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)
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
Explanation of Solution
Given info: The edge of the ice cube is
Formula to calculate the weight of the ice is,
Here,
Formula to calculate the buoyant force is,
Here,
By the Archimedes’s principle the buoyant force is equal to the weight of the ice cube.
Substitute
Rearrange the above expression for
Substitute
Conclusion:
Therefore, the distance between the water surface and the bottom face of the ice block is
(b)
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
Explanation of Solution
Given info: The edge of the ice cube is
Formula to calculate the buoyant force due to water is,
Here,
Formula to calculate the buoyant force due to alcohol is,
Here,
By the Archimedes’s principle the buoyant force is equal to the weight of the ice cube.
Substitute
Rearrange the above expression for
Substitute
Conclusion:
Therefore, the distance between the top of the water and the bottom face of the block is
(c)
The thickness of the layer of ethyl alcohol.
Answer to Problem 14.85CP
The thickness of the layer of ethyl alcohol is
Explanation of Solution
Given info: The edge of the ice cube is
Formula to calculate the buoyant force due to alcohol is,
Here,
Formula to calculate the buoyant force due to water is,
Here,
By the Archimedes’s principle the buoyant force is equal to the weight of the ice cube.
Substitute
Rearrange the above expression for
Substitute
Conclusion:
Therefore, the thickness of the layer of ethyl alcohol is
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Chapter 14 Solutions
Physics for Scientists and Engineers (AP Edition)
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