Concept explainers
A rectangular barge 5 m long and 2 m wide floats in fresh water.
a. Show that the barge will sink 5 cm lower when loaded with 500 kg of sand.
b. If the barge can only be pushed 10 cm deeper into the water before water overflows to sink it, how many kilograms of sand can it carry?
(a)
To show:The barge will sink
Explanation of Solution
Given:
The mass of the sand is
The length of the rectangular barge
The width of the rectangular barge
Formula used:
The expression for pressure is,
Here,
The expression for the volume is,
Here,
Calculation:
Consider the density of water as
The height of sink for the barge is,
Conclusion:
Thus, the barge will sink
(b)
The mass of the sand carried.
Answer to Problem 59A
The mass of the sand is
Explanation of Solution
Given:
The length of the rectangular barge
The width of the rectangular barge
The height of sink for the barge is
Formula used:
The expression for pressure is,
Here,
The expression for the volume is,
Here,
Calculation:
Consider the density of water as
The mass of the sand is,
Conclusion:
Thus, the mass of the sand is
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Conceptual Physics: The High School Physics Program
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