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Pressure and force in 3 different containers

  1. Dec 5, 2008 #1
    1. The problem statement, all variables and given/known data
    A.
    [​IMG]

    B.
    [​IMG]

    C.
    [​IMG]

    The three tanks shown above are filled with water to an equal depth. All the tanks have an equal height. Tank A has the greatest surface area at the bottom, tank B the least and tank C the middle.
    (Select T-True, F-False, G-Greater than, L-Less than, E-Equal to. If the first is F the second L and the rest G, enter
    FLGGGG).

    A) The force exerted by the water on the bottom of tank A is ... the force exerted by the water on the bottom of tank C
    B) The pressure at the bottom of tank A is ... the pressure at the bottom of tank B
    C) The water in tank B exerts an upward force on the sides of the tank.
    D) The force due to the water on the bottom of tank A is .... the weight of the water in the tank.
    E) The pressure exerted on the bottom of tank B is smaller than for the other tanks.


    2. Relevant equations
    F= p*A
    p = density*g*d


    3. The attempt at a solution

    I hate these types of problems because I know I'll have all but one wrong...
    A: Greater Than, A has a larger surface area on the bottom, and thus has a larger force since pressure is the same because they have the same depth.
    B: Equal To, pressure is just related to depth. Since they all have the same depth, the pressures are equal.
    C: False, water does not come in contact vertically with the tank.
    D: Equal To, even though the wall is exerting some force down on the water the water is exerting some force up on the walls.
    E: False, the pressure is the same because all the containers are filled to the same height with the same liquid.

    I greatly appreciate any help.
     
  2. jcsd
  3. Dec 5, 2008 #2

    Doc Al

    User Avatar

    Staff: Mentor

    Perfectly correct answers and reasoning.
    I don't understand the reason for your answer. The water certainly makes contact with the sides of the tank.
    What does the force of the wall on the water have to do with the weight of the water?
    Perfectly correct answer and reasoning.
     
  4. Dec 5, 2008 #3
    Well, what I think the question is asking is that does the water exert an upward force on the container (i think), so I presume it means something like this
    [​IMG]
    Which it certainly is not making contact with, so it should be false.

    It shouldnt. F = pressure*area right? But Im not sure how to figure out if pressure*area = or < or > density*volume*g...
     
  5. Dec 6, 2008 #4

    Doc Al

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    Staff: Mentor

    The question asks about the force the water exerts on the sides of the container. Is the water in contact with those sides? Yes. Does the water exert a force on those sides? Yes.

    In what direction? (Does the force exerted by the water on the sides of the container have an upward component or a downward component?)
    Hint: Pressure = density*g*height. Combine that with force = pressure*area.
     
  6. Dec 6, 2008 #5
    The water only exerts a downward force on the tank, so the answer must be false since its asking for does it have an upward component.

    Force/area = pressure
    Force/area = density*g*height
    Force = density*g*height*area
    BUT the area does not stay the same with height. it is larger on the bottom so, density*g*height*area at the bottom > density*g*volume

    Thank you very much, I appreciate your help, the above are correct.
     
  7. Dec 6, 2008 #6

    Doc Al

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    Staff: Mentor

    Very good!
     
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