A child playing in a swimming pool realizes that it is easy to push a small inflated ball under the surface of?
A child playing in a swimming pool observes that it is easy to push a small inflated ball under the water’s surface, while a larger ball requires significantly more force. The child also has a styrofoam ball, which maintains its shape when being submerged. If the child needs to exert a force of 635 N to fully submerge the styrofoam ball, calculate the diameter of the ball. Given that 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, please provide your answer in meters. Thank you!
2 Answers
The 635 N (F, the buoyancy) is the weight of the displaced water minus the weight of the ball itself:
F = (ρw - ρfoam) V g
V = 4/3 pi R^3 = 4/3 pi (D/2)^3 = 1/6 pi D^3
So
F = (ρw - ρfoam) pi D^3 / 6 g
D^3 = 6 F / ( pig(ρw - ρfoam))
D = ( 6 F / ( pig(ρw - ρfoam)) )^(1/3)
D = 0.515 m
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