Concept explainers
(a)
The force exerted by the water on the bottom.
(a)
Answer to Problem 8P
The force exerted by the water on the bottom is
Explanation of Solution
Write the equation for pressure on the bottom due to water.
Here,
Rewrite the above equation for
Write the equation for the pressure on the bottom due to water.
Here,
Conclusion:
Substitute
Substitute
Therefore, the force exerted by the water on the bottom is
(b)
The force exerted by the water on each end.
(b)
Answer to Problem 8P
The force exerted by the water on each end is
Explanation of Solution
Pressure varies with depth.
Write the equation for the force on a strip of height
Here,
Write the equation for
Write the equation for
Here,
Put the above two equations in equation (III).
Integrate the above equation over the entire height of the strip.
Write the equation for the total area.
The pressure at the top of the pool is zero.
Write the equation for the pressure at surface of the pool.
Here,
Write the equation for the average pressure.
Here,
Put equations (II) and (VI) in the above equation.
Put equations (V) and (VII) in equation (IV).
Put equation (II) in equation (VII).
Conclusion:
Substitute
The length of each end will be
Substitute
Substitute
The force will be directed outward.
Therefore, the force exerted by the water on each end is
(c)
The force exerted by the water on each side.
(c)
Answer to Problem 8P
The force exerted by the water on each side is
Explanation of Solution
Equation (VIII) gives the force exerted on each side of the swimming pool by water.
Conclusion:
The length of each side will be
Substitute
Substitute
The force will be directed outward.
Therefore, the force exerted by the water on each side is
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Chapter 15 Solutions
Principles of Physics: A Calculus-Based Text
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