A child is floating in an inner tube in a swimming pool. The child\'s mass is 32

Question

A child is floating in an inner tube in a swimming pool. The child's mass is 32 kg. The inner tube is completely submerged, just below the water line, and 2.0*10^-3 m^3 of the child's body is submerged under the water. The density of the inner tube is 350 kg/m^3. The density of the water is 1.0*10^3 kg/m^3. a) What is the volume of the inner tube? b) What is the magnitude of the buoyant force acting on the inner tube/child system? c) If this buoyant force was acting on the inner tube only, with a surface area of 2.0*10^-3 m^2, what pressure would be applied to the inner tube by this force?

Explanation / Answer

buoyancy force = weight of inner tube + weight of child weight of inner tube = volume *density*g V*1000*9.8 + 2 x 10^-3*1000*9.8 = V*350*9.8 +32*9.8 1) volume of the inner tube V = 4.6 x 10^-2 m^3 2) Total buoyant force = V*1000*9.8 + 2 x 10^-3*1000*9.8 = 490.4 N 3) in this case V*1000*9.8 = V*350*9.8 +32*9.8 V = 4.92 x 10^-2 m^3 buoyant force = V*1000*9.8 = 482.16 N

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