Concept explainers
A rectangular block of Styrofoam 25.0 cm in length, 15.0 cm in width, and 12.0 cm in height is placed in a large tub of water. Assume the density of Styrofoam is 3.00 × 102 kg/m3. a. What volume of the block is submerged? b. A copper block is now placed atop the Styrofoam block so that the top of the Styrofoam block is level with the surface of the water. What is the mass of the copper block?
(a)
The submerged volume of the block.
Answer to Problem 33PQ
The submerged volume of the block is
Explanation of Solution
The submerged volume of the object is equal to the volume of the water displaced.
Write the equation of force at equilibrium.
Here,
Write the expression for the buoyant force.
Here,
Write the expression for the gravity force.
Here,
Write the expression of the volume of the block.
Here,
Rewrite the expression from equation (I) to express displaced volume by using (II), (III) and (IV).
Conclusion:
Substitute
Thus, the submerged volume of the block is
(b)
The mass of the copper block.
Answer to Problem 33PQ
The mass of the copper block is
Explanation of Solution
Write the equation of force at equilibrium.
Here,
Write the expression for the buoyant force.
Here,
Write the expression for the gravity force.
Here,
Write the expression of the volume of the block.
Here,
Rewrite the expression from equation (VI) to express mass of copper block by using (VII), (VIII) and (IX).
Conclusion:
Substitute
Thus, the mass of the copper block is
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Chapter 15 Solutions
Physics for Scientists and Engineers: Foundations and Connections
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