PhysicsLAB AP Free Response Question
2007 B4

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The large container shown in the cross section above is filled with a liquid of density 1.1 x 103 kg/m3 . A small hole of area 2.5 x 10-6 m2 is opened in the side of the container a distance h below the liquid surface, which allows a stream of liquid to flow through the hole and into a beaker placed to the right of the container. At the same time, liquid is also added to the container at an appropriate rate so that h remains constant. The amount of liquid collected in the beaker in 2.0 minutes is 7.2 x 10-4 m3.
 (a) Calculate the volume rate of flow of liquid from the hole in m3/sec.

 (b) Calculate the speed of the liquid as it exits from the hole.

 (c) Calculate the height h of liquid needed above the hole to cause the speed you determined in part (b).

(d) Suppose that there is now less liquid in the container so that the height h is reduced to h/2. In relation to the container, where will the liquid hit the tabletop?
Justify your answer.

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