Concept explainers
A 200-L iron tank has a mass of 36 kg. (a) Will it float in seawater when empty? (b) When filled with freshwater? (c) When filled with gasoline?
(a)

Whether the tank will float in seawater when empty or not.
Answer to Problem 53E
The tank will float in seawater when empty.
Explanation of Solution
Given info: The volume of the tank is
Write the expression for the mass of a substance in terms of volume and density.
Here,
Substitute
Thus, the empty tank can support up to
Conclusion:
Therefore, the tank will float in seawater when empty.
(b)

Whether the tank will float in sea water when filled with freshwater or not.
Answer to Problem 53E
The tank will not float in seawater when filled with freshwater.
Explanation of Solution
Given info: The empty tank can support up to
Write the expression for the mass of a substance in terms of volume and density.
Substitute
Thus, when the tank is filled with fresh water, the total mass (
Since the mass tank filled with freshwater is greater than that of the maximum mass that the tank can support (
Conclusion:
Therefore, the tank will not float in seawater when filled with freshwater.
(c)

Whether the tank will float in sea water when filled with gasoline or not.
Answer to Problem 53E
The tank will float in seawater when filled with gasoline.
Explanation of Solution
Given info: The empty tank can support up to
Write the expression for the mass of a substance in terms of volume and density.
Substitute
Thus, when the tank is filled with fresh water, the total mass of the system is,
Since the mass tank filled with gasoline is less than that of the maximum mass that the tank can support (
Conclusion:
Therefore, the tank will float in seawater when filled with gasoline.
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