Question

a) You come across an open container that is filled with two liquids. Since the two liquids have different densities, there is a distinct separation between them. Water, which has a density of ρw=1.00×103 kg/m3, fills the lower portion of the container to a depth of 0.215 m. The fluid that is floating on top of the water is 0.349 m deep. If the absolute pressure on the bottom of the container is 1.049×105 Pa, what is the density, ρl, of the unknown fluid? The acceleration due to gravity is g=9.81 m/s2 and atmospheric pressure is P0=1.013×105 Pa. b) A child playing in a swimming pool realizes that it is easy to push a small inflated ball under the surface of the water whereas a large ball requires a lot of force. The child happens to have a styrofoam ball (the shape of the ball will not distort when it is forced under the surface), which he forces under the surface of the water. If the child needs to supply 554 N to totally submerge the ball, calculate the diameter d of the ball. The density of water is ρw=1.000×103 kg/m3, the density of styrofoam is ρfoam=95.0 kg/m3, and the acceleration due to gravity is g=9.81 m/s2.

          a) You come across an open container that is filled with two liquids. Since the two liquids have different densities, there is a distinct separation between them. Water, which has a density of ρw=1.00×103 kg/m3, fills the lower portion of the container to a depth of 0.215 m. The fluid that is floating on top of the water is 0.349 m deep. If the absolute pressure on the bottom of the container is 1.049×105 Pa, what is the density, ρl, of the unknown fluid? The acceleration due to gravity is g=9.81 m/s2 and atmospheric pressure is P0=1.013×105 Pa.
b) A child playing in a swimming pool realizes that it is easy to push a small inflated ball under the surface of the water whereas a large ball requires a lot of force. The child happens to have a styrofoam ball (the shape of the ball will not distort when it is forced under the surface), which he forces under the surface of the water. If the child needs to supply 554 N to totally submerge the ball, calculate the diameter d of the ball. The density of water is ρw=1.000×103 kg/m3, the density of styrofoam is ρfoam=95.0 kg/m3, and the acceleration due to gravity is g=9.81 m/s2.

Added by Eva C.

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