A container has a large cylindrical lower part with a long thin cylindrical neck

Question

A container has a large cylindrical lower part with a long thin cylindrical neck. The lower part of the container holds 12.5 m3 of water and the surface area of the bottom of the container is 5.32 m2. The height of the lower part of the container is h1 = 2.40 m and the neck contains a column of water h2 = 7.70 m high. The total volume of the column of water in the neck is 0.200 m3. What is the magnitude of the force exerted by the water on the bottom of the container? Incorrect: Your answer is incorrect. (In MN)

Explanation / Answer

You can actually ignore most of the numbers in the question; they were probably put in there just to throw you off. The relevant facts are: 1. The force on the bottom is: F = P × A (where "P" is the water pressure at the bottom; and "A" is the area of the bottom surface); 2. The pressure "P" depends only on the height of the water column; it doesn't depend at all on the volume of the water or the shape of the container. The formula for "P" is: P = ?gh + P0 where: ? = density of water g = acceleration due to gravity = 9.8 m/sec² h = height of water column = 1.80m + 8.00m = 9.80 m P0 = air pressure at top of column = 1 atmosphere. Then the force at the bottom is: F = PA = (?gh + P0)(4.65 m²) = (?g(9.80m) + 1 atm.)(4.65 m²) You still need to plug in the value for "?" and convert to the proper units to get Newtons. I leave that as an exercise for you

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