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 m^3 of water and the surface area of the bottom of the container is 5.00 m^2. The height of the lower part of the container is 2.50 m and the neck contains a column of water 8.50 high. The total volum of the column of water in the neck is .200 m^3. What is the magnitude of the force exerted by the water on the bottom of the container? The answer is 1.0 MN I just do not know why.

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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