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- The density of ice is 917 kg/m3, and the density of sea water is 1025 kg/m3. A swimming polar bear climbs onto a piece of floating ice that has a volume of 6.29 m3. (a) What is the weight of the heaviest bear that the ice can support without sinking completely beneath the water? To verify her suspicion that a rock specimen is hollow, a geologist weighs the specimen in air and in water. She finds that the specimen weighs twice as much in air as it does in water. The density of the solid part of the specimen is 5.42 × 103 kg/m3. (b) What fraction of the specimen’s apparent volume is solid?A block of mass 0.80 kg and density 2900 kg/m³ is completely submerged under the water in static equilibrium on top of a spring (k = 80.0 N/m) that is fixed to the bottom of the container as shown in the figure. How much is the spring compressed? (the density of water is 1000 kg/m³).A wooden raft has a mass of 50 kg. When empty it floats in water (density 1000 kg/m3) with 69% of its volume submerged. What mass of sand can be put on the raft without it sinking?
- (a) If the density of an object is exactly equal to the density of a fluid, the object will (1) float, (2) sink, (3) stay at any height in the fluid, as long as it is totally immersed. (b) A cube 8.5 cm on each side has a mass of 0.65 kg. Will the cube float or sink in water? Prove your answer.In the figure, a cube of edge length L = 0.633 m and mass 1040 kg is suspended by a rope in an open tank of liquid of density 1.03E+3 kg/m³. Find (a) the magnitude of the total downward force on the top of the cube from the liquid and the atmosphere, assuming atmospheric pressure is 1.00 atm, (b) the magnitude of the total upward force on the bottom of the cube, and (c) the tension in the rope. (d) Calculate the magnitude of the buoyant force on the cube using Archimede's principle. (a) Number 18340.3 (b) Number i 3992.2 (c) Number i 14348.1 (d) Number i 3992.2 Units L N Units N Units Units N N L/2 ◄► ◄►In the figure, the fresh water behind a reservoir dam has depth D-13.4 m. A horizontal pipe 4.39 cm in diameter passes through the dam at depth d - 6.37 m. A plug secures the pipe opening. (a) Find the magnitude of the frictional force between plug and pipe wall. (b) The plug is removed. What water volume exits the pipe in 2.92 h? (a) Number (b) Number Units Units N m3