(a)
The distance below the water surface at which is the bottom face of the block.
(a)
Answer to Problem 65P
The distance below the water surface at which is the bottom face of the block is
Explanation of Solution
Write the condition for equilibrium.
Here,
Write the equation for the buoyant force.
Here,
Write the equation for
Here,
Put equation (III) in equation (II).
Write the equation for the force of gravity on the ice cube.
Here,
Write the equation for density of ice.
Here,
Rewrite the above equation for
Write the equation for
Put the above equation in equation (VI).
Put the above equation in equation (V).
Put equations (IV) and (VII) in equation (I) and rearrange it for
Conclusion:
The density of ice is
Substitute
Therefore, the distance below the water surface at which is the bottom face of the block is
(b)
The distance below the water surface at which is the bottom face of the block after the alcohol is poured into water surface.
(b)
Answer to Problem 65P
The distance below the water surface at which is the bottom face of the block after the alcohol is poured into water surface is
Explanation of Solution
Assume that the top of the cube is still above the alcohol surface.
Write the equation for the buoyant force.
Here,
Write the equation for
Here,
Put equations (III) and (X) in equation (IX).
Put equations (VII) and (XI) in equation (I) and rearrange it for
Conclusion:
The density of alcohol is
Substitute
Therefore, the distance below the water surface at which is the bottom face of the block after the alcohol is poured into water surface is
(c)
The thickness of the layer of ethyl alcohol required.
(c)
Answer to Problem 65P
The thickness of the layer of ethyl alcohol required is
Explanation of Solution
Write the equation of
Here,
Write the equation of
Put the above equation in equation (III).
Put equations (XIII) and (XIV) in equation (IX).
Put equations (VII) and (XV) in equation (I) and rearrange it for
Conclusion:
Substitute
Therefore, the thickness of the layer of ethyl alcohol required is
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Chapter 15 Solutions
Principles of Physics: A Calculus-Based Text
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