Concept explainers
(a)
The density of the salt water.
(a)
Answer to Problem 34PQ
The density of the salt water is
Explanation of Solution
Write the expression for density of salt water.
Here,
Write the expression for mass of the salt water.
Here,
Write the expression for mass of the water.
Here,
Write the equation for total volume of the salt and water.
Conclusion:
Substitute the equation (II), (IIII, and (IV) in the equation (I).
Substitute
Thus, the density of the salt water is
(b)
The density and mass of a grape.
(b)
Answer to Problem 34PQ
The density of a grape is
Explanation of Solution
Since the grapes are floating, so their acceleration is zero, and the buoyant force equals to the weight of the grape.
Write the expression for the buoyant force equals to the weight of the grape.
Write the expression for force due to gravity of the grape.
Here,
Write the expression for buoyant force.
Write the expression for mass of a grape.
Here,
Conclusion:
Substitute the equation (VI) and (VII) in the equation (V).
Substitute
Substitute
Therefore, The density of a grape is
(c)
If the raisin is denser than a grape.
(c)
Answer to Problem 34PQ
Yes, the raisin is denser than a grape.
Explanation of Solution
Raisins have a complicated, wrinkly surface and even though they are dried out grapes can contain a substantial amount of water inside.
Since the raisin remains in the bottom of the glass, it must be denser than salt water and thus, it is denser than a grape.
Conclusion:
Thus, the raisin is denser than a grape.
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Chapter 15 Solutions
Physics for Scientists and Engineers: Foundations and Connections
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