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 608 N608 N to totally submerge the ball, calculate the diameter dd of the ball. The density of water is ρw=1.000×103 kg/m3,ρw=1.000×103 kg/m3, the density of styrofoam is ρfoam=95.0 kg/m3,ρfoam=95.0 kg/m3, and the acceleration due to gravity is g=9.81 m/s2.

Answer 1

According to the question,

Downward force = upward force

608N + Weight of the ball = buoyant force

608N + mass of the ball * g = weight of the displaced water

608N + density of ball * volume of ball*g = density of water*volume of ball*g

Hence, diameter of the ball = 2r = 2.46m