Concept explainers
A 10.0-kg block of metal measuring 12.0 cm by 10.0 cm by 10.0 cm is suspended from a scale and immersed in water as shown in Figure P14.11b. The 12.0-cm dimension is vertical, and the top of the block is 5.00 cm below the surface of the water. (a) What are the magnitudes of the forces acting on the top and on the bottom of the block due to the surrounding water? (b) What is the reading of the spring scale? (c) Show that the buoyant force equals the difference between the forces at the top and bottom of the block.
Figure P14.11 Problems 11 and 12.
(a)
The magnitudes of the forces acting on the top and on the bottom of the block due to the surrounding water.
Answer to Problem 12P
The magnitudes of the forces acting on the top and on the bottom of the block due to the surrounding water is
Explanation of Solution
Section 1:
To determine: The magnitudes of the force acting on the top of the block due to the surrounding water.
Answer: The magnitudes of the force acting on the top of the block due to the surrounding water is
Given information:
The mass of the block is
Formula to calculate the absolute pressure at the top of the block is,
Formula to calculate the force acting on the top of the block is,
Substitute
Substitute
Conclusion:
Therefore, the magnitudes of the force acting on the top of the block due to the surrounding water is
Section 2:
To determine: The magnitudes of the force acting on the bottom of the block due to the surrounding water.
Answer: The magnitudes of the force acting on the bottom of the block due to the surrounding water is
Given information:
The mass of the block is
Formula to calculate the absolute pressure at the bottom of the block is,
Formula to calculate the force acting on the bottom of the block is,
Substitute
Substitute
Conclusion:
Therefore, the magnitudes of the force acting on the bottom of the block due to the surrounding water is
(b)
The reading of the spring scale.
Answer to Problem 12P
The reading in the spring scale is
Explanation of Solution
Given information:
The mass of the block is
The scale reading when the block is immersed in water is equal to the tension in the chord supporting the block.
Apply the equilibrium condition.
Rearrange the above equation for
Substitute
Conclusion:
Therefore, the reading in the spring scale is
(c)
To show: That the buoyant force equals the difference between the force at the top and bottom of the block.
Explanation of Solution
Given information:
The mass of the block is
When an object is immersed in a liquid, then the upward force exerted on it by fluid is called buoyant force and its magnitude equals the weight of the liquid displaced by the object.
Formula to calculate the buoyant force is,
Substitute
From part (a), the difference between the force at the top and bottom of the block is,
From the above calculations it is clear that,
Conclusion:
Therefore, the buoyant force equals the difference between the force at the top and bottom of the block.
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Chapter 14 Solutions
Physics for Scientists and Engineers with Modern Physics