Question

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 ρ10am , = 95.0 kg/m", and the acceleration due to gravity is g = 9.81 m/s

Answer 1

F is the buoyancy force which is the weight of the displaced water minus the weight of the ball itself

F = (p_w - p_foam ) *V*g

Where, V = (4/3)*pi*r^3 = (4/3)*pi*(d/2)^3 = (1/6)pi*d^3

F = (1*10^3 - 95)*(1/6)*pi*d^3*9.8

554 = 4643.8d^3

d = cuberoot(554/4643.8)

= 0.49 m