Bookmarks Tools Window Help Child Playing In A Swimming x+ is/view.php?id-389686

Question

Bookmarks Tools Window Help Child Playing In A Swimming x+ is/view.php?id-3896864 w.saping a Getting Startedon Brightspace Lo.. Meservices atMirres--BOME Free APAS D C Search Jump to... stion 11 ol 1 Sapling Learning A child playing in a swimming pool realizes that it is easy to push a small nftaced ball under the surface af the water while a large ball requires a lot of force. The shape of the ball will not distort when it is forced under the surlace) which is being forced under the surface of the water. If the child needs to supply 581 N to totally submerge the ball, calculate the diameter of the bal The density of water is A-1000 x1Pkgm. the density of styroloam is Aum=95.0 kgand the acceleration due to gravity is g- 9.81 mis child happens to have a styrofoam ball (this way the d- 0.240 There is additional feedback View this feedback bottom dvbide the wodiional

Explanation / Answer

The 581 N (F, the buoyancy) is the weight of the displaced water minus the weight of the ball itself:

F = (w - foam) * V * g

V = 4/3 pi R^3 = 4/3 pi (D/2)^3 = 1/6 pi D^3

So

F = (w - foam) * pi D^3 / 6 * g

D^3 = 6 F / ( pi*g*(w - foam))

D = ( 6*581 / ( 3.14*9.8*(1000 - 95)) )^(1/3)

D = 0.500 m

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