Concept explainers
The dolphin tank at an amusement park is rectangular in shape with a length of 40.0 m, a width of 15.0 m, and a depth of 7.50 m. The tank is filled to the brim to provide maximum splash during dolphin shows. What is the total amount of force exerted by the water on a. the bottom of the tank, b. the longer wall of the tank, and c. the shorter wall of the tank?
(a)
The total amount of force exerted by the water on the bottom of the tank.
Answer to Problem 17PQ
The total amount of force exerted by the water on the bottom of the tank is
Explanation of Solution
Write the expression for the hydrostatic pressure on the bottom due to water.
Here,
Write the expression for the force acting on the bottom of tank.
Here,
Write the expression for the area of the tank.
Here,
Substitute equation (III) in (II).
`
Conclusion:
The length of the tank is
Substitute
Substitute
Therefore, the total amount of force exerted by the water on the bottom of the tank is
(b)
The total amount of force exerted by the water on the longer wall of the tank.
Answer to Problem 17PQ
The total amount of force exerted by the water on the longer wall of the tank is
Explanation of Solution
Consider strip of height
Write the expression for the force on the strip.
Here,
Write the expression for the pressure at height
Write the area of the strip.
Put equations (VI) and (VII) in equation (V) to get force acting the strip.
The above equation is written in terms of differential height. Therefore, integrating above equation with limit from 0 to
Integrate equation (VIII) to get total force acting on the wall of greater length.
Conclusion:
Substitute
Therefore, the total amount of force exerted by the water on the longer wall of the tank is
(c)
The total amount of force exerted by the water on the shorter wall of the tank.
Answer to Problem 17PQ
The total amount of force exerted by the water on the shorter wall of the tank is
Explanation of Solution
The total force acting on the shorter side of the tank can be obtained from the equation (IX) with length
Write the expression for the total force acting on the shorter side of the tank.
Here,
Conclusion:
Substitute
Therefore, the total amount of force exerted by the water on the shorter wall of the tank is
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Chapter 15 Solutions
Physics for Scientists and Engineers: Foundations and Connections
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