(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
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- What fraction of ice is submerged when it floats in freshwater, given the density of water 0°C is very close to 1000 kg/m3?arrow_forwardWater flows through a fire hose of diameter 6.35 cm at a rate of 0.0120 m3/s. The fire hose ends in a nozzle of inner diameter 2.20 cm. What is the speed with which the water exits the nozzle?arrow_forwardBird bones have air pockets to reduce their weight—this also gives them an average density significantly less than that of the bones of other animals. Suppose an ornithologist weighs a bird bone air and in water and finds its mass is 45.0 g ad its apparent mass when submerged is 3.60 g (assume the bone is watertight.)(a) What mass of is displaced? (b) What is the volume of the bone? (c) What is its average density?arrow_forward
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