A swimming pool has dimensions 30.0 m 10.0 m and...Ch. 14 - (a) Calculate the absolute pressure at the bottom...Ch. 14 - Prob. 14.12PCh. 14 - Prob. 14.13PCh. 14 - A container is filled to a depth of 20.0 cm with...Ch. 14 - Review. 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The...Ch. 14 - The human brain and spinal cord are immersed in...Ch. 14 - Blaise Pascal duplicated Torricellis barometer...Ch. 14 - Prob. 14.22PCh. 14 - A backyard swimming pool with a circular base of...Ch. 14 - A tank with a flat bottom of area A and vertical...Ch. 14 - A table-tennis ball has a diameter of 3.80 cm and...Ch. 14 - Prob. 14.26PCh. 14 - A 10.0-kg block of metal measuring 12.0 cm by 10.0...Ch. 14 - A light balloon is filled with 400 m3 of helium at...Ch. 14 - A cube of wood having an edge dimension of 20.0 cm...Ch. 14 - The United States possesses the ten largest...Ch. 14 - A plastic sphere floats in water with 50.0% of its...Ch. 14 - A spherical vessel used for deep-sea exploration...Ch. 14 - A wooden block of volume 5.24 104 m3 floats in...Ch. 14 - The weight of a rectangular block of low-density...Ch. 14 - A large weather balloon whose mass is 226 kg is...Ch. 14 - A hydrometer is an instrument used to determine...Ch. 14 - Refer to Problem 16 and Figure P14.16. A...Ch. 14 - On October 21, 2001, Ian Ashpole of the United...Ch. 14 - How many cubic meters of helium are required to...Ch. 14 - Water flowing through a garden hose of diameter...Ch. 14 - A large storage tank, open at the top and filled...Ch. 14 - Prob. 14.42PCh. 14 - Prob. 14.43PCh. 14 - A village maintains a large tank with ail open...Ch. 14 - A legendary Dutch boy saved Holland by plugging a...Ch. 14 - Water falls over a dam of height h with a mass...Ch. 14 - Water is pumped up from the Colorado River to...Ch. 14 - In ideal flow, a liquid of density 850 kg/m3 moves...Ch. 14 - The Venturi tube discussed in Example 14.8 and...Ch. 14 - Review. Old Faithful Geyser in Yellowstone...Ch. 14 - An airplane is cruising al altitude 10 km. The...Ch. 14 - An airplane has a mass of 1.60 104 kg, and each...Ch. 14 - Prob. 14.53PCh. 14 - The Bernoulli effect can have important...Ch. 14 - Prob. 14.55PCh. 14 - Decades ago, it was thought that huge herbivorous...Ch. 14 - (a) Calculate the absolute pressure at an ocean...Ch. 14 - Prob. 14.58APCh. 14 - A spherical aluminum ball of mass 1.26 kg contains...Ch. 14 - Prob. 14.60APCh. 14 - Review. Figure P14.61 shows a valve separating a...Ch. 14 - The true weight of an object can be measured in a...Ch. 14 - Water is forced out of a fire extinguisher by air...Ch. 14 - Review. Assume a certain liquid, with density 1...Ch. 14 - Prob. 14.65APCh. 14 - Prob. 14.66APCh. 14 - Prob. 14.67APCh. 14 - A common parameter that can be used to predict...Ch. 14 - Evangelista Torricelli was the first person to...Ch. 14 - Review. With reference to the dam studied in...Ch. 14 - A 1.00-kg beaker containing 2.00 kg of oil...Ch. 14 - A beaker of mass mb containing oil of mass mu and...Ch. 14 - In 1983, the United States began coining the...Ch. 14 - Review. A long, cylindrical rod of radius r is...Ch. 14 - Prob. 14.75APCh. 14 - The spirit-in-glass thermometer, invented in...Ch. 14 - Prob. 14.77APCh. 14 - Review. In a water pistol, a piston drives water...Ch. 14 - Prob. 14.79APCh. 14 - The water supply of a building is fed through a...Ch. 14 - A U-tube open at both ends is partially filled...Ch. 14 - A woman is draining her fish tank by siphoning the...Ch. 14 - The hull of an experimental boat is to be lifted...Ch. 14 - Prob. 14.84APCh. 14 - An ice cube whose edges measure 20.0 mm is...Ch. 14 - Why is the following situation impossible? A barge...Ch. 14 - Show that the variation of atmospheric pressure...
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